- : unit = ()
h : heuristic = <heuristic>
- : unit = ()
APPLY CRITERIA (Marked dependency pairs)

TRS termination of:
[1] active(U101(tt,V2)) -> mark(U102(isLNat(V2)))
[2] active(U102(tt)) -> mark(tt)
[3] active(U11(tt,N,XS)) -> mark(U12(isLNat(XS),N,XS))
[4] active(U111(tt)) -> mark(tt)
[5] active(U12(tt,N,XS)) -> mark(snd(splitAt(N,XS)))
[6] active(U121(tt)) -> mark(tt)
[7] active(U131(tt,V2)) -> mark(U132(isLNat(V2)))
[8] active(U132(tt)) -> mark(tt)
[9] active(U141(tt,V2)) -> mark(U142(isLNat(V2)))
[10] active(U142(tt)) -> mark(tt)
[11] active(U151(tt,V2)) -> mark(U152(isLNat(V2)))
[12] active(U152(tt)) -> mark(tt)
[13] active(U161(tt,N)) -> mark(cons(N,natsFrom(s(N))))
[14] active(U171(tt,N,XS)) -> mark(U172(isLNat(XS),N,XS))
[15] active(U172(tt,N,XS)) -> mark(head(afterNth(N,XS)))
[16] active(U181(tt,Y)) -> mark(U182(isLNat(Y),Y))
[17] active(U182(tt,Y)) -> mark(Y)
[18] active(U191(tt,XS)) -> mark(pair(nil,XS))
[19] active(U201(tt,N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
[20] active(U202(tt,N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
[21] active(U203(tt,N,X,XS)) -> mark(U204(splitAt(N,XS),X))
[22] active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
[23] active(U21(tt,X,Y)) -> mark(U22(isLNat(Y),X))
[24] active(U211(tt,XS)) -> mark(U212(isLNat(XS),XS))
[25] active(U212(tt,XS)) -> mark(XS)
[26] active(U22(tt,X)) -> mark(X)
[27] active(U221(tt,N,XS)) -> mark(U222(isLNat(XS),N,XS))
[28] active(U222(tt,N,XS)) -> mark(fst(splitAt(N,XS)))
[29] active(U31(tt,N,XS)) -> mark(U32(isLNat(XS),N))
[30] active(U32(tt,N)) -> mark(N)
[31] active(U41(tt,V2)) -> mark(U42(isLNat(V2)))
[32] active(U42(tt)) -> mark(tt)
[33] active(U51(tt,V2)) -> mark(U52(isLNat(V2)))
[34] active(U52(tt)) -> mark(tt)
[35] active(U61(tt)) -> mark(tt)
[36] active(U71(tt)) -> mark(tt)
[37] active(U81(tt)) -> mark(tt)
[38] active(U91(tt)) -> mark(tt)
[39] active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
[40] active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
[41] active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
[42] active(isLNat(nil)) -> mark(tt)
[43] active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
[44] active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
[45] active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
[46] active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
[47] active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
[48] active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
[49] active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
[50] active(isNatural(0)) -> mark(tt)
[51] active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
[52] active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
[53] active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
[54] active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
[55] active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
[56] active(natsFrom(N)) -> mark(U161(isNatural(N),N))
[57] active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
[58] active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
[59] active(splitAt(0,XS)) -> mark(U191(isLNat(XS),XS))
[60] active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
[61] active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
[62] active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
[63] active(U101(X1,X2)) -> U101(active(X1),X2)
[64] active(U102(X)) -> U102(active(X))
[65] active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
[66] active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
[67] active(U111(X)) -> U111(active(X))
[68] active(snd(X)) -> snd(active(X))
[69] active(splitAt(X1,X2)) -> splitAt(active(X1),X2)
[70] active(splitAt(X1,X2)) -> splitAt(X1,active(X2))
[71] active(U121(X)) -> U121(active(X))
[72] active(U131(X1,X2)) -> U131(active(X1),X2)
[73] active(U132(X)) -> U132(active(X))
[74] active(U141(X1,X2)) -> U141(active(X1),X2)
[75] active(U142(X)) -> U142(active(X))
[76] active(U151(X1,X2)) -> U151(active(X1),X2)
[77] active(U152(X)) -> U152(active(X))
[78] active(U161(X1,X2)) -> U161(active(X1),X2)
[79] active(cons(X1,X2)) -> cons(active(X1),X2)
[80] active(natsFrom(X)) -> natsFrom(active(X))
[81] active(s(X)) -> s(active(X))
[82] active(U171(X1,X2,X3)) -> U171(active(X1),X2,X3)
[83] active(U172(X1,X2,X3)) -> U172(active(X1),X2,X3)
[84] active(head(X)) -> head(active(X))
[85] active(afterNth(X1,X2)) -> afterNth(active(X1),X2)
[86] active(afterNth(X1,X2)) -> afterNth(X1,active(X2))
[87] active(U181(X1,X2)) -> U181(active(X1),X2)
[88] active(U182(X1,X2)) -> U182(active(X1),X2)
[89] active(U191(X1,X2)) -> U191(active(X1),X2)
[90] active(pair(X1,X2)) -> pair(active(X1),X2)
[91] active(pair(X1,X2)) -> pair(X1,active(X2))
[92] active(U201(X1,X2,X3,X4)) -> U201(active(X1),X2,X3,X4)
[93] active(U202(X1,X2,X3,X4)) -> U202(active(X1),X2,X3,X4)
[94] active(U203(X1,X2,X3,X4)) -> U203(active(X1),X2,X3,X4)
[95] active(U204(X1,X2)) -> U204(active(X1),X2)
[96] active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
[97] active(U22(X1,X2)) -> U22(active(X1),X2)
[98] active(U211(X1,X2)) -> U211(active(X1),X2)
[99] active(U212(X1,X2)) -> U212(active(X1),X2)
[100] active(U221(X1,X2,X3)) -> U221(active(X1),X2,X3)
[101] active(U222(X1,X2,X3)) -> U222(active(X1),X2,X3)
[102] active(fst(X)) -> fst(active(X))
[103] active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3)
[104] active(U32(X1,X2)) -> U32(active(X1),X2)
[105] active(U41(X1,X2)) -> U41(active(X1),X2)
[106] active(U42(X)) -> U42(active(X))
[107] active(U51(X1,X2)) -> U51(active(X1),X2)
[108] active(U52(X)) -> U52(active(X))
[109] active(U61(X)) -> U61(active(X))
[110] active(U71(X)) -> U71(active(X))
[111] active(U81(X)) -> U81(active(X))
[112] active(U91(X)) -> U91(active(X))
[113] active(tail(X)) -> tail(active(X))
[114] active(take(X1,X2)) -> take(active(X1),X2)
[115] active(take(X1,X2)) -> take(X1,active(X2))
[116] active(sel(X1,X2)) -> sel(active(X1),X2)
[117] active(sel(X1,X2)) -> sel(X1,active(X2))
[118] U101(mark(X1),X2) -> mark(U101(X1,X2))
[119] U102(mark(X)) -> mark(U102(X))
[120] U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
[121] U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
[122] U111(mark(X)) -> mark(U111(X))
[123] snd(mark(X)) -> mark(snd(X))
[124] splitAt(mark(X1),X2) -> mark(splitAt(X1,X2))
[125] splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2))
[126] U121(mark(X)) -> mark(U121(X))
[127] U131(mark(X1),X2) -> mark(U131(X1,X2))
[128] U132(mark(X)) -> mark(U132(X))
[129] U141(mark(X1),X2) -> mark(U141(X1,X2))
[130] U142(mark(X)) -> mark(U142(X))
[131] U151(mark(X1),X2) -> mark(U151(X1,X2))
[132] U152(mark(X)) -> mark(U152(X))
[133] U161(mark(X1),X2) -> mark(U161(X1,X2))
[134] cons(mark(X1),X2) -> mark(cons(X1,X2))
[135] natsFrom(mark(X)) -> mark(natsFrom(X))
[136] s(mark(X)) -> mark(s(X))
[137] U171(mark(X1),X2,X3) -> mark(U171(X1,X2,X3))
[138] U172(mark(X1),X2,X3) -> mark(U172(X1,X2,X3))
[139] head(mark(X)) -> mark(head(X))
[140] afterNth(mark(X1),X2) -> mark(afterNth(X1,X2))
[141] afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2))
[142] U181(mark(X1),X2) -> mark(U181(X1,X2))
[143] U182(mark(X1),X2) -> mark(U182(X1,X2))
[144] U191(mark(X1),X2) -> mark(U191(X1,X2))
[145] pair(mark(X1),X2) -> mark(pair(X1,X2))
[146] pair(X1,mark(X2)) -> mark(pair(X1,X2))
[147] U201(mark(X1),X2,X3,X4) -> mark(U201(X1,X2,X3,X4))
[148] U202(mark(X1),X2,X3,X4) -> mark(U202(X1,X2,X3,X4))
[149] U203(mark(X1),X2,X3,X4) -> mark(U203(X1,X2,X3,X4))
[150] U204(mark(X1),X2) -> mark(U204(X1,X2))
[151] U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
[152] U22(mark(X1),X2) -> mark(U22(X1,X2))
[153] U211(mark(X1),X2) -> mark(U211(X1,X2))
[154] U212(mark(X1),X2) -> mark(U212(X1,X2))
[155] U221(mark(X1),X2,X3) -> mark(U221(X1,X2,X3))
[156] U222(mark(X1),X2,X3) -> mark(U222(X1,X2,X3))
[157] fst(mark(X)) -> mark(fst(X))
[158] U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3))
[159] U32(mark(X1),X2) -> mark(U32(X1,X2))
[160] U41(mark(X1),X2) -> mark(U41(X1,X2))
[161] U42(mark(X)) -> mark(U42(X))
[162] U51(mark(X1),X2) -> mark(U51(X1,X2))
[163] U52(mark(X)) -> mark(U52(X))
[164] U61(mark(X)) -> mark(U61(X))
[165] U71(mark(X)) -> mark(U71(X))
[166] U81(mark(X)) -> mark(U81(X))
[167] U91(mark(X)) -> mark(U91(X))
[168] tail(mark(X)) -> mark(tail(X))
[169] take(mark(X1),X2) -> mark(take(X1,X2))
[170] take(X1,mark(X2)) -> mark(take(X1,X2))
[171] sel(mark(X1),X2) -> mark(sel(X1,X2))
[172] sel(X1,mark(X2)) -> mark(sel(X1,X2))
[173] proper(U101(X1,X2)) -> U101(proper(X1),proper(X2))
[174] proper(tt) -> ok(tt)
[175] proper(U102(X)) -> U102(proper(X))
[176] proper(isLNat(X)) -> isLNat(proper(X))
[177] proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
[178] proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
[179] proper(U111(X)) -> U111(proper(X))
[180] proper(snd(X)) -> snd(proper(X))
[181] proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2))
[182] proper(U121(X)) -> U121(proper(X))
[183] proper(U131(X1,X2)) -> U131(proper(X1),proper(X2))
[184] proper(U132(X)) -> U132(proper(X))
[185] proper(U141(X1,X2)) -> U141(proper(X1),proper(X2))
[186] proper(U142(X)) -> U142(proper(X))
[187] proper(U151(X1,X2)) -> U151(proper(X1),proper(X2))
[188] proper(U152(X)) -> U152(proper(X))
[189] proper(U161(X1,X2)) -> U161(proper(X1),proper(X2))
[190] proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
[191] proper(natsFrom(X)) -> natsFrom(proper(X))
[192] proper(s(X)) -> s(proper(X))
[193] proper(U171(X1,X2,X3)) -> U171(proper(X1),proper(X2),proper(X3))
[194] proper(U172(X1,X2,X3)) -> U172(proper(X1),proper(X2),proper(X3))
[195] proper(head(X)) -> head(proper(X))
[196] proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2))
[197] proper(U181(X1,X2)) -> U181(proper(X1),proper(X2))
[198] proper(U182(X1,X2)) -> U182(proper(X1),proper(X2))
[199] proper(U191(X1,X2)) -> U191(proper(X1),proper(X2))
[200] proper(pair(X1,X2)) -> pair(proper(X1),proper(X2))
[201] proper(nil) -> ok(nil)
[202] proper(U201(X1,X2,X3,X4)) ->
 U201(proper(X1),proper(X2),proper(X3),proper(X4))
[203] proper(U202(X1,X2,X3,X4)) ->
 U202(proper(X1),proper(X2),proper(X3),proper(X4))
[204] proper(isNatural(X)) -> isNatural(proper(X))
[205] proper(U203(X1,X2,X3,X4)) ->
 U203(proper(X1),proper(X2),proper(X3),proper(X4))
[206] proper(U204(X1,X2)) -> U204(proper(X1),proper(X2))
[207] proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
[208] proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
[209] proper(U211(X1,X2)) -> U211(proper(X1),proper(X2))
[210] proper(U212(X1,X2)) -> U212(proper(X1),proper(X2))
[211] proper(U221(X1,X2,X3)) -> U221(proper(X1),proper(X2),proper(X3))
[212] proper(U222(X1,X2,X3)) -> U222(proper(X1),proper(X2),proper(X3))
[213] proper(fst(X)) -> fst(proper(X))
[214] proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3))
[215] proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
[216] proper(U41(X1,X2)) -> U41(proper(X1),proper(X2))
[217] proper(U42(X)) -> U42(proper(X))
[218] proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
[219] proper(U52(X)) -> U52(proper(X))
[220] proper(U61(X)) -> U61(proper(X))
[221] proper(U71(X)) -> U71(proper(X))
[222] proper(U81(X)) -> U81(proper(X))
[223] proper(U91(X)) -> U91(proper(X))
[224] proper(isPLNat(X)) -> isPLNat(proper(X))
[225] proper(tail(X)) -> tail(proper(X))
[226] proper(take(X1,X2)) -> take(proper(X1),proper(X2))
[227] proper(0) -> ok(0)
[228] proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
[229] U101(ok(X1),ok(X2)) -> ok(U101(X1,X2))
[230] U102(ok(X)) -> ok(U102(X))
[231] isLNat(ok(X)) -> ok(isLNat(X))
[232] U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
[233] U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
[234] U111(ok(X)) -> ok(U111(X))
[235] snd(ok(X)) -> ok(snd(X))
[236] splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2))
[237] U121(ok(X)) -> ok(U121(X))
[238] U131(ok(X1),ok(X2)) -> ok(U131(X1,X2))
[239] U132(ok(X)) -> ok(U132(X))
[240] U141(ok(X1),ok(X2)) -> ok(U141(X1,X2))
[241] U142(ok(X)) -> ok(U142(X))
[242] U151(ok(X1),ok(X2)) -> ok(U151(X1,X2))
[243] U152(ok(X)) -> ok(U152(X))
[244] U161(ok(X1),ok(X2)) -> ok(U161(X1,X2))
[245] cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
[246] natsFrom(ok(X)) -> ok(natsFrom(X))
[247] s(ok(X)) -> ok(s(X))
[248] U171(ok(X1),ok(X2),ok(X3)) -> ok(U171(X1,X2,X3))
[249] U172(ok(X1),ok(X2),ok(X3)) -> ok(U172(X1,X2,X3))
[250] head(ok(X)) -> ok(head(X))
[251] afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2))
[252] U181(ok(X1),ok(X2)) -> ok(U181(X1,X2))
[253] U182(ok(X1),ok(X2)) -> ok(U182(X1,X2))
[254] U191(ok(X1),ok(X2)) -> ok(U191(X1,X2))
[255] pair(ok(X1),ok(X2)) -> ok(pair(X1,X2))
[256] U201(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U201(X1,X2,X3,X4))
[257] U202(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U202(X1,X2,X3,X4))
[258] isNatural(ok(X)) -> ok(isNatural(X))
[259] U203(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U203(X1,X2,X3,X4))
[260] U204(ok(X1),ok(X2)) -> ok(U204(X1,X2))
[261] U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
[262] U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
[263] U211(ok(X1),ok(X2)) -> ok(U211(X1,X2))
[264] U212(ok(X1),ok(X2)) -> ok(U212(X1,X2))
[265] U221(ok(X1),ok(X2),ok(X3)) -> ok(U221(X1,X2,X3))
[266] U222(ok(X1),ok(X2),ok(X3)) -> ok(U222(X1,X2,X3))
[267] fst(ok(X)) -> ok(fst(X))
[268] U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3))
[269] U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
[270] U41(ok(X1),ok(X2)) -> ok(U41(X1,X2))
[271] U42(ok(X)) -> ok(U42(X))
[272] U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
[273] U52(ok(X)) -> ok(U52(X))
[274] U61(ok(X)) -> ok(U61(X))
[275] U71(ok(X)) -> ok(U71(X))
[276] U81(ok(X)) -> ok(U81(X))
[277] U91(ok(X)) -> ok(U91(X))
[278] isPLNat(ok(X)) -> ok(isPLNat(X))
[279] tail(ok(X)) -> ok(tail(X))
[280] take(ok(X1),ok(X2)) -> ok(take(X1,X2))
[281] sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
[282] top(mark(X)) -> top(proper(X))
[283] top(ok(X)) -> top(active(X))


Sub problem: 
guided: 

DP termination of:
<Marked_active(U101(tt,V2)) , Marked_U102(isLNat(V2))>
<Marked_active(U101(tt,V2)) , Marked_isLNat(V2)>
<Marked_active(U11(tt,N,XS)) , Marked_U12(isLNat(XS),N,XS)>
<Marked_active(U11(tt,N,XS)) , Marked_isLNat(XS)>
<Marked_active(U12(tt,N,XS)) , Marked_snd(splitAt(N,XS))>
<Marked_active(U12(tt,N,XS)) , Marked_splitAt(N,XS)>
<Marked_active(U131(tt,V2)) , Marked_U132(isLNat(V2))>
<Marked_active(U131(tt,V2)) , Marked_isLNat(V2)>
<Marked_active(U141(tt,V2)) , Marked_U142(isLNat(V2))>
<Marked_active(U141(tt,V2)) , Marked_isLNat(V2)>
<Marked_active(U151(tt,V2)) , Marked_U152(isLNat(V2))>
<Marked_active(U151(tt,V2)) , Marked_isLNat(V2)>
<Marked_active(U161(tt,N)) , Marked_cons(N,natsFrom(s(N)))>
<Marked_active(U161(tt,N)) , Marked_natsFrom(s(N))>
<Marked_active(U161(tt,N)) , Marked_s(N)>
<Marked_active(U171(tt,N,XS)) , Marked_U172(isLNat(XS),N,XS)>
<Marked_active(U171(tt,N,XS)) , Marked_isLNat(XS)>
<Marked_active(U172(tt,N,XS)) , Marked_head(afterNth(N,XS))>
<Marked_active(U172(tt,N,XS)) , Marked_afterNth(N,XS)>
<Marked_active(U181(tt,Y)) , Marked_U182(isLNat(Y),Y)>
<Marked_active(U181(tt,Y)) , Marked_isLNat(Y)>
<Marked_active(U191(tt,XS)) , Marked_pair(nil,XS)>
<Marked_active(U201(tt,N,X,XS)) , Marked_U202(isNatural(X),N,X,XS)>
<Marked_active(U201(tt,N,X,XS)) , Marked_isNatural(X)>
<Marked_active(U202(tt,N,X,XS)) , Marked_U203(isLNat(XS),N,X,XS)>
<Marked_active(U202(tt,N,X,XS)) , Marked_isLNat(XS)>
<Marked_active(U203(tt,N,X,XS)) , Marked_U204(splitAt(N,XS),X)>
<Marked_active(U203(tt,N,X,XS)) , Marked_splitAt(N,XS)>
<Marked_active(U204(pair(YS,ZS),X)) , Marked_pair(cons(X,YS),ZS)>
<Marked_active(U204(pair(YS,ZS),X)) , Marked_cons(X,YS)>
<Marked_active(U21(tt,X,Y)) , Marked_U22(isLNat(Y),X)>
<Marked_active(U21(tt,X,Y)) , Marked_isLNat(Y)>
<Marked_active(U211(tt,XS)) , Marked_U212(isLNat(XS),XS)>
<Marked_active(U211(tt,XS)) , Marked_isLNat(XS)>
<Marked_active(U221(tt,N,XS)) , Marked_U222(isLNat(XS),N,XS)>
<Marked_active(U221(tt,N,XS)) , Marked_isLNat(XS)>
<Marked_active(U222(tt,N,XS)) , Marked_fst(splitAt(N,XS))>
<Marked_active(U222(tt,N,XS)) , Marked_splitAt(N,XS)>
<Marked_active(U31(tt,N,XS)) , Marked_U32(isLNat(XS),N)>
<Marked_active(U31(tt,N,XS)) , Marked_isLNat(XS)>
<Marked_active(U41(tt,V2)) , Marked_U42(isLNat(V2))>
<Marked_active(U41(tt,V2)) , Marked_isLNat(V2)>
<Marked_active(U51(tt,V2)) , Marked_U52(isLNat(V2))>
<Marked_active(U51(tt,V2)) , Marked_isLNat(V2)>
<Marked_active(afterNth(N,XS)) , Marked_U11(isNatural(N),N,XS)>
<Marked_active(afterNth(N,XS)) , Marked_isNatural(N)>
<Marked_active(fst(pair(X,Y))) , Marked_U21(isLNat(X),X,Y)>
<Marked_active(fst(pair(X,Y))) , Marked_isLNat(X)>
<Marked_active(head(cons(N,XS))) , Marked_U31(isNatural(N),N,XS)>
<Marked_active(head(cons(N,XS))) , Marked_isNatural(N)>
<Marked_active(isLNat(afterNth(V1,V2))) , Marked_U41(isNatural(V1),V2)>
<Marked_active(isLNat(afterNth(V1,V2))) , Marked_isNatural(V1)>
<Marked_active(isLNat(cons(V1,V2))) , Marked_U51(isNatural(V1),V2)>
<Marked_active(isLNat(cons(V1,V2))) , Marked_isNatural(V1)>
<Marked_active(isLNat(fst(V1))) , Marked_U61(isPLNat(V1))>
<Marked_active(isLNat(fst(V1))) , Marked_isPLNat(V1)>
<Marked_active(isLNat(natsFrom(V1))) , Marked_U71(isNatural(V1))>
<Marked_active(isLNat(natsFrom(V1))) , Marked_isNatural(V1)>
<Marked_active(isLNat(snd(V1))) , Marked_U81(isPLNat(V1))>
<Marked_active(isLNat(snd(V1))) , Marked_isPLNat(V1)>
<Marked_active(isLNat(tail(V1))) , Marked_U91(isLNat(V1))>
<Marked_active(isLNat(tail(V1))) , Marked_isLNat(V1)>
<Marked_active(isLNat(take(V1,V2))) , Marked_U101(isNatural(V1),V2)>
<Marked_active(isLNat(take(V1,V2))) , Marked_isNatural(V1)>
<Marked_active(isNatural(head(V1))) , Marked_U111(isLNat(V1))>
<Marked_active(isNatural(head(V1))) , Marked_isLNat(V1)>
<Marked_active(isNatural(s(V1))) , Marked_U121(isNatural(V1))>
<Marked_active(isNatural(s(V1))) , Marked_isNatural(V1)>
<Marked_active(isNatural(sel(V1,V2))) , Marked_U131(isNatural(V1),V2)>
<Marked_active(isNatural(sel(V1,V2))) , Marked_isNatural(V1)>
<Marked_active(isPLNat(pair(V1,V2))) , Marked_U141(isLNat(V1),V2)>
<Marked_active(isPLNat(pair(V1,V2))) , Marked_isLNat(V1)>
<Marked_active(isPLNat(splitAt(V1,V2))) , Marked_U151(isNatural(V1),V2)>
<Marked_active(isPLNat(splitAt(V1,V2))) , Marked_isNatural(V1)>
<Marked_active(natsFrom(N)) , Marked_U161(isNatural(N),N)>
<Marked_active(natsFrom(N)) , Marked_isNatural(N)>
<Marked_active(sel(N,XS)) , Marked_U171(isNatural(N),N,XS)>
<Marked_active(sel(N,XS)) , Marked_isNatural(N)>
<Marked_active(snd(pair(X,Y))) , Marked_U181(isLNat(X),Y)>
<Marked_active(snd(pair(X,Y))) , Marked_isLNat(X)>
<Marked_active(splitAt(0,XS)) , Marked_U191(isLNat(XS),XS)>
<Marked_active(splitAt(0,XS)) , Marked_isLNat(XS)>
<Marked_active(splitAt(s(N),cons(X,XS))) , Marked_U201(isNatural(N),N,X,XS)>
<Marked_active(splitAt(s(N),cons(X,XS))) , Marked_isNatural(N)>
<Marked_active(tail(cons(N,XS))) , Marked_U211(isNatural(N),XS)>
<Marked_active(tail(cons(N,XS))) , Marked_isNatural(N)>
<Marked_active(take(N,XS)) , Marked_U221(isNatural(N),N,XS)>
<Marked_active(take(N,XS)) , Marked_isNatural(N)>
<Marked_active(U101(X1,X2)) , Marked_U101(active(X1),X2)>
<Marked_active(U101(X1,X2)) , Marked_active(X1)>
<Marked_active(U102(X)) , Marked_U102(active(X))>
<Marked_active(U102(X)) , Marked_active(X)>
<Marked_active(U11(X1,X2,X3)) , Marked_U11(active(X1),X2,X3)>
<Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
<Marked_active(U12(X1,X2,X3)) , Marked_U12(active(X1),X2,X3)>
<Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
<Marked_active(U111(X)) , Marked_U111(active(X))>
<Marked_active(U111(X)) , Marked_active(X)>
<Marked_active(snd(X)) , Marked_snd(active(X))>
<Marked_active(snd(X)) , Marked_active(X)>
<Marked_active(splitAt(X1,X2)) , Marked_splitAt(active(X1),X2)>
<Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
<Marked_active(splitAt(X1,X2)) , Marked_splitAt(X1,active(X2))>
<Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
<Marked_active(U121(X)) , Marked_U121(active(X))>
<Marked_active(U121(X)) , Marked_active(X)>
<Marked_active(U131(X1,X2)) , Marked_U131(active(X1),X2)>
<Marked_active(U131(X1,X2)) , Marked_active(X1)>
<Marked_active(U132(X)) , Marked_U132(active(X))>
<Marked_active(U132(X)) , Marked_active(X)>
<Marked_active(U141(X1,X2)) , Marked_U141(active(X1),X2)>
<Marked_active(U141(X1,X2)) , Marked_active(X1)>
<Marked_active(U142(X)) , Marked_U142(active(X))>
<Marked_active(U142(X)) , Marked_active(X)>
<Marked_active(U151(X1,X2)) , Marked_U151(active(X1),X2)>
<Marked_active(U151(X1,X2)) , Marked_active(X1)>
<Marked_active(U152(X)) , Marked_U152(active(X))>
<Marked_active(U152(X)) , Marked_active(X)>
<Marked_active(U161(X1,X2)) , Marked_U161(active(X1),X2)>
<Marked_active(U161(X1,X2)) , Marked_active(X1)>
<Marked_active(cons(X1,X2)) , Marked_cons(active(X1),X2)>
<Marked_active(cons(X1,X2)) , Marked_active(X1)>
<Marked_active(natsFrom(X)) , Marked_natsFrom(active(X))>
<Marked_active(natsFrom(X)) , Marked_active(X)>
<Marked_active(s(X)) , Marked_s(active(X))>
<Marked_active(s(X)) , Marked_active(X)>
<Marked_active(U171(X1,X2,X3)) , Marked_U171(active(X1),X2,X3)>
<Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
<Marked_active(U172(X1,X2,X3)) , Marked_U172(active(X1),X2,X3)>
<Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
<Marked_active(head(X)) , Marked_head(active(X))>
<Marked_active(head(X)) , Marked_active(X)>
<Marked_active(afterNth(X1,X2)) , Marked_afterNth(active(X1),X2)>
<Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
<Marked_active(afterNth(X1,X2)) , Marked_afterNth(X1,active(X2))>
<Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
<Marked_active(U181(X1,X2)) , Marked_U181(active(X1),X2)>
<Marked_active(U181(X1,X2)) , Marked_active(X1)>
<Marked_active(U182(X1,X2)) , Marked_U182(active(X1),X2)>
<Marked_active(U182(X1,X2)) , Marked_active(X1)>
<Marked_active(U191(X1,X2)) , Marked_U191(active(X1),X2)>
<Marked_active(U191(X1,X2)) , Marked_active(X1)>
<Marked_active(pair(X1,X2)) , Marked_pair(active(X1),X2)>
<Marked_active(pair(X1,X2)) , Marked_active(X1)>
<Marked_active(pair(X1,X2)) , Marked_pair(X1,active(X2))>
<Marked_active(pair(X1,X2)) , Marked_active(X2)>
<Marked_active(U201(X1,X2,X3,X4)) , Marked_U201(active(X1),X2,X3,X4)>
<Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
<Marked_active(U202(X1,X2,X3,X4)) , Marked_U202(active(X1),X2,X3,X4)>
<Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
<Marked_active(U203(X1,X2,X3,X4)) , Marked_U203(active(X1),X2,X3,X4)>
<Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
<Marked_active(U204(X1,X2)) , Marked_U204(active(X1),X2)>
<Marked_active(U204(X1,X2)) , Marked_active(X1)>
<Marked_active(U21(X1,X2,X3)) , Marked_U21(active(X1),X2,X3)>
<Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
<Marked_active(U22(X1,X2)) , Marked_U22(active(X1),X2)>
<Marked_active(U22(X1,X2)) , Marked_active(X1)>
<Marked_active(U211(X1,X2)) , Marked_U211(active(X1),X2)>
<Marked_active(U211(X1,X2)) , Marked_active(X1)>
<Marked_active(U212(X1,X2)) , Marked_U212(active(X1),X2)>
<Marked_active(U212(X1,X2)) , Marked_active(X1)>
<Marked_active(U221(X1,X2,X3)) , Marked_U221(active(X1),X2,X3)>
<Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
<Marked_active(U222(X1,X2,X3)) , Marked_U222(active(X1),X2,X3)>
<Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
<Marked_active(fst(X)) , Marked_fst(active(X))>
<Marked_active(fst(X)) , Marked_active(X)>
<Marked_active(U31(X1,X2,X3)) , Marked_U31(active(X1),X2,X3)>
<Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
<Marked_active(U32(X1,X2)) , Marked_U32(active(X1),X2)>
<Marked_active(U32(X1,X2)) , Marked_active(X1)>
<Marked_active(U41(X1,X2)) , Marked_U41(active(X1),X2)>
<Marked_active(U41(X1,X2)) , Marked_active(X1)>
<Marked_active(U42(X)) , Marked_U42(active(X))>
<Marked_active(U42(X)) , Marked_active(X)>
<Marked_active(U51(X1,X2)) , Marked_U51(active(X1),X2)>
<Marked_active(U51(X1,X2)) , Marked_active(X1)>
<Marked_active(U52(X)) , Marked_U52(active(X))>
<Marked_active(U52(X)) , Marked_active(X)>
<Marked_active(U61(X)) , Marked_U61(active(X))>
<Marked_active(U61(X)) , Marked_active(X)>
<Marked_active(U71(X)) , Marked_U71(active(X))>
<Marked_active(U71(X)) , Marked_active(X)>
<Marked_active(U81(X)) , Marked_U81(active(X))>
<Marked_active(U81(X)) , Marked_active(X)>
<Marked_active(U91(X)) , Marked_U91(active(X))>
<Marked_active(U91(X)) , Marked_active(X)>
<Marked_active(tail(X)) , Marked_tail(active(X))>
<Marked_active(tail(X)) , Marked_active(X)>
<Marked_active(take(X1,X2)) , Marked_take(active(X1),X2)>
<Marked_active(take(X1,X2)) , Marked_active(X1)>
<Marked_active(take(X1,X2)) , Marked_take(X1,active(X2))>
<Marked_active(take(X1,X2)) , Marked_active(X2)>
<Marked_active(sel(X1,X2)) , Marked_sel(active(X1),X2)>
<Marked_active(sel(X1,X2)) , Marked_active(X1)>
<Marked_active(sel(X1,X2)) , Marked_sel(X1,active(X2))>
<Marked_active(sel(X1,X2)) , Marked_active(X2)>
<Marked_U101(mark(X1),X2) , Marked_U101(X1,X2)>
<Marked_U102(mark(X)) , Marked_U102(X)>
<Marked_U11(mark(X1),X2,X3) , Marked_U11(X1,X2,X3)>
<Marked_U12(mark(X1),X2,X3) , Marked_U12(X1,X2,X3)>
<Marked_U111(mark(X)) , Marked_U111(X)>
<Marked_snd(mark(X)) , Marked_snd(X)>
<Marked_splitAt(mark(X1),X2) , Marked_splitAt(X1,X2)>
<Marked_splitAt(X1,mark(X2)) , Marked_splitAt(X1,X2)>
<Marked_U121(mark(X)) , Marked_U121(X)>
<Marked_U131(mark(X1),X2) , Marked_U131(X1,X2)>
<Marked_U132(mark(X)) , Marked_U132(X)>
<Marked_U141(mark(X1),X2) , Marked_U141(X1,X2)>
<Marked_U142(mark(X)) , Marked_U142(X)>
<Marked_U151(mark(X1),X2) , Marked_U151(X1,X2)>
<Marked_U152(mark(X)) , Marked_U152(X)>
<Marked_U161(mark(X1),X2) , Marked_U161(X1,X2)>
<Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
<Marked_natsFrom(mark(X)) , Marked_natsFrom(X)>
<Marked_s(mark(X)) , Marked_s(X)>
<Marked_U171(mark(X1),X2,X3) , Marked_U171(X1,X2,X3)>
<Marked_U172(mark(X1),X2,X3) , Marked_U172(X1,X2,X3)>
<Marked_head(mark(X)) , Marked_head(X)>
<Marked_afterNth(mark(X1),X2) , Marked_afterNth(X1,X2)>
<Marked_afterNth(X1,mark(X2)) , Marked_afterNth(X1,X2)>
<Marked_U181(mark(X1),X2) , Marked_U181(X1,X2)>
<Marked_U182(mark(X1),X2) , Marked_U182(X1,X2)>
<Marked_U191(mark(X1),X2) , Marked_U191(X1,X2)>
<Marked_pair(mark(X1),X2) , Marked_pair(X1,X2)>
<Marked_pair(X1,mark(X2)) , Marked_pair(X1,X2)>
<Marked_U201(mark(X1),X2,X3,X4) , Marked_U201(X1,X2,X3,X4)>
<Marked_U202(mark(X1),X2,X3,X4) , Marked_U202(X1,X2,X3,X4)>
<Marked_U203(mark(X1),X2,X3,X4) , Marked_U203(X1,X2,X3,X4)>
<Marked_U204(mark(X1),X2) , Marked_U204(X1,X2)>
<Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)>
<Marked_U22(mark(X1),X2) , Marked_U22(X1,X2)>
<Marked_U211(mark(X1),X2) , Marked_U211(X1,X2)>
<Marked_U212(mark(X1),X2) , Marked_U212(X1,X2)>
<Marked_U221(mark(X1),X2,X3) , Marked_U221(X1,X2,X3)>
<Marked_U222(mark(X1),X2,X3) , Marked_U222(X1,X2,X3)>
<Marked_fst(mark(X)) , Marked_fst(X)>
<Marked_U31(mark(X1),X2,X3) , Marked_U31(X1,X2,X3)>
<Marked_U32(mark(X1),X2) , Marked_U32(X1,X2)>
<Marked_U41(mark(X1),X2) , Marked_U41(X1,X2)>
<Marked_U42(mark(X)) , Marked_U42(X)>
<Marked_U51(mark(X1),X2) , Marked_U51(X1,X2)>
<Marked_U52(mark(X)) , Marked_U52(X)>
<Marked_U61(mark(X)) , Marked_U61(X)>
<Marked_U71(mark(X)) , Marked_U71(X)>
<Marked_U81(mark(X)) , Marked_U81(X)>
<Marked_U91(mark(X)) , Marked_U91(X)>
<Marked_tail(mark(X)) , Marked_tail(X)>
<Marked_take(mark(X1),X2) , Marked_take(X1,X2)>
<Marked_take(X1,mark(X2)) , Marked_take(X1,X2)>
<Marked_sel(mark(X1),X2) , Marked_sel(X1,X2)>
<Marked_sel(X1,mark(X2)) , Marked_sel(X1,X2)>
<Marked_proper(U101(X1,X2)) , Marked_U101(proper(X1),proper(X2))>
<Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U102(X)) , Marked_U102(proper(X))>
<Marked_proper(U102(X)) , Marked_proper(X)>
<Marked_proper(isLNat(X)) , Marked_isLNat(proper(X))>
<Marked_proper(isLNat(X)) , Marked_proper(X)>
<Marked_proper(U11(X1,X2,X3)) , Marked_U11(proper(X1),proper(X2),proper(X3))>
<Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
<Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
<Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
<Marked_proper(U12(X1,X2,X3)) , Marked_U12(proper(X1),proper(X2),proper(X3))>
<Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
<Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
<Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
<Marked_proper(U111(X)) , Marked_U111(proper(X))>
<Marked_proper(U111(X)) , Marked_proper(X)>
<Marked_proper(snd(X)) , Marked_snd(proper(X))>
<Marked_proper(snd(X)) , Marked_proper(X)>
<Marked_proper(splitAt(X1,X2)) , Marked_splitAt(proper(X1),proper(X2))>
<Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
<Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U121(X)) , Marked_U121(proper(X))>
<Marked_proper(U121(X)) , Marked_proper(X)>
<Marked_proper(U131(X1,X2)) , Marked_U131(proper(X1),proper(X2))>
<Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U132(X)) , Marked_U132(proper(X))>
<Marked_proper(U132(X)) , Marked_proper(X)>
<Marked_proper(U141(X1,X2)) , Marked_U141(proper(X1),proper(X2))>
<Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U142(X)) , Marked_U142(proper(X))>
<Marked_proper(U142(X)) , Marked_proper(X)>
<Marked_proper(U151(X1,X2)) , Marked_U151(proper(X1),proper(X2))>
<Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U152(X)) , Marked_U152(proper(X))>
<Marked_proper(U152(X)) , Marked_proper(X)>
<Marked_proper(U161(X1,X2)) , Marked_U161(proper(X1),proper(X2))>
<Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
<Marked_proper(cons(X1,X2)) , Marked_cons(proper(X1),proper(X2))>
<Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
<Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
<Marked_proper(natsFrom(X)) , Marked_natsFrom(proper(X))>
<Marked_proper(natsFrom(X)) , Marked_proper(X)>
<Marked_proper(s(X)) , Marked_s(proper(X))>
<Marked_proper(s(X)) , Marked_proper(X)>
<Marked_proper(U171(X1,X2,X3)) , Marked_U171(proper(X1),proper(X2),proper(X3))>
<Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
<Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
<Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
<Marked_proper(U172(X1,X2,X3)) , Marked_U172(proper(X1),proper(X2),proper(X3))>
<Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
<Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
<Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
<Marked_proper(head(X)) , Marked_head(proper(X))>
<Marked_proper(head(X)) , Marked_proper(X)>
<Marked_proper(afterNth(X1,X2)) , Marked_afterNth(proper(X1),proper(X2))>
<Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
<Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U181(X1,X2)) , Marked_U181(proper(X1),proper(X2))>
<Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U182(X1,X2)) , Marked_U182(proper(X1),proper(X2))>
<Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U191(X1,X2)) , Marked_U191(proper(X1),proper(X2))>
<Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
<Marked_proper(pair(X1,X2)) , Marked_pair(proper(X1),proper(X2))>
<Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
<Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U201(X1,X2,X3,X4)) , Marked_U201(proper(X1),proper(X2),
                                     proper(X3),proper(X4))>
<Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
<Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
<Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
<Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
<Marked_proper(U202(X1,X2,X3,X4)) , Marked_U202(proper(X1),proper(X2),
                                     proper(X3),proper(X4))>
<Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
<Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
<Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
<Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
<Marked_proper(isNatural(X)) , Marked_isNatural(proper(X))>
<Marked_proper(isNatural(X)) , Marked_proper(X)>
<Marked_proper(U203(X1,X2,X3,X4)) , Marked_U203(proper(X1),proper(X2),
                                     proper(X3),proper(X4))>
<Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
<Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
<Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
<Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
<Marked_proper(U204(X1,X2)) , Marked_U204(proper(X1),proper(X2))>
<Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U21(X1,X2,X3)) , Marked_U21(proper(X1),proper(X2),proper(X3))>
<Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
<Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
<Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
<Marked_proper(U22(X1,X2)) , Marked_U22(proper(X1),proper(X2))>
<Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U211(X1,X2)) , Marked_U211(proper(X1),proper(X2))>
<Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U212(X1,X2)) , Marked_U212(proper(X1),proper(X2))>
<Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U221(X1,X2,X3)) , Marked_U221(proper(X1),proper(X2),proper(X3))>
<Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
<Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
<Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
<Marked_proper(U222(X1,X2,X3)) , Marked_U222(proper(X1),proper(X2),proper(X3))>
<Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
<Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
<Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
<Marked_proper(fst(X)) , Marked_fst(proper(X))>
<Marked_proper(fst(X)) , Marked_proper(X)>
<Marked_proper(U31(X1,X2,X3)) , Marked_U31(proper(X1),proper(X2),proper(X3))>
<Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
<Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
<Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
<Marked_proper(U32(X1,X2)) , Marked_U32(proper(X1),proper(X2))>
<Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U41(X1,X2)) , Marked_U41(proper(X1),proper(X2))>
<Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U42(X)) , Marked_U42(proper(X))>
<Marked_proper(U42(X)) , Marked_proper(X)>
<Marked_proper(U51(X1,X2)) , Marked_U51(proper(X1),proper(X2))>
<Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U52(X)) , Marked_U52(proper(X))>
<Marked_proper(U52(X)) , Marked_proper(X)>
<Marked_proper(U61(X)) , Marked_U61(proper(X))>
<Marked_proper(U61(X)) , Marked_proper(X)>
<Marked_proper(U71(X)) , Marked_U71(proper(X))>
<Marked_proper(U71(X)) , Marked_proper(X)>
<Marked_proper(U81(X)) , Marked_U81(proper(X))>
<Marked_proper(U81(X)) , Marked_proper(X)>
<Marked_proper(U91(X)) , Marked_U91(proper(X))>
<Marked_proper(U91(X)) , Marked_proper(X)>
<Marked_proper(isPLNat(X)) , Marked_isPLNat(proper(X))>
<Marked_proper(isPLNat(X)) , Marked_proper(X)>
<Marked_proper(tail(X)) , Marked_tail(proper(X))>
<Marked_proper(tail(X)) , Marked_proper(X)>
<Marked_proper(take(X1,X2)) , Marked_take(proper(X1),proper(X2))>
<Marked_proper(take(X1,X2)) , Marked_proper(X1)>
<Marked_proper(take(X1,X2)) , Marked_proper(X2)>
<Marked_proper(sel(X1,X2)) , Marked_sel(proper(X1),proper(X2))>
<Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
<Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
<Marked_U101(ok(X1),ok(X2)) , Marked_U101(X1,X2)>
<Marked_U102(ok(X)) , Marked_U102(X)>
<Marked_isLNat(ok(X)) , Marked_isLNat(X)>
<Marked_U11(ok(X1),ok(X2),ok(X3)) , Marked_U11(X1,X2,X3)>
<Marked_U12(ok(X1),ok(X2),ok(X3)) , Marked_U12(X1,X2,X3)>
<Marked_U111(ok(X)) , Marked_U111(X)>
<Marked_snd(ok(X)) , Marked_snd(X)>
<Marked_splitAt(ok(X1),ok(X2)) , Marked_splitAt(X1,X2)>
<Marked_U121(ok(X)) , Marked_U121(X)>
<Marked_U131(ok(X1),ok(X2)) , Marked_U131(X1,X2)>
<Marked_U132(ok(X)) , Marked_U132(X)>
<Marked_U141(ok(X1),ok(X2)) , Marked_U141(X1,X2)>
<Marked_U142(ok(X)) , Marked_U142(X)>
<Marked_U151(ok(X1),ok(X2)) , Marked_U151(X1,X2)>
<Marked_U152(ok(X)) , Marked_U152(X)>
<Marked_U161(ok(X1),ok(X2)) , Marked_U161(X1,X2)>
<Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)>
<Marked_natsFrom(ok(X)) , Marked_natsFrom(X)>
<Marked_s(ok(X)) , Marked_s(X)>
<Marked_U171(ok(X1),ok(X2),ok(X3)) , Marked_U171(X1,X2,X3)>
<Marked_U172(ok(X1),ok(X2),ok(X3)) , Marked_U172(X1,X2,X3)>
<Marked_head(ok(X)) , Marked_head(X)>
<Marked_afterNth(ok(X1),ok(X2)) , Marked_afterNth(X1,X2)>
<Marked_U181(ok(X1),ok(X2)) , Marked_U181(X1,X2)>
<Marked_U182(ok(X1),ok(X2)) , Marked_U182(X1,X2)>
<Marked_U191(ok(X1),ok(X2)) , Marked_U191(X1,X2)>
<Marked_pair(ok(X1),ok(X2)) , Marked_pair(X1,X2)>
<Marked_U201(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U201(X1,X2,X3,X4)>
<Marked_U202(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U202(X1,X2,X3,X4)>
<Marked_isNatural(ok(X)) , Marked_isNatural(X)>
<Marked_U203(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U203(X1,X2,X3,X4)>
<Marked_U204(ok(X1),ok(X2)) , Marked_U204(X1,X2)>
<Marked_U21(ok(X1),ok(X2),ok(X3)) , Marked_U21(X1,X2,X3)>
<Marked_U22(ok(X1),ok(X2)) , Marked_U22(X1,X2)>
<Marked_U211(ok(X1),ok(X2)) , Marked_U211(X1,X2)>
<Marked_U212(ok(X1),ok(X2)) , Marked_U212(X1,X2)>
<Marked_U221(ok(X1),ok(X2),ok(X3)) , Marked_U221(X1,X2,X3)>
<Marked_U222(ok(X1),ok(X2),ok(X3)) , Marked_U222(X1,X2,X3)>
<Marked_fst(ok(X)) , Marked_fst(X)>
<Marked_U31(ok(X1),ok(X2),ok(X3)) , Marked_U31(X1,X2,X3)>
<Marked_U32(ok(X1),ok(X2)) , Marked_U32(X1,X2)>
<Marked_U41(ok(X1),ok(X2)) , Marked_U41(X1,X2)>
<Marked_U42(ok(X)) , Marked_U42(X)>
<Marked_U51(ok(X1),ok(X2)) , Marked_U51(X1,X2)>
<Marked_U52(ok(X)) , Marked_U52(X)>
<Marked_U61(ok(X)) , Marked_U61(X)>
<Marked_U71(ok(X)) , Marked_U71(X)>
<Marked_U81(ok(X)) , Marked_U81(X)>
<Marked_U91(ok(X)) , Marked_U91(X)>
<Marked_isPLNat(ok(X)) , Marked_isPLNat(X)>
<Marked_tail(ok(X)) , Marked_tail(X)>
<Marked_take(ok(X1),ok(X2)) , Marked_take(X1,X2)>
<Marked_sel(ok(X1),ok(X2)) , Marked_sel(X1,X2)>
<Marked_top(mark(X)) , Marked_top(proper(X))>
<Marked_top(mark(X)) , Marked_proper(X)>
<Marked_top(ok(X)) , Marked_top(active(X))>
<Marked_top(ok(X)) , Marked_active(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 56 components:

{  <Marked_top(ok(X)) , Marked_top(active(X))> 
      --> <Marked_top(ok(X)) , Marked_top(active(X))>
  <Marked_top(ok(X)) , Marked_top(active(X))> 
     --> <Marked_top(mark(X)) , Marked_top(proper(X))>
  <Marked_top(mark(X)) , Marked_top(proper(X))> 
     --> <Marked_top(ok(X)) , Marked_top(active(X))>
  <Marked_top(mark(X)) , Marked_top(proper(X))> 
     --> <Marked_top(mark(X)) , Marked_top(proper(X))>
}

{  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
      --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U212(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U204(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U182(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U121(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U111(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U102(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U222(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U212(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U204(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U203(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U182(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U172(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2)) , Marked_proper(X1)>
}

{  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
      --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U91(X)) , Marked_active(X)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U81(X)) , Marked_active(X)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U71(X)) , Marked_active(X)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U61(X)) , Marked_active(X)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U32(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U212(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U211(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U22(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U204(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U191(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U182(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U181(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U161(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U152(X)) , Marked_active(X)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U151(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U142(X)) , Marked_active(X)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U141(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U132(X)) , Marked_active(X)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U131(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U121(X)) , Marked_active(X)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U111(X)) , Marked_active(X)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U102(X)) , Marked_active(X)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X)) , Marked_active(X)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X)) , Marked_active(X)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X)) , Marked_active(X)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X)) , Marked_active(X)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U32(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U222(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U221(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U212(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U211(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U204(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U203(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U202(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U201(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U191(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U182(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U181(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U172(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U171(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U161(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U152(X)) , Marked_active(X)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U151(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U142(X)) , Marked_active(X)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U141(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U132(X)) , Marked_active(X)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U131(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U121(X)) , Marked_active(X)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U111(X)) , Marked_active(X)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U102(X)) , Marked_active(X)>
  <Marked_active(U101(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2)) , Marked_active(X1)>
}

{  <Marked_isPLNat(ok(X)) , Marked_isPLNat(X)> 
      --> <Marked_isPLNat(ok(X)) , Marked_isPLNat(X)>
}

{  <Marked_isLNat(ok(X)) , Marked_isLNat(X)> 
      --> <Marked_isLNat(ok(X)) , Marked_isLNat(X)>
}

{  <Marked_isNatural(ok(X)) , Marked_isNatural(X)> 
      --> <Marked_isNatural(ok(X)) , Marked_isNatural(X)>
}

{  <Marked_U101(ok(X1),ok(X2)) , Marked_U101(X1,X2)> 
      --> <Marked_U101(ok(X1),ok(X2)) , Marked_U101(X1,X2)>
  <Marked_U101(ok(X1),ok(X2)) , Marked_U101(X1,X2)> 
     --> <Marked_U101(mark(X1),X2) , Marked_U101(X1,X2)>
  <Marked_U101(mark(X1),X2) , Marked_U101(X1,X2)> 
     --> <Marked_U101(ok(X1),ok(X2)) , Marked_U101(X1,X2)>
  <Marked_U101(mark(X1),X2) , Marked_U101(X1,X2)> 
     --> <Marked_U101(mark(X1),X2) , Marked_U101(X1,X2)>
}

{  <Marked_U102(ok(X)) , Marked_U102(X)> 
      --> <Marked_U102(ok(X)) , Marked_U102(X)>
  <Marked_U102(ok(X)) , Marked_U102(X)> 
     --> <Marked_U102(mark(X)) , Marked_U102(X)>
  <Marked_U102(mark(X)) , Marked_U102(X)> 
     --> <Marked_U102(ok(X)) , Marked_U102(X)>
  <Marked_U102(mark(X)) , Marked_U102(X)> 
     --> <Marked_U102(mark(X)) , Marked_U102(X)>
}

{  <Marked_U11(ok(X1),ok(X2),ok(X3)) , Marked_U11(X1,X2,X3)> 
      --> <Marked_U11(ok(X1),ok(X2),ok(X3)) , Marked_U11(X1,X2,X3)>
  <Marked_U11(ok(X1),ok(X2),ok(X3)) , Marked_U11(X1,X2,X3)> 
     --> <Marked_U11(mark(X1),X2,X3) , Marked_U11(X1,X2,X3)>
  <Marked_U11(mark(X1),X2,X3) , Marked_U11(X1,X2,X3)> 
     --> <Marked_U11(ok(X1),ok(X2),ok(X3)) , Marked_U11(X1,X2,X3)>
  <Marked_U11(mark(X1),X2,X3) , Marked_U11(X1,X2,X3)> 
     --> <Marked_U11(mark(X1),X2,X3) , Marked_U11(X1,X2,X3)>
}

{  <Marked_U12(ok(X1),ok(X2),ok(X3)) , Marked_U12(X1,X2,X3)> 
      --> <Marked_U12(ok(X1),ok(X2),ok(X3)) , Marked_U12(X1,X2,X3)>
  <Marked_U12(ok(X1),ok(X2),ok(X3)) , Marked_U12(X1,X2,X3)> 
     --> <Marked_U12(mark(X1),X2,X3) , Marked_U12(X1,X2,X3)>
  <Marked_U12(mark(X1),X2,X3) , Marked_U12(X1,X2,X3)> 
     --> <Marked_U12(ok(X1),ok(X2),ok(X3)) , Marked_U12(X1,X2,X3)>
  <Marked_U12(mark(X1),X2,X3) , Marked_U12(X1,X2,X3)> 
     --> <Marked_U12(mark(X1),X2,X3) , Marked_U12(X1,X2,X3)>
}

{  <Marked_U111(ok(X)) , Marked_U111(X)> 
      --> <Marked_U111(ok(X)) , Marked_U111(X)>
  <Marked_U111(ok(X)) , Marked_U111(X)> 
     --> <Marked_U111(mark(X)) , Marked_U111(X)>
  <Marked_U111(mark(X)) , Marked_U111(X)> 
     --> <Marked_U111(ok(X)) , Marked_U111(X)>
  <Marked_U111(mark(X)) , Marked_U111(X)> 
     --> <Marked_U111(mark(X)) , Marked_U111(X)>
}

{  <Marked_snd(ok(X)) , Marked_snd(X)> --> <Marked_snd(ok(X)) , Marked_snd(X)>
  <Marked_snd(ok(X)) , Marked_snd(X)> --> <Marked_snd(mark(X)) , Marked_snd(X)>
  <Marked_snd(mark(X)) , Marked_snd(X)> --> <Marked_snd(ok(X)) , Marked_snd(X)>
  <Marked_snd(mark(X)) , Marked_snd(X)> 
     --> <Marked_snd(mark(X)) , Marked_snd(X)>
}

{  <Marked_splitAt(ok(X1),ok(X2)) , Marked_splitAt(X1,X2)> 
      --> <Marked_splitAt(ok(X1),ok(X2)) , Marked_splitAt(X1,X2)>
  <Marked_splitAt(ok(X1),ok(X2)) , Marked_splitAt(X1,X2)> 
     --> <Marked_splitAt(X1,mark(X2)) , Marked_splitAt(X1,X2)>
  <Marked_splitAt(ok(X1),ok(X2)) , Marked_splitAt(X1,X2)> 
     --> <Marked_splitAt(mark(X1),X2) , Marked_splitAt(X1,X2)>
  <Marked_splitAt(X1,mark(X2)) , Marked_splitAt(X1,X2)> 
     --> <Marked_splitAt(ok(X1),ok(X2)) , Marked_splitAt(X1,X2)>
  <Marked_splitAt(X1,mark(X2)) , Marked_splitAt(X1,X2)> 
     --> <Marked_splitAt(X1,mark(X2)) , Marked_splitAt(X1,X2)>
  <Marked_splitAt(X1,mark(X2)) , Marked_splitAt(X1,X2)> 
     --> <Marked_splitAt(mark(X1),X2) , Marked_splitAt(X1,X2)>
  <Marked_splitAt(mark(X1),X2) , Marked_splitAt(X1,X2)> 
     --> <Marked_splitAt(ok(X1),ok(X2)) , Marked_splitAt(X1,X2)>
  <Marked_splitAt(mark(X1),X2) , Marked_splitAt(X1,X2)> 
     --> <Marked_splitAt(X1,mark(X2)) , Marked_splitAt(X1,X2)>
  <Marked_splitAt(mark(X1),X2) , Marked_splitAt(X1,X2)> 
     --> <Marked_splitAt(mark(X1),X2) , Marked_splitAt(X1,X2)>
}

{  <Marked_U121(ok(X)) , Marked_U121(X)> 
      --> <Marked_U121(ok(X)) , Marked_U121(X)>
  <Marked_U121(ok(X)) , Marked_U121(X)> 
     --> <Marked_U121(mark(X)) , Marked_U121(X)>
  <Marked_U121(mark(X)) , Marked_U121(X)> 
     --> <Marked_U121(ok(X)) , Marked_U121(X)>
  <Marked_U121(mark(X)) , Marked_U121(X)> 
     --> <Marked_U121(mark(X)) , Marked_U121(X)>
}

{  <Marked_U131(ok(X1),ok(X2)) , Marked_U131(X1,X2)> 
      --> <Marked_U131(ok(X1),ok(X2)) , Marked_U131(X1,X2)>
  <Marked_U131(ok(X1),ok(X2)) , Marked_U131(X1,X2)> 
     --> <Marked_U131(mark(X1),X2) , Marked_U131(X1,X2)>
  <Marked_U131(mark(X1),X2) , Marked_U131(X1,X2)> 
     --> <Marked_U131(ok(X1),ok(X2)) , Marked_U131(X1,X2)>
  <Marked_U131(mark(X1),X2) , Marked_U131(X1,X2)> 
     --> <Marked_U131(mark(X1),X2) , Marked_U131(X1,X2)>
}

{  <Marked_U132(ok(X)) , Marked_U132(X)> 
      --> <Marked_U132(ok(X)) , Marked_U132(X)>
  <Marked_U132(ok(X)) , Marked_U132(X)> 
     --> <Marked_U132(mark(X)) , Marked_U132(X)>
  <Marked_U132(mark(X)) , Marked_U132(X)> 
     --> <Marked_U132(ok(X)) , Marked_U132(X)>
  <Marked_U132(mark(X)) , Marked_U132(X)> 
     --> <Marked_U132(mark(X)) , Marked_U132(X)>
}

{  <Marked_U141(ok(X1),ok(X2)) , Marked_U141(X1,X2)> 
      --> <Marked_U141(ok(X1),ok(X2)) , Marked_U141(X1,X2)>
  <Marked_U141(ok(X1),ok(X2)) , Marked_U141(X1,X2)> 
     --> <Marked_U141(mark(X1),X2) , Marked_U141(X1,X2)>
  <Marked_U141(mark(X1),X2) , Marked_U141(X1,X2)> 
     --> <Marked_U141(ok(X1),ok(X2)) , Marked_U141(X1,X2)>
  <Marked_U141(mark(X1),X2) , Marked_U141(X1,X2)> 
     --> <Marked_U141(mark(X1),X2) , Marked_U141(X1,X2)>
}

{  <Marked_U142(ok(X)) , Marked_U142(X)> 
      --> <Marked_U142(ok(X)) , Marked_U142(X)>
  <Marked_U142(ok(X)) , Marked_U142(X)> 
     --> <Marked_U142(mark(X)) , Marked_U142(X)>
  <Marked_U142(mark(X)) , Marked_U142(X)> 
     --> <Marked_U142(ok(X)) , Marked_U142(X)>
  <Marked_U142(mark(X)) , Marked_U142(X)> 
     --> <Marked_U142(mark(X)) , Marked_U142(X)>
}

{  <Marked_U151(ok(X1),ok(X2)) , Marked_U151(X1,X2)> 
      --> <Marked_U151(ok(X1),ok(X2)) , Marked_U151(X1,X2)>
  <Marked_U151(ok(X1),ok(X2)) , Marked_U151(X1,X2)> 
     --> <Marked_U151(mark(X1),X2) , Marked_U151(X1,X2)>
  <Marked_U151(mark(X1),X2) , Marked_U151(X1,X2)> 
     --> <Marked_U151(ok(X1),ok(X2)) , Marked_U151(X1,X2)>
  <Marked_U151(mark(X1),X2) , Marked_U151(X1,X2)> 
     --> <Marked_U151(mark(X1),X2) , Marked_U151(X1,X2)>
}

{  <Marked_U152(ok(X)) , Marked_U152(X)> 
      --> <Marked_U152(ok(X)) , Marked_U152(X)>
  <Marked_U152(ok(X)) , Marked_U152(X)> 
     --> <Marked_U152(mark(X)) , Marked_U152(X)>
  <Marked_U152(mark(X)) , Marked_U152(X)> 
     --> <Marked_U152(ok(X)) , Marked_U152(X)>
  <Marked_U152(mark(X)) , Marked_U152(X)> 
     --> <Marked_U152(mark(X)) , Marked_U152(X)>
}

{  <Marked_U161(ok(X1),ok(X2)) , Marked_U161(X1,X2)> 
      --> <Marked_U161(ok(X1),ok(X2)) , Marked_U161(X1,X2)>
  <Marked_U161(ok(X1),ok(X2)) , Marked_U161(X1,X2)> 
     --> <Marked_U161(mark(X1),X2) , Marked_U161(X1,X2)>
  <Marked_U161(mark(X1),X2) , Marked_U161(X1,X2)> 
     --> <Marked_U161(ok(X1),ok(X2)) , Marked_U161(X1,X2)>
  <Marked_U161(mark(X1),X2) , Marked_U161(X1,X2)> 
     --> <Marked_U161(mark(X1),X2) , Marked_U161(X1,X2)>
}

{  <Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)> 
      --> <Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)>
  <Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)> 
     --> <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
  <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)> 
     --> <Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)>
  <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)> 
     --> <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
}

{  <Marked_natsFrom(ok(X)) , Marked_natsFrom(X)> 
      --> <Marked_natsFrom(ok(X)) , Marked_natsFrom(X)>
  <Marked_natsFrom(ok(X)) , Marked_natsFrom(X)> 
     --> <Marked_natsFrom(mark(X)) , Marked_natsFrom(X)>
  <Marked_natsFrom(mark(X)) , Marked_natsFrom(X)> 
     --> <Marked_natsFrom(ok(X)) , Marked_natsFrom(X)>
  <Marked_natsFrom(mark(X)) , Marked_natsFrom(X)> 
     --> <Marked_natsFrom(mark(X)) , Marked_natsFrom(X)>
}

{  <Marked_s(ok(X)) , Marked_s(X)> --> <Marked_s(ok(X)) , Marked_s(X)>
  <Marked_s(ok(X)) , Marked_s(X)> --> <Marked_s(mark(X)) , Marked_s(X)>
  <Marked_s(mark(X)) , Marked_s(X)> --> <Marked_s(ok(X)) , Marked_s(X)>
  <Marked_s(mark(X)) , Marked_s(X)> --> <Marked_s(mark(X)) , Marked_s(X)>
}

{  <Marked_U171(ok(X1),ok(X2),ok(X3)) , Marked_U171(X1,X2,X3)> 
      --> <Marked_U171(ok(X1),ok(X2),ok(X3)) , Marked_U171(X1,X2,X3)>
  <Marked_U171(ok(X1),ok(X2),ok(X3)) , Marked_U171(X1,X2,X3)> 
     --> <Marked_U171(mark(X1),X2,X3) , Marked_U171(X1,X2,X3)>
  <Marked_U171(mark(X1),X2,X3) , Marked_U171(X1,X2,X3)> 
     --> <Marked_U171(ok(X1),ok(X2),ok(X3)) , Marked_U171(X1,X2,X3)>
  <Marked_U171(mark(X1),X2,X3) , Marked_U171(X1,X2,X3)> 
     --> <Marked_U171(mark(X1),X2,X3) , Marked_U171(X1,X2,X3)>
}

{  <Marked_U172(ok(X1),ok(X2),ok(X3)) , Marked_U172(X1,X2,X3)> 
      --> <Marked_U172(ok(X1),ok(X2),ok(X3)) , Marked_U172(X1,X2,X3)>
  <Marked_U172(ok(X1),ok(X2),ok(X3)) , Marked_U172(X1,X2,X3)> 
     --> <Marked_U172(mark(X1),X2,X3) , Marked_U172(X1,X2,X3)>
  <Marked_U172(mark(X1),X2,X3) , Marked_U172(X1,X2,X3)> 
     --> <Marked_U172(ok(X1),ok(X2),ok(X3)) , Marked_U172(X1,X2,X3)>
  <Marked_U172(mark(X1),X2,X3) , Marked_U172(X1,X2,X3)> 
     --> <Marked_U172(mark(X1),X2,X3) , Marked_U172(X1,X2,X3)>
}

{  <Marked_head(ok(X)) , Marked_head(X)> 
      --> <Marked_head(ok(X)) , Marked_head(X)>
  <Marked_head(ok(X)) , Marked_head(X)> 
     --> <Marked_head(mark(X)) , Marked_head(X)>
  <Marked_head(mark(X)) , Marked_head(X)> 
     --> <Marked_head(ok(X)) , Marked_head(X)>
  <Marked_head(mark(X)) , Marked_head(X)> 
     --> <Marked_head(mark(X)) , Marked_head(X)>
}

{  <Marked_afterNth(ok(X1),ok(X2)) , Marked_afterNth(X1,X2)> 
      --> <Marked_afterNth(ok(X1),ok(X2)) , Marked_afterNth(X1,X2)>
  <Marked_afterNth(ok(X1),ok(X2)) , Marked_afterNth(X1,X2)> 
     --> <Marked_afterNth(X1,mark(X2)) , Marked_afterNth(X1,X2)>
  <Marked_afterNth(ok(X1),ok(X2)) , Marked_afterNth(X1,X2)> 
     --> <Marked_afterNth(mark(X1),X2) , Marked_afterNth(X1,X2)>
  <Marked_afterNth(X1,mark(X2)) , Marked_afterNth(X1,X2)> 
     --> <Marked_afterNth(ok(X1),ok(X2)) , Marked_afterNth(X1,X2)>
  <Marked_afterNth(X1,mark(X2)) , Marked_afterNth(X1,X2)> 
     --> <Marked_afterNth(X1,mark(X2)) , Marked_afterNth(X1,X2)>
  <Marked_afterNth(X1,mark(X2)) , Marked_afterNth(X1,X2)> 
     --> <Marked_afterNth(mark(X1),X2) , Marked_afterNth(X1,X2)>
  <Marked_afterNth(mark(X1),X2) , Marked_afterNth(X1,X2)> 
     --> <Marked_afterNth(ok(X1),ok(X2)) , Marked_afterNth(X1,X2)>
  <Marked_afterNth(mark(X1),X2) , Marked_afterNth(X1,X2)> 
     --> <Marked_afterNth(X1,mark(X2)) , Marked_afterNth(X1,X2)>
  <Marked_afterNth(mark(X1),X2) , Marked_afterNth(X1,X2)> 
     --> <Marked_afterNth(mark(X1),X2) , Marked_afterNth(X1,X2)>
}

{  <Marked_U181(ok(X1),ok(X2)) , Marked_U181(X1,X2)> 
      --> <Marked_U181(ok(X1),ok(X2)) , Marked_U181(X1,X2)>
  <Marked_U181(ok(X1),ok(X2)) , Marked_U181(X1,X2)> 
     --> <Marked_U181(mark(X1),X2) , Marked_U181(X1,X2)>
  <Marked_U181(mark(X1),X2) , Marked_U181(X1,X2)> 
     --> <Marked_U181(ok(X1),ok(X2)) , Marked_U181(X1,X2)>
  <Marked_U181(mark(X1),X2) , Marked_U181(X1,X2)> 
     --> <Marked_U181(mark(X1),X2) , Marked_U181(X1,X2)>
}

{  <Marked_U182(ok(X1),ok(X2)) , Marked_U182(X1,X2)> 
      --> <Marked_U182(ok(X1),ok(X2)) , Marked_U182(X1,X2)>
  <Marked_U182(ok(X1),ok(X2)) , Marked_U182(X1,X2)> 
     --> <Marked_U182(mark(X1),X2) , Marked_U182(X1,X2)>
  <Marked_U182(mark(X1),X2) , Marked_U182(X1,X2)> 
     --> <Marked_U182(ok(X1),ok(X2)) , Marked_U182(X1,X2)>
  <Marked_U182(mark(X1),X2) , Marked_U182(X1,X2)> 
     --> <Marked_U182(mark(X1),X2) , Marked_U182(X1,X2)>
}

{  <Marked_U191(ok(X1),ok(X2)) , Marked_U191(X1,X2)> 
      --> <Marked_U191(ok(X1),ok(X2)) , Marked_U191(X1,X2)>
  <Marked_U191(ok(X1),ok(X2)) , Marked_U191(X1,X2)> 
     --> <Marked_U191(mark(X1),X2) , Marked_U191(X1,X2)>
  <Marked_U191(mark(X1),X2) , Marked_U191(X1,X2)> 
     --> <Marked_U191(ok(X1),ok(X2)) , Marked_U191(X1,X2)>
  <Marked_U191(mark(X1),X2) , Marked_U191(X1,X2)> 
     --> <Marked_U191(mark(X1),X2) , Marked_U191(X1,X2)>
}

{  <Marked_pair(ok(X1),ok(X2)) , Marked_pair(X1,X2)> 
      --> <Marked_pair(ok(X1),ok(X2)) , Marked_pair(X1,X2)>
  <Marked_pair(ok(X1),ok(X2)) , Marked_pair(X1,X2)> 
     --> <Marked_pair(X1,mark(X2)) , Marked_pair(X1,X2)>
  <Marked_pair(ok(X1),ok(X2)) , Marked_pair(X1,X2)> 
     --> <Marked_pair(mark(X1),X2) , Marked_pair(X1,X2)>
  <Marked_pair(X1,mark(X2)) , Marked_pair(X1,X2)> 
     --> <Marked_pair(ok(X1),ok(X2)) , Marked_pair(X1,X2)>
  <Marked_pair(X1,mark(X2)) , Marked_pair(X1,X2)> 
     --> <Marked_pair(X1,mark(X2)) , Marked_pair(X1,X2)>
  <Marked_pair(X1,mark(X2)) , Marked_pair(X1,X2)> 
     --> <Marked_pair(mark(X1),X2) , Marked_pair(X1,X2)>
  <Marked_pair(mark(X1),X2) , Marked_pair(X1,X2)> 
     --> <Marked_pair(ok(X1),ok(X2)) , Marked_pair(X1,X2)>
  <Marked_pair(mark(X1),X2) , Marked_pair(X1,X2)> 
     --> <Marked_pair(X1,mark(X2)) , Marked_pair(X1,X2)>
  <Marked_pair(mark(X1),X2) , Marked_pair(X1,X2)> 
     --> <Marked_pair(mark(X1),X2) , Marked_pair(X1,X2)>
}

{  <Marked_U201(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U201(X1,X2,X3,X4)> 
      --> <Marked_U201(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U201(X1,X2,X3,X4)>
  <Marked_U201(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U201(X1,X2,X3,X4)> 
     --> <Marked_U201(mark(X1),X2,X3,X4) , Marked_U201(X1,X2,X3,X4)>
  <Marked_U201(mark(X1),X2,X3,X4) , Marked_U201(X1,X2,X3,X4)> 
     --> <Marked_U201(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U201(X1,X2,X3,X4)>
  <Marked_U201(mark(X1),X2,X3,X4) , Marked_U201(X1,X2,X3,X4)> 
     --> <Marked_U201(mark(X1),X2,X3,X4) , Marked_U201(X1,X2,X3,X4)>
}

{  <Marked_U202(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U202(X1,X2,X3,X4)> 
      --> <Marked_U202(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U202(X1,X2,X3,X4)>
  <Marked_U202(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U202(X1,X2,X3,X4)> 
     --> <Marked_U202(mark(X1),X2,X3,X4) , Marked_U202(X1,X2,X3,X4)>
  <Marked_U202(mark(X1),X2,X3,X4) , Marked_U202(X1,X2,X3,X4)> 
     --> <Marked_U202(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U202(X1,X2,X3,X4)>
  <Marked_U202(mark(X1),X2,X3,X4) , Marked_U202(X1,X2,X3,X4)> 
     --> <Marked_U202(mark(X1),X2,X3,X4) , Marked_U202(X1,X2,X3,X4)>
}

{  <Marked_U203(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U203(X1,X2,X3,X4)> 
      --> <Marked_U203(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U203(X1,X2,X3,X4)>
  <Marked_U203(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U203(X1,X2,X3,X4)> 
     --> <Marked_U203(mark(X1),X2,X3,X4) , Marked_U203(X1,X2,X3,X4)>
  <Marked_U203(mark(X1),X2,X3,X4) , Marked_U203(X1,X2,X3,X4)> 
     --> <Marked_U203(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U203(X1,X2,X3,X4)>
  <Marked_U203(mark(X1),X2,X3,X4) , Marked_U203(X1,X2,X3,X4)> 
     --> <Marked_U203(mark(X1),X2,X3,X4) , Marked_U203(X1,X2,X3,X4)>
}

{  <Marked_U204(ok(X1),ok(X2)) , Marked_U204(X1,X2)> 
      --> <Marked_U204(ok(X1),ok(X2)) , Marked_U204(X1,X2)>
  <Marked_U204(ok(X1),ok(X2)) , Marked_U204(X1,X2)> 
     --> <Marked_U204(mark(X1),X2) , Marked_U204(X1,X2)>
  <Marked_U204(mark(X1),X2) , Marked_U204(X1,X2)> 
     --> <Marked_U204(ok(X1),ok(X2)) , Marked_U204(X1,X2)>
  <Marked_U204(mark(X1),X2) , Marked_U204(X1,X2)> 
     --> <Marked_U204(mark(X1),X2) , Marked_U204(X1,X2)>
}

{  <Marked_U21(ok(X1),ok(X2),ok(X3)) , Marked_U21(X1,X2,X3)> 
      --> <Marked_U21(ok(X1),ok(X2),ok(X3)) , Marked_U21(X1,X2,X3)>
  <Marked_U21(ok(X1),ok(X2),ok(X3)) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(ok(X1),ok(X2),ok(X3)) , Marked_U21(X1,X2,X3)>
  <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)>
}

{  <Marked_U22(ok(X1),ok(X2)) , Marked_U22(X1,X2)> 
      --> <Marked_U22(ok(X1),ok(X2)) , Marked_U22(X1,X2)>
  <Marked_U22(ok(X1),ok(X2)) , Marked_U22(X1,X2)> 
     --> <Marked_U22(mark(X1),X2) , Marked_U22(X1,X2)>
  <Marked_U22(mark(X1),X2) , Marked_U22(X1,X2)> 
     --> <Marked_U22(ok(X1),ok(X2)) , Marked_U22(X1,X2)>
  <Marked_U22(mark(X1),X2) , Marked_U22(X1,X2)> 
     --> <Marked_U22(mark(X1),X2) , Marked_U22(X1,X2)>
}

{  <Marked_U211(ok(X1),ok(X2)) , Marked_U211(X1,X2)> 
      --> <Marked_U211(ok(X1),ok(X2)) , Marked_U211(X1,X2)>
  <Marked_U211(ok(X1),ok(X2)) , Marked_U211(X1,X2)> 
     --> <Marked_U211(mark(X1),X2) , Marked_U211(X1,X2)>
  <Marked_U211(mark(X1),X2) , Marked_U211(X1,X2)> 
     --> <Marked_U211(ok(X1),ok(X2)) , Marked_U211(X1,X2)>
  <Marked_U211(mark(X1),X2) , Marked_U211(X1,X2)> 
     --> <Marked_U211(mark(X1),X2) , Marked_U211(X1,X2)>
}

{  <Marked_U212(ok(X1),ok(X2)) , Marked_U212(X1,X2)> 
      --> <Marked_U212(ok(X1),ok(X2)) , Marked_U212(X1,X2)>
  <Marked_U212(ok(X1),ok(X2)) , Marked_U212(X1,X2)> 
     --> <Marked_U212(mark(X1),X2) , Marked_U212(X1,X2)>
  <Marked_U212(mark(X1),X2) , Marked_U212(X1,X2)> 
     --> <Marked_U212(ok(X1),ok(X2)) , Marked_U212(X1,X2)>
  <Marked_U212(mark(X1),X2) , Marked_U212(X1,X2)> 
     --> <Marked_U212(mark(X1),X2) , Marked_U212(X1,X2)>
}

{  <Marked_U221(ok(X1),ok(X2),ok(X3)) , Marked_U221(X1,X2,X3)> 
      --> <Marked_U221(ok(X1),ok(X2),ok(X3)) , Marked_U221(X1,X2,X3)>
  <Marked_U221(ok(X1),ok(X2),ok(X3)) , Marked_U221(X1,X2,X3)> 
     --> <Marked_U221(mark(X1),X2,X3) , Marked_U221(X1,X2,X3)>
  <Marked_U221(mark(X1),X2,X3) , Marked_U221(X1,X2,X3)> 
     --> <Marked_U221(ok(X1),ok(X2),ok(X3)) , Marked_U221(X1,X2,X3)>
  <Marked_U221(mark(X1),X2,X3) , Marked_U221(X1,X2,X3)> 
     --> <Marked_U221(mark(X1),X2,X3) , Marked_U221(X1,X2,X3)>
}

{  <Marked_U222(ok(X1),ok(X2),ok(X3)) , Marked_U222(X1,X2,X3)> 
      --> <Marked_U222(ok(X1),ok(X2),ok(X3)) , Marked_U222(X1,X2,X3)>
  <Marked_U222(ok(X1),ok(X2),ok(X3)) , Marked_U222(X1,X2,X3)> 
     --> <Marked_U222(mark(X1),X2,X3) , Marked_U222(X1,X2,X3)>
  <Marked_U222(mark(X1),X2,X3) , Marked_U222(X1,X2,X3)> 
     --> <Marked_U222(ok(X1),ok(X2),ok(X3)) , Marked_U222(X1,X2,X3)>
  <Marked_U222(mark(X1),X2,X3) , Marked_U222(X1,X2,X3)> 
     --> <Marked_U222(mark(X1),X2,X3) , Marked_U222(X1,X2,X3)>
}

{  <Marked_fst(ok(X)) , Marked_fst(X)> --> <Marked_fst(ok(X)) , Marked_fst(X)>
  <Marked_fst(ok(X)) , Marked_fst(X)> --> <Marked_fst(mark(X)) , Marked_fst(X)>
  <Marked_fst(mark(X)) , Marked_fst(X)> --> <Marked_fst(ok(X)) , Marked_fst(X)>
  <Marked_fst(mark(X)) , Marked_fst(X)> 
     --> <Marked_fst(mark(X)) , Marked_fst(X)>
}

{  <Marked_U31(ok(X1),ok(X2),ok(X3)) , Marked_U31(X1,X2,X3)> 
      --> <Marked_U31(ok(X1),ok(X2),ok(X3)) , Marked_U31(X1,X2,X3)>
  <Marked_U31(ok(X1),ok(X2),ok(X3)) , Marked_U31(X1,X2,X3)> 
     --> <Marked_U31(mark(X1),X2,X3) , Marked_U31(X1,X2,X3)>
  <Marked_U31(mark(X1),X2,X3) , Marked_U31(X1,X2,X3)> 
     --> <Marked_U31(ok(X1),ok(X2),ok(X3)) , Marked_U31(X1,X2,X3)>
  <Marked_U31(mark(X1),X2,X3) , Marked_U31(X1,X2,X3)> 
     --> <Marked_U31(mark(X1),X2,X3) , Marked_U31(X1,X2,X3)>
}

{  <Marked_U32(ok(X1),ok(X2)) , Marked_U32(X1,X2)> 
      --> <Marked_U32(ok(X1),ok(X2)) , Marked_U32(X1,X2)>
  <Marked_U32(ok(X1),ok(X2)) , Marked_U32(X1,X2)> 
     --> <Marked_U32(mark(X1),X2) , Marked_U32(X1,X2)>
  <Marked_U32(mark(X1),X2) , Marked_U32(X1,X2)> 
     --> <Marked_U32(ok(X1),ok(X2)) , Marked_U32(X1,X2)>
  <Marked_U32(mark(X1),X2) , Marked_U32(X1,X2)> 
     --> <Marked_U32(mark(X1),X2) , Marked_U32(X1,X2)>
}

{  <Marked_U41(ok(X1),ok(X2)) , Marked_U41(X1,X2)> 
      --> <Marked_U41(ok(X1),ok(X2)) , Marked_U41(X1,X2)>
  <Marked_U41(ok(X1),ok(X2)) , Marked_U41(X1,X2)> 
     --> <Marked_U41(mark(X1),X2) , Marked_U41(X1,X2)>
  <Marked_U41(mark(X1),X2) , Marked_U41(X1,X2)> 
     --> <Marked_U41(ok(X1),ok(X2)) , Marked_U41(X1,X2)>
  <Marked_U41(mark(X1),X2) , Marked_U41(X1,X2)> 
     --> <Marked_U41(mark(X1),X2) , Marked_U41(X1,X2)>
}

{  <Marked_U42(ok(X)) , Marked_U42(X)> --> <Marked_U42(ok(X)) , Marked_U42(X)>
  <Marked_U42(ok(X)) , Marked_U42(X)> --> <Marked_U42(mark(X)) , Marked_U42(X)>
  <Marked_U42(mark(X)) , Marked_U42(X)> --> <Marked_U42(ok(X)) , Marked_U42(X)>
  <Marked_U42(mark(X)) , Marked_U42(X)> 
     --> <Marked_U42(mark(X)) , Marked_U42(X)>
}

{  <Marked_U51(ok(X1),ok(X2)) , Marked_U51(X1,X2)> 
      --> <Marked_U51(ok(X1),ok(X2)) , Marked_U51(X1,X2)>
  <Marked_U51(ok(X1),ok(X2)) , Marked_U51(X1,X2)> 
     --> <Marked_U51(mark(X1),X2) , Marked_U51(X1,X2)>
  <Marked_U51(mark(X1),X2) , Marked_U51(X1,X2)> 
     --> <Marked_U51(ok(X1),ok(X2)) , Marked_U51(X1,X2)>
  <Marked_U51(mark(X1),X2) , Marked_U51(X1,X2)> 
     --> <Marked_U51(mark(X1),X2) , Marked_U51(X1,X2)>
}

{  <Marked_U52(ok(X)) , Marked_U52(X)> --> <Marked_U52(ok(X)) , Marked_U52(X)>
  <Marked_U52(ok(X)) , Marked_U52(X)> --> <Marked_U52(mark(X)) , Marked_U52(X)>
  <Marked_U52(mark(X)) , Marked_U52(X)> --> <Marked_U52(ok(X)) , Marked_U52(X)>
  <Marked_U52(mark(X)) , Marked_U52(X)> 
     --> <Marked_U52(mark(X)) , Marked_U52(X)>
}

{  <Marked_U61(ok(X)) , Marked_U61(X)> --> <Marked_U61(ok(X)) , Marked_U61(X)>
  <Marked_U61(ok(X)) , Marked_U61(X)> --> <Marked_U61(mark(X)) , Marked_U61(X)>
  <Marked_U61(mark(X)) , Marked_U61(X)> --> <Marked_U61(ok(X)) , Marked_U61(X)>
  <Marked_U61(mark(X)) , Marked_U61(X)> 
     --> <Marked_U61(mark(X)) , Marked_U61(X)>
}

{  <Marked_U71(ok(X)) , Marked_U71(X)> --> <Marked_U71(ok(X)) , Marked_U71(X)>
  <Marked_U71(ok(X)) , Marked_U71(X)> --> <Marked_U71(mark(X)) , Marked_U71(X)>
  <Marked_U71(mark(X)) , Marked_U71(X)> --> <Marked_U71(ok(X)) , Marked_U71(X)>
  <Marked_U71(mark(X)) , Marked_U71(X)> 
     --> <Marked_U71(mark(X)) , Marked_U71(X)>
}

{  <Marked_U81(ok(X)) , Marked_U81(X)> --> <Marked_U81(ok(X)) , Marked_U81(X)>
  <Marked_U81(ok(X)) , Marked_U81(X)> --> <Marked_U81(mark(X)) , Marked_U81(X)>
  <Marked_U81(mark(X)) , Marked_U81(X)> --> <Marked_U81(ok(X)) , Marked_U81(X)>
  <Marked_U81(mark(X)) , Marked_U81(X)> 
     --> <Marked_U81(mark(X)) , Marked_U81(X)>
}

{  <Marked_U91(ok(X)) , Marked_U91(X)> --> <Marked_U91(ok(X)) , Marked_U91(X)>
  <Marked_U91(ok(X)) , Marked_U91(X)> --> <Marked_U91(mark(X)) , Marked_U91(X)>
  <Marked_U91(mark(X)) , Marked_U91(X)> --> <Marked_U91(ok(X)) , Marked_U91(X)>
  <Marked_U91(mark(X)) , Marked_U91(X)> 
     --> <Marked_U91(mark(X)) , Marked_U91(X)>
}

{  <Marked_tail(ok(X)) , Marked_tail(X)> 
      --> <Marked_tail(ok(X)) , Marked_tail(X)>
  <Marked_tail(ok(X)) , Marked_tail(X)> 
     --> <Marked_tail(mark(X)) , Marked_tail(X)>
  <Marked_tail(mark(X)) , Marked_tail(X)> 
     --> <Marked_tail(ok(X)) , Marked_tail(X)>
  <Marked_tail(mark(X)) , Marked_tail(X)> 
     --> <Marked_tail(mark(X)) , Marked_tail(X)>
}

{  <Marked_take(ok(X1),ok(X2)) , Marked_take(X1,X2)> 
      --> <Marked_take(ok(X1),ok(X2)) , Marked_take(X1,X2)>
  <Marked_take(ok(X1),ok(X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(X1,mark(X2)) , Marked_take(X1,X2)>
  <Marked_take(ok(X1),ok(X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(mark(X1),X2) , Marked_take(X1,X2)>
  <Marked_take(X1,mark(X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(ok(X1),ok(X2)) , Marked_take(X1,X2)>
  <Marked_take(X1,mark(X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(X1,mark(X2)) , Marked_take(X1,X2)>
  <Marked_take(X1,mark(X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(mark(X1),X2) , Marked_take(X1,X2)>
  <Marked_take(mark(X1),X2) , Marked_take(X1,X2)> 
     --> <Marked_take(ok(X1),ok(X2)) , Marked_take(X1,X2)>
  <Marked_take(mark(X1),X2) , Marked_take(X1,X2)> 
     --> <Marked_take(X1,mark(X2)) , Marked_take(X1,X2)>
  <Marked_take(mark(X1),X2) , Marked_take(X1,X2)> 
     --> <Marked_take(mark(X1),X2) , Marked_take(X1,X2)>
}

{  <Marked_sel(ok(X1),ok(X2)) , Marked_sel(X1,X2)> 
      --> <Marked_sel(ok(X1),ok(X2)) , Marked_sel(X1,X2)>
  <Marked_sel(ok(X1),ok(X2)) , Marked_sel(X1,X2)> 
     --> <Marked_sel(X1,mark(X2)) , Marked_sel(X1,X2)>
  <Marked_sel(ok(X1),ok(X2)) , Marked_sel(X1,X2)> 
     --> <Marked_sel(mark(X1),X2) , Marked_sel(X1,X2)>
  <Marked_sel(X1,mark(X2)) , Marked_sel(X1,X2)> 
     --> <Marked_sel(ok(X1),ok(X2)) , Marked_sel(X1,X2)>
  <Marked_sel(X1,mark(X2)) , Marked_sel(X1,X2)> 
     --> <Marked_sel(X1,mark(X2)) , Marked_sel(X1,X2)>
  <Marked_sel(X1,mark(X2)) , Marked_sel(X1,X2)> 
     --> <Marked_sel(mark(X1),X2) , Marked_sel(X1,X2)>
  <Marked_sel(mark(X1),X2) , Marked_sel(X1,X2)> 
     --> <Marked_sel(ok(X1),ok(X2)) , Marked_sel(X1,X2)>
  <Marked_sel(mark(X1),X2) , Marked_sel(X1,X2)> 
     --> <Marked_sel(X1,mark(X2)) , Marked_sel(X1,X2)>
  <Marked_sel(mark(X1),X2) , Marked_sel(X1,X2)> 
     --> <Marked_sel(mark(X1),X2) , Marked_sel(X1,X2)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  U102(mark(X)) >= mark(U102(X)) ;
  U102(ok(X)) >= ok(U102(X)) ;
  isLNat(ok(X)) >= ok(isLNat(X)) ;
  active(U102(tt)) >= mark(tt) ;
  active(U102(X)) >= U102(active(X)) ;
  active(isLNat(snd(V1))) >= mark(U81(isPLNat(V1))) ;
  active(isLNat(cons(V1,V2))) >= mark(U51(isNatural(V1),V2)) ;
  active(isLNat(natsFrom(V1))) >= mark(U71(isNatural(V1))) ;
  active(isLNat(afterNth(V1,V2))) >= mark(U41(isNatural(V1),V2)) ;
  active(isLNat(nil)) >= mark(tt) ;
  active(isLNat(fst(V1))) >= mark(U61(isPLNat(V1))) ;
  active(isLNat(tail(V1))) >= mark(U91(isLNat(V1))) ;
  active(isLNat(take(V1,V2))) >= mark(U101(isNatural(V1),V2)) ;
  active(U101(tt,V2)) >= mark(U102(isLNat(V2))) ;
  active(U101(X1,X2)) >= U101(active(X1),X2) ;
  active(U12(tt,N,XS)) >= mark(snd(splitAt(N,XS))) ;
  active(U12(X1,X2,X3)) >= U12(active(X1),X2,X3) ;
  active(U11(tt,N,XS)) >= mark(U12(isLNat(XS),N,XS)) ;
  active(U11(X1,X2,X3)) >= U11(active(X1),X2,X3) ;
  active(U111(tt)) >= mark(tt) ;
  active(U111(X)) >= U111(active(X)) ;
  active(snd(pair(X,Y))) >= mark(U181(isLNat(X),Y)) ;
  active(snd(X)) >= snd(active(X)) ;
  active(splitAt(s(N),cons(X,XS))) >= mark(U201(isNatural(N),N,X,XS)) ;
  active(splitAt(0,XS)) >= mark(U191(isLNat(XS),XS)) ;
  active(splitAt(X1,X2)) >= splitAt(active(X1),X2) ;
  active(splitAt(X1,X2)) >= splitAt(X1,active(X2)) ;
  active(U121(tt)) >= mark(tt) ;
  active(U121(X)) >= U121(active(X)) ;
  active(U132(tt)) >= mark(tt) ;
  active(U132(X)) >= U132(active(X)) ;
  active(U131(tt,V2)) >= mark(U132(isLNat(V2))) ;
  active(U131(X1,X2)) >= U131(active(X1),X2) ;
  active(U142(tt)) >= mark(tt) ;
  active(U142(X)) >= U142(active(X)) ;
  active(U141(tt,V2)) >= mark(U142(isLNat(V2))) ;
  active(U141(X1,X2)) >= U141(active(X1),X2) ;
  active(U152(tt)) >= mark(tt) ;
  active(U152(X)) >= U152(active(X)) ;
  active(U151(tt,V2)) >= mark(U152(isLNat(V2))) ;
  active(U151(X1,X2)) >= U151(active(X1),X2) ;
  active(cons(X1,X2)) >= cons(active(X1),X2) ;
  active(natsFrom(N)) >= mark(U161(isNatural(N),N)) ;
  active(natsFrom(X)) >= natsFrom(active(X)) ;
  active(s(X)) >= s(active(X)) ;
  active(U161(tt,N)) >= mark(cons(N,natsFrom(s(N)))) ;
  active(U161(X1,X2)) >= U161(active(X1),X2) ;
  active(U172(tt,N,XS)) >= mark(head(afterNth(N,XS))) ;
  active(U172(X1,X2,X3)) >= U172(active(X1),X2,X3) ;
  active(U171(tt,N,XS)) >= mark(U172(isLNat(XS),N,XS)) ;
  active(U171(X1,X2,X3)) >= U171(active(X1),X2,X3) ;
  active(head(cons(N,XS))) >= mark(U31(isNatural(N),N,XS)) ;
  active(head(X)) >= head(active(X)) ;
  active(afterNth(N,XS)) >= mark(U11(isNatural(N),N,XS)) ;
  active(afterNth(X1,X2)) >= afterNth(active(X1),X2) ;
  active(afterNth(X1,X2)) >= afterNth(X1,active(X2)) ;
  active(U182(tt,Y)) >= mark(Y) ;
  active(U182(X1,X2)) >= U182(active(X1),X2) ;
  active(U181(tt,Y)) >= mark(U182(isLNat(Y),Y)) ;
  active(U181(X1,X2)) >= U181(active(X1),X2) ;
  active(pair(X1,X2)) >= pair(active(X1),X2) ;
  active(pair(X1,X2)) >= pair(X1,active(X2)) ;
  active(U191(tt,XS)) >= mark(pair(nil,XS)) ;
  active(U191(X1,X2)) >= U191(active(X1),X2) ;
  active(U202(tt,N,X,XS)) >= mark(U203(isLNat(XS),N,X,XS)) ;
  active(U202(X1,X2,X3,X4)) >= U202(active(X1),X2,X3,X4) ;
  active(isNatural(s(V1))) >= mark(U121(isNatural(V1))) ;
  active(isNatural(head(V1))) >= mark(U111(isLNat(V1))) ;
  active(isNatural(0)) >= mark(tt) ;
  active(isNatural(sel(V1,V2))) >= mark(U131(isNatural(V1),V2)) ;
  active(U201(tt,N,X,XS)) >= mark(U202(isNatural(X),N,X,XS)) ;
  active(U201(X1,X2,X3,X4)) >= U201(active(X1),X2,X3,X4) ;
  active(U203(tt,N,X,XS)) >= mark(U204(splitAt(N,XS),X)) ;
  active(U203(X1,X2,X3,X4)) >= U203(active(X1),X2,X3,X4) ;
  active(U204(pair(YS,ZS),X)) >= mark(pair(cons(X,YS),ZS)) ;
  active(U204(X1,X2)) >= U204(active(X1),X2) ;
  active(U22(tt,X)) >= mark(X) ;
  active(U22(X1,X2)) >= U22(active(X1),X2) ;
  active(U21(tt,X,Y)) >= mark(U22(isLNat(Y),X)) ;
  active(U21(X1,X2,X3)) >= U21(active(X1),X2,X3) ;
  active(U212(tt,XS)) >= mark(XS) ;
  active(U212(X1,X2)) >= U212(active(X1),X2) ;
  active(U211(tt,XS)) >= mark(U212(isLNat(XS),XS)) ;
  active(U211(X1,X2)) >= U211(active(X1),X2) ;
  active(U222(tt,N,XS)) >= mark(fst(splitAt(N,XS))) ;
  active(U222(X1,X2,X3)) >= U222(active(X1),X2,X3) ;
  active(U221(tt,N,XS)) >= mark(U222(isLNat(XS),N,XS)) ;
  active(U221(X1,X2,X3)) >= U221(active(X1),X2,X3) ;
  active(fst(pair(X,Y))) >= mark(U21(isLNat(X),X,Y)) ;
  active(fst(X)) >= fst(active(X)) ;
  active(U32(tt,N)) >= mark(N) ;
  active(U32(X1,X2)) >= U32(active(X1),X2) ;
  active(U31(tt,N,XS)) >= mark(U32(isLNat(XS),N)) ;
  active(U31(X1,X2,X3)) >= U31(active(X1),X2,X3) ;
  active(U42(tt)) >= mark(tt) ;
  active(U42(X)) >= U42(active(X)) ;
  active(U41(tt,V2)) >= mark(U42(isLNat(V2))) ;
  active(U41(X1,X2)) >= U41(active(X1),X2) ;
  active(U52(tt)) >= mark(tt) ;
  active(U52(X)) >= U52(active(X)) ;
  active(U51(tt,V2)) >= mark(U52(isLNat(V2))) ;
  active(U51(X1,X2)) >= U51(active(X1),X2) ;
  active(U61(tt)) >= mark(tt) ;
  active(U61(X)) >= U61(active(X)) ;
  active(U71(tt)) >= mark(tt) ;
  active(U71(X)) >= U71(active(X)) ;
  active(U81(tt)) >= mark(tt) ;
  active(U81(X)) >= U81(active(X)) ;
  active(U91(tt)) >= mark(tt) ;
  active(U91(X)) >= U91(active(X)) ;
  active(isPLNat(splitAt(V1,V2))) >= mark(U151(isNatural(V1),V2)) ;
  active(isPLNat(pair(V1,V2))) >= mark(U141(isLNat(V1),V2)) ;
  active(tail(cons(N,XS))) >= mark(U211(isNatural(N),XS)) ;
  active(tail(X)) >= tail(active(X)) ;
  active(take(N,XS)) >= mark(U221(isNatural(N),N,XS)) ;
  active(take(X1,X2)) >= take(active(X1),X2) ;
  active(take(X1,X2)) >= take(X1,active(X2)) ;
  active(sel(N,XS)) >= mark(U171(isNatural(N),N,XS)) ;
  active(sel(X1,X2)) >= sel(active(X1),X2) ;
  active(sel(X1,X2)) >= sel(X1,active(X2)) ;
  U101(mark(X1),X2) >= mark(U101(X1,X2)) ;
  U101(ok(X1),ok(X2)) >= ok(U101(X1,X2)) ;
  U12(mark(X1),X2,X3) >= mark(U12(X1,X2,X3)) ;
  U12(ok(X1),ok(X2),ok(X3)) >= ok(U12(X1,X2,X3)) ;
  U11(mark(X1),X2,X3) >= mark(U11(X1,X2,X3)) ;
  U11(ok(X1),ok(X2),ok(X3)) >= ok(U11(X1,X2,X3)) ;
  U111(mark(X)) >= mark(U111(X)) ;
  U111(ok(X)) >= ok(U111(X)) ;
  snd(mark(X)) >= mark(snd(X)) ;
  snd(ok(X)) >= ok(snd(X)) ;
  splitAt(mark(X1),X2) >= mark(splitAt(X1,X2)) ;
  splitAt(ok(X1),ok(X2)) >= ok(splitAt(X1,X2)) ;
  splitAt(X1,mark(X2)) >= mark(splitAt(X1,X2)) ;
  U121(mark(X)) >= mark(U121(X)) ;
  U121(ok(X)) >= ok(U121(X)) ;
  U132(mark(X)) >= mark(U132(X)) ;
  U132(ok(X)) >= ok(U132(X)) ;
  U131(mark(X1),X2) >= mark(U131(X1,X2)) ;
  U131(ok(X1),ok(X2)) >= ok(U131(X1,X2)) ;
  U142(mark(X)) >= mark(U142(X)) ;
  U142(ok(X)) >= ok(U142(X)) ;
  U141(mark(X1),X2) >= mark(U141(X1,X2)) ;
  U141(ok(X1),ok(X2)) >= ok(U141(X1,X2)) ;
  U152(mark(X)) >= mark(U152(X)) ;
  U152(ok(X)) >= ok(U152(X)) ;
  U151(mark(X1),X2) >= mark(U151(X1,X2)) ;
  U151(ok(X1),ok(X2)) >= ok(U151(X1,X2)) ;
  cons(mark(X1),X2) >= mark(cons(X1,X2)) ;
  cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ;
  natsFrom(mark(X)) >= mark(natsFrom(X)) ;
  natsFrom(ok(X)) >= ok(natsFrom(X)) ;
  s(mark(X)) >= mark(s(X)) ;
  s(ok(X)) >= ok(s(X)) ;
  U161(mark(X1),X2) >= mark(U161(X1,X2)) ;
  U161(ok(X1),ok(X2)) >= ok(U161(X1,X2)) ;
  U172(mark(X1),X2,X3) >= mark(U172(X1,X2,X3)) ;
  U172(ok(X1),ok(X2),ok(X3)) >= ok(U172(X1,X2,X3)) ;
  U171(mark(X1),X2,X3) >= mark(U171(X1,X2,X3)) ;
  U171(ok(X1),ok(X2),ok(X3)) >= ok(U171(X1,X2,X3)) ;
  head(mark(X)) >= mark(head(X)) ;
  head(ok(X)) >= ok(head(X)) ;
  afterNth(mark(X1),X2) >= mark(afterNth(X1,X2)) ;
  afterNth(ok(X1),ok(X2)) >= ok(afterNth(X1,X2)) ;
  afterNth(X1,mark(X2)) >= mark(afterNth(X1,X2)) ;
  U182(mark(X1),X2) >= mark(U182(X1,X2)) ;
  U182(ok(X1),ok(X2)) >= ok(U182(X1,X2)) ;
  U181(mark(X1),X2) >= mark(U181(X1,X2)) ;
  U181(ok(X1),ok(X2)) >= ok(U181(X1,X2)) ;
  pair(mark(X1),X2) >= mark(pair(X1,X2)) ;
  pair(ok(X1),ok(X2)) >= ok(pair(X1,X2)) ;
  pair(X1,mark(X2)) >= mark(pair(X1,X2)) ;
  U191(mark(X1),X2) >= mark(U191(X1,X2)) ;
  U191(ok(X1),ok(X2)) >= ok(U191(X1,X2)) ;
  U202(mark(X1),X2,X3,X4) >= mark(U202(X1,X2,X3,X4)) ;
  U202(ok(X1),ok(X2),ok(X3),ok(X4)) >= ok(U202(X1,X2,X3,X4)) ;
  isNatural(ok(X)) >= ok(isNatural(X)) ;
  U201(mark(X1),X2,X3,X4) >= mark(U201(X1,X2,X3,X4)) ;
  U201(ok(X1),ok(X2),ok(X3),ok(X4)) >= ok(U201(X1,X2,X3,X4)) ;
  U203(mark(X1),X2,X3,X4) >= mark(U203(X1,X2,X3,X4)) ;
  U203(ok(X1),ok(X2),ok(X3),ok(X4)) >= ok(U203(X1,X2,X3,X4)) ;
  U204(mark(X1),X2) >= mark(U204(X1,X2)) ;
  U204(ok(X1),ok(X2)) >= ok(U204(X1,X2)) ;
  U22(mark(X1),X2) >= mark(U22(X1,X2)) ;
  U22(ok(X1),ok(X2)) >= ok(U22(X1,X2)) ;
  U21(mark(X1),X2,X3) >= mark(U21(X1,X2,X3)) ;
  U21(ok(X1),ok(X2),ok(X3)) >= ok(U21(X1,X2,X3)) ;
  U212(mark(X1),X2) >= mark(U212(X1,X2)) ;
  U212(ok(X1),ok(X2)) >= ok(U212(X1,X2)) ;
  U211(mark(X1),X2) >= mark(U211(X1,X2)) ;
  U211(ok(X1),ok(X2)) >= ok(U211(X1,X2)) ;
  U222(mark(X1),X2,X3) >= mark(U222(X1,X2,X3)) ;
  U222(ok(X1),ok(X2),ok(X3)) >= ok(U222(X1,X2,X3)) ;
  U221(mark(X1),X2,X3) >= mark(U221(X1,X2,X3)) ;
  U221(ok(X1),ok(X2),ok(X3)) >= ok(U221(X1,X2,X3)) ;
  fst(mark(X)) >= mark(fst(X)) ;
  fst(ok(X)) >= ok(fst(X)) ;
  U32(mark(X1),X2) >= mark(U32(X1,X2)) ;
  U32(ok(X1),ok(X2)) >= ok(U32(X1,X2)) ;
  U31(mark(X1),X2,X3) >= mark(U31(X1,X2,X3)) ;
  U31(ok(X1),ok(X2),ok(X3)) >= ok(U31(X1,X2,X3)) ;
  U42(mark(X)) >= mark(U42(X)) ;
  U42(ok(X)) >= ok(U42(X)) ;
  U41(mark(X1),X2) >= mark(U41(X1,X2)) ;
  U41(ok(X1),ok(X2)) >= ok(U41(X1,X2)) ;
  U52(mark(X)) >= mark(U52(X)) ;
  U52(ok(X)) >= ok(U52(X)) ;
  U51(mark(X1),X2) >= mark(U51(X1,X2)) ;
  U51(ok(X1),ok(X2)) >= ok(U51(X1,X2)) ;
  U61(mark(X)) >= mark(U61(X)) ;
  U61(ok(X)) >= ok(U61(X)) ;
  U71(mark(X)) >= mark(U71(X)) ;
  U71(ok(X)) >= ok(U71(X)) ;
  U81(mark(X)) >= mark(U81(X)) ;
  U81(ok(X)) >= ok(U81(X)) ;
  U91(mark(X)) >= mark(U91(X)) ;
  U91(ok(X)) >= ok(U91(X)) ;
  isPLNat(ok(X)) >= ok(isPLNat(X)) ;
  tail(mark(X)) >= mark(tail(X)) ;
  tail(ok(X)) >= ok(tail(X)) ;
  take(mark(X1),X2) >= mark(take(X1,X2)) ;
  take(ok(X1),ok(X2)) >= ok(take(X1,X2)) ;
  take(X1,mark(X2)) >= mark(take(X1,X2)) ;
  sel(mark(X1),X2) >= mark(sel(X1,X2)) ;
  sel(ok(X1),ok(X2)) >= ok(sel(X1,X2)) ;
  sel(X1,mark(X2)) >= mark(sel(X1,X2)) ;
  proper(U102(X)) >= U102(proper(X)) ;
  proper(isLNat(X)) >= isLNat(proper(X)) ;
  proper(U101(X1,X2)) >= U101(proper(X1),proper(X2)) ;
  proper(tt) >= ok(tt) ;
  proper(U12(X1,X2,X3)) >= U12(proper(X1),proper(X2),proper(X3)) ;
  proper(U11(X1,X2,X3)) >= U11(proper(X1),proper(X2),proper(X3)) ;
  proper(U111(X)) >= U111(proper(X)) ;
  proper(snd(X)) >= snd(proper(X)) ;
  proper(splitAt(X1,X2)) >= splitAt(proper(X1),proper(X2)) ;
  proper(U121(X)) >= U121(proper(X)) ;
  proper(U132(X)) >= U132(proper(X)) ;
  proper(U131(X1,X2)) >= U131(proper(X1),proper(X2)) ;
  proper(U142(X)) >= U142(proper(X)) ;
  proper(U141(X1,X2)) >= U141(proper(X1),proper(X2)) ;
  proper(U152(X)) >= U152(proper(X)) ;
  proper(U151(X1,X2)) >= U151(proper(X1),proper(X2)) ;
  proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ;
  proper(natsFrom(X)) >= natsFrom(proper(X)) ;
  proper(s(X)) >= s(proper(X)) ;
  proper(U161(X1,X2)) >= U161(proper(X1),proper(X2)) ;
  proper(U172(X1,X2,X3)) >= U172(proper(X1),proper(X2),proper(X3)) ;
  proper(U171(X1,X2,X3)) >= U171(proper(X1),proper(X2),proper(X3)) ;
  proper(head(X)) >= head(proper(X)) ;
  proper(afterNth(X1,X2)) >= afterNth(proper(X1),proper(X2)) ;
  proper(U182(X1,X2)) >= U182(proper(X1),proper(X2)) ;
  proper(U181(X1,X2)) >= U181(proper(X1),proper(X2)) ;
  proper(pair(X1,X2)) >= pair(proper(X1),proper(X2)) ;
  proper(nil) >= ok(nil) ;
  proper(U191(X1,X2)) >= U191(proper(X1),proper(X2)) ;
  proper(U202(X1,X2,X3,X4)) >= U202(proper(X1),proper(X2),proper(X3),
                                proper(X4)) ;
  proper(isNatural(X)) >= isNatural(proper(X)) ;
  proper(U201(X1,X2,X3,X4)) >= U201(proper(X1),proper(X2),proper(X3),
                                proper(X4)) ;
  proper(U203(X1,X2,X3,X4)) >= U203(proper(X1),proper(X2),proper(X3),
                                proper(X4)) ;
  proper(U204(X1,X2)) >= U204(proper(X1),proper(X2)) ;
  proper(U22(X1,X2)) >= U22(proper(X1),proper(X2)) ;
  proper(U21(X1,X2,X3)) >= U21(proper(X1),proper(X2),proper(X3)) ;
  proper(U212(X1,X2)) >= U212(proper(X1),proper(X2)) ;
  proper(U211(X1,X2)) >= U211(proper(X1),proper(X2)) ;
  proper(U222(X1,X2,X3)) >= U222(proper(X1),proper(X2),proper(X3)) ;
  proper(U221(X1,X2,X3)) >= U221(proper(X1),proper(X2),proper(X3)) ;
  proper(fst(X)) >= fst(proper(X)) ;
  proper(U32(X1,X2)) >= U32(proper(X1),proper(X2)) ;
  proper(U31(X1,X2,X3)) >= U31(proper(X1),proper(X2),proper(X3)) ;
  proper(U42(X)) >= U42(proper(X)) ;
  proper(U41(X1,X2)) >= U41(proper(X1),proper(X2)) ;
  proper(U52(X)) >= U52(proper(X)) ;
  proper(U51(X1,X2)) >= U51(proper(X1),proper(X2)) ;
  proper(U61(X)) >= U61(proper(X)) ;
  proper(U71(X)) >= U71(proper(X)) ;
  proper(U81(X)) >= U81(proper(X)) ;
  proper(U91(X)) >= U91(proper(X)) ;
  proper(isPLNat(X)) >= isPLNat(proper(X)) ;
  proper(tail(X)) >= tail(proper(X)) ;
  proper(take(X1,X2)) >= take(proper(X1),proper(X2)) ;
  proper(0) >= ok(0) ;
  proper(sel(X1,X2)) >= sel(proper(X1),proper(X2)) ;
  top(mark(X)) >= top(proper(X)) ;
  top(ok(X)) >= top(active(X)) ;
  Marked_top(mark(X)) >= Marked_top(proper(X)) ;
  Marked_top(ok(X)) >= Marked_top(active(X)) ;
 }
 + Disjunctions:{ 
{
  Marked_top(mark(X)) > Marked_top(proper(X)) ;
 }
{
  Marked_top(ok(X)) > Marked_top(active(X)) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
Time out for these parameters.
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat timeout reached
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (ID_CRIT)
NOT SOLVED
No proof found
Cime worked for 96.755039 seconds (real time)
Cime Exit Status: 0