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

TRS termination of:
[1] active(U101(tt,V1,V2)) -> mark(U102(isNatural(V1),V2))
[2] active(U102(tt,V2)) -> mark(U103(isLNat(V2)))
[3] active(U103(tt)) -> mark(tt)
[4] active(U11(tt,N,XS)) -> mark(snd(splitAt(N,XS)))
[5] active(U111(tt,V1)) -> mark(U112(isLNat(V1)))
[6] active(U112(tt)) -> mark(tt)
[7] active(U121(tt,V1)) -> mark(U122(isNatural(V1)))
[8] active(U122(tt)) -> mark(tt)
[9] active(U131(tt,V1,V2)) -> mark(U132(isNatural(V1),V2))
[10] active(U132(tt,V2)) -> mark(U133(isLNat(V2)))
[11] active(U133(tt)) -> mark(tt)
[12] active(U141(tt,V1,V2)) -> mark(U142(isLNat(V1),V2))
[13] active(U142(tt,V2)) -> mark(U143(isLNat(V2)))
[14] active(U143(tt)) -> mark(tt)
[15] active(U151(tt,V1,V2)) -> mark(U152(isNatural(V1),V2))
[16] active(U152(tt,V2)) -> mark(U153(isLNat(V2)))
[17] active(U153(tt)) -> mark(tt)
[18] active(U161(tt,N)) -> mark(cons(N,natsFrom(s(N))))
[19] active(U171(tt,N,XS)) -> mark(head(afterNth(N,XS)))
[20] active(U181(tt,Y)) -> mark(Y)
[21] active(U191(tt,XS)) -> mark(pair(nil,XS))
[22] active(U201(tt,N,X,XS)) -> mark(U202(splitAt(N,XS),X))
[23] active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
[24] active(U21(tt,X)) -> mark(X)
[25] active(U211(tt,XS)) -> mark(XS)
[26] active(U221(tt,N,XS)) -> mark(fst(splitAt(N,XS)))
[27] active(U31(tt,N)) -> mark(N)
[28] active(U41(tt,V1,V2)) -> mark(U42(isNatural(V1),V2))
[29] active(U42(tt,V2)) -> mark(U43(isLNat(V2)))
[30] active(U43(tt)) -> mark(tt)
[31] active(U51(tt,V1,V2)) -> mark(U52(isNatural(V1),V2))
[32] active(U52(tt,V2)) -> mark(U53(isLNat(V2)))
[33] active(U53(tt)) -> mark(tt)
[34] active(U61(tt,V1)) -> mark(U62(isPLNat(V1)))
[35] active(U62(tt)) -> mark(tt)
[36] active(U71(tt,V1)) -> mark(U72(isNatural(V1)))
[37] active(U72(tt)) -> mark(tt)
[38] active(U81(tt,V1)) -> mark(U82(isPLNat(V1)))
[39] active(U82(tt)) -> mark(tt)
[40] active(U91(tt,V1)) -> mark(U92(isLNat(V1)))
[41] active(U92(tt)) -> mark(tt)
[42] active(afterNth(N,XS)) ->
 mark(U11(and(and(isNatural(N),isNaturalKind(N)),
           and(isLNat(XS),isLNatKind(XS))),N,XS))
[43] active(and(tt,X)) -> mark(X)
[44] active(fst(pair(X,Y))) ->
 mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
[45] active(head(cons(N,XS))) ->
 mark(U31(and(and(isNatural(N),isNaturalKind(N)),
           and(isLNat(XS),isLNatKind(XS))),N))
[46] active(isLNat(nil)) -> mark(tt)
[47] active(isLNat(afterNth(V1,V2))) ->
 mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
[48] active(isLNat(cons(V1,V2))) ->
 mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
[49] active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
[50] active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
[51] active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
[52] active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
[53] active(isLNat(take(V1,V2))) ->
 mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
[54] active(isLNatKind(nil)) -> mark(tt)
[55] active(isLNatKind(afterNth(V1,V2))) ->
 mark(and(isNaturalKind(V1),isLNatKind(V2)))
[56] active(isLNatKind(cons(V1,V2))) ->
 mark(and(isNaturalKind(V1),isLNatKind(V2)))
[57] active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
[58] active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
[59] active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
[60] active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
[61] active(isLNatKind(take(V1,V2))) ->
 mark(and(isNaturalKind(V1),isLNatKind(V2)))
[62] active(isNatural(0)) -> mark(tt)
[63] active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
[64] active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
[65] active(isNatural(sel(V1,V2))) ->
 mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
[66] active(isNaturalKind(0)) -> mark(tt)
[67] active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
[68] active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
[69] active(isNaturalKind(sel(V1,V2))) ->
 mark(and(isNaturalKind(V1),isLNatKind(V2)))
[70] active(isPLNat(pair(V1,V2))) ->
 mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
[71] active(isPLNat(splitAt(V1,V2))) ->
 mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
[72] active(isPLNatKind(pair(V1,V2))) ->
 mark(and(isLNatKind(V1),isLNatKind(V2)))
[73] active(isPLNatKind(splitAt(V1,V2))) ->
 mark(and(isNaturalKind(V1),isLNatKind(V2)))
[74] active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
[75] active(sel(N,XS)) ->
 mark(U171(and(and(isNatural(N),isNaturalKind(N)),
            and(isLNat(XS),isLNatKind(XS))),N,XS))
[76] active(snd(pair(X,Y))) ->
 mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
[77] active(splitAt(0,XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
[78] active(splitAt(s(N),cons(X,XS))) ->
 mark(U201(and(and(isNatural(N),isNaturalKind(N)),
            and(and(isNatural(X),isNaturalKind(X)),
             and(isLNat(XS),isLNatKind(XS)))),N,X,XS))
[79] active(tail(cons(N,XS))) ->
 mark(U211(and(and(isNatural(N),isNaturalKind(N)),
            and(isLNat(XS),isLNatKind(XS))),XS))
[80] active(take(N,XS)) ->
 mark(U221(and(and(isNatural(N),isNaturalKind(N)),
            and(isLNat(XS),isLNatKind(XS))),N,XS))
[81] active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
[82] active(U102(X1,X2)) -> U102(active(X1),X2)
[83] active(U103(X)) -> U103(active(X))
[84] active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
[85] active(snd(X)) -> snd(active(X))
[86] active(splitAt(X1,X2)) -> splitAt(active(X1),X2)
[87] active(splitAt(X1,X2)) -> splitAt(X1,active(X2))
[88] active(U111(X1,X2)) -> U111(active(X1),X2)
[89] active(U112(X)) -> U112(active(X))
[90] active(U121(X1,X2)) -> U121(active(X1),X2)
[91] active(U122(X)) -> U122(active(X))
[92] active(U131(X1,X2,X3)) -> U131(active(X1),X2,X3)
[93] active(U132(X1,X2)) -> U132(active(X1),X2)
[94] active(U133(X)) -> U133(active(X))
[95] active(U141(X1,X2,X3)) -> U141(active(X1),X2,X3)
[96] active(U142(X1,X2)) -> U142(active(X1),X2)
[97] active(U143(X)) -> U143(active(X))
[98] active(U151(X1,X2,X3)) -> U151(active(X1),X2,X3)
[99] active(U152(X1,X2)) -> U152(active(X1),X2)
[100] active(U153(X)) -> U153(active(X))
[101] active(U161(X1,X2)) -> U161(active(X1),X2)
[102] active(cons(X1,X2)) -> cons(active(X1),X2)
[103] active(natsFrom(X)) -> natsFrom(active(X))
[104] active(s(X)) -> s(active(X))
[105] active(U171(X1,X2,X3)) -> U171(active(X1),X2,X3)
[106] active(head(X)) -> head(active(X))
[107] active(afterNth(X1,X2)) -> afterNth(active(X1),X2)
[108] active(afterNth(X1,X2)) -> afterNth(X1,active(X2))
[109] active(U181(X1,X2)) -> U181(active(X1),X2)
[110] active(U191(X1,X2)) -> U191(active(X1),X2)
[111] active(pair(X1,X2)) -> pair(active(X1),X2)
[112] active(pair(X1,X2)) -> pair(X1,active(X2))
[113] active(U201(X1,X2,X3,X4)) -> U201(active(X1),X2,X3,X4)
[114] active(U202(X1,X2)) -> U202(active(X1),X2)
[115] active(U21(X1,X2)) -> U21(active(X1),X2)
[116] active(U211(X1,X2)) -> U211(active(X1),X2)
[117] active(U221(X1,X2,X3)) -> U221(active(X1),X2,X3)
[118] active(fst(X)) -> fst(active(X))
[119] active(U31(X1,X2)) -> U31(active(X1),X2)
[120] active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
[121] active(U42(X1,X2)) -> U42(active(X1),X2)
[122] active(U43(X)) -> U43(active(X))
[123] active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
[124] active(U52(X1,X2)) -> U52(active(X1),X2)
[125] active(U53(X)) -> U53(active(X))
[126] active(U61(X1,X2)) -> U61(active(X1),X2)
[127] active(U62(X)) -> U62(active(X))
[128] active(U71(X1,X2)) -> U71(active(X1),X2)
[129] active(U72(X)) -> U72(active(X))
[130] active(U81(X1,X2)) -> U81(active(X1),X2)
[131] active(U82(X)) -> U82(active(X))
[132] active(U91(X1,X2)) -> U91(active(X1),X2)
[133] active(U92(X)) -> U92(active(X))
[134] active(and(X1,X2)) -> and(active(X1),X2)
[135] active(tail(X)) -> tail(active(X))
[136] active(take(X1,X2)) -> take(active(X1),X2)
[137] active(take(X1,X2)) -> take(X1,active(X2))
[138] active(sel(X1,X2)) -> sel(active(X1),X2)
[139] active(sel(X1,X2)) -> sel(X1,active(X2))
[140] U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
[141] U102(mark(X1),X2) -> mark(U102(X1,X2))
[142] U103(mark(X)) -> mark(U103(X))
[143] U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
[144] snd(mark(X)) -> mark(snd(X))
[145] splitAt(mark(X1),X2) -> mark(splitAt(X1,X2))
[146] splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2))
[147] U111(mark(X1),X2) -> mark(U111(X1,X2))
[148] U112(mark(X)) -> mark(U112(X))
[149] U121(mark(X1),X2) -> mark(U121(X1,X2))
[150] U122(mark(X)) -> mark(U122(X))
[151] U131(mark(X1),X2,X3) -> mark(U131(X1,X2,X3))
[152] U132(mark(X1),X2) -> mark(U132(X1,X2))
[153] U133(mark(X)) -> mark(U133(X))
[154] U141(mark(X1),X2,X3) -> mark(U141(X1,X2,X3))
[155] U142(mark(X1),X2) -> mark(U142(X1,X2))
[156] U143(mark(X)) -> mark(U143(X))
[157] U151(mark(X1),X2,X3) -> mark(U151(X1,X2,X3))
[158] U152(mark(X1),X2) -> mark(U152(X1,X2))
[159] U153(mark(X)) -> mark(U153(X))
[160] U161(mark(X1),X2) -> mark(U161(X1,X2))
[161] cons(mark(X1),X2) -> mark(cons(X1,X2))
[162] natsFrom(mark(X)) -> mark(natsFrom(X))
[163] s(mark(X)) -> mark(s(X))
[164] U171(mark(X1),X2,X3) -> mark(U171(X1,X2,X3))
[165] head(mark(X)) -> mark(head(X))
[166] afterNth(mark(X1),X2) -> mark(afterNth(X1,X2))
[167] afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2))
[168] U181(mark(X1),X2) -> mark(U181(X1,X2))
[169] U191(mark(X1),X2) -> mark(U191(X1,X2))
[170] pair(mark(X1),X2) -> mark(pair(X1,X2))
[171] pair(X1,mark(X2)) -> mark(pair(X1,X2))
[172] U201(mark(X1),X2,X3,X4) -> mark(U201(X1,X2,X3,X4))
[173] U202(mark(X1),X2) -> mark(U202(X1,X2))
[174] U21(mark(X1),X2) -> mark(U21(X1,X2))
[175] U211(mark(X1),X2) -> mark(U211(X1,X2))
[176] U221(mark(X1),X2,X3) -> mark(U221(X1,X2,X3))
[177] fst(mark(X)) -> mark(fst(X))
[178] U31(mark(X1),X2) -> mark(U31(X1,X2))
[179] U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
[180] U42(mark(X1),X2) -> mark(U42(X1,X2))
[181] U43(mark(X)) -> mark(U43(X))
[182] U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
[183] U52(mark(X1),X2) -> mark(U52(X1,X2))
[184] U53(mark(X)) -> mark(U53(X))
[185] U61(mark(X1),X2) -> mark(U61(X1,X2))
[186] U62(mark(X)) -> mark(U62(X))
[187] U71(mark(X1),X2) -> mark(U71(X1,X2))
[188] U72(mark(X)) -> mark(U72(X))
[189] U81(mark(X1),X2) -> mark(U81(X1,X2))
[190] U82(mark(X)) -> mark(U82(X))
[191] U91(mark(X1),X2) -> mark(U91(X1,X2))
[192] U92(mark(X)) -> mark(U92(X))
[193] and(mark(X1),X2) -> mark(and(X1,X2))
[194] tail(mark(X)) -> mark(tail(X))
[195] take(mark(X1),X2) -> mark(take(X1,X2))
[196] take(X1,mark(X2)) -> mark(take(X1,X2))
[197] sel(mark(X1),X2) -> mark(sel(X1,X2))
[198] sel(X1,mark(X2)) -> mark(sel(X1,X2))
[199] proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
[200] proper(tt) -> ok(tt)
[201] proper(U102(X1,X2)) -> U102(proper(X1),proper(X2))
[202] proper(isNatural(X)) -> isNatural(proper(X))
[203] proper(U103(X)) -> U103(proper(X))
[204] proper(isLNat(X)) -> isLNat(proper(X))
[205] proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
[206] proper(snd(X)) -> snd(proper(X))
[207] proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2))
[208] proper(U111(X1,X2)) -> U111(proper(X1),proper(X2))
[209] proper(U112(X)) -> U112(proper(X))
[210] proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
[211] proper(U122(X)) -> U122(proper(X))
[212] proper(U131(X1,X2,X3)) -> U131(proper(X1),proper(X2),proper(X3))
[213] proper(U132(X1,X2)) -> U132(proper(X1),proper(X2))
[214] proper(U133(X)) -> U133(proper(X))
[215] proper(U141(X1,X2,X3)) -> U141(proper(X1),proper(X2),proper(X3))
[216] proper(U142(X1,X2)) -> U142(proper(X1),proper(X2))
[217] proper(U143(X)) -> U143(proper(X))
[218] proper(U151(X1,X2,X3)) -> U151(proper(X1),proper(X2),proper(X3))
[219] proper(U152(X1,X2)) -> U152(proper(X1),proper(X2))
[220] proper(U153(X)) -> U153(proper(X))
[221] proper(U161(X1,X2)) -> U161(proper(X1),proper(X2))
[222] proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
[223] proper(natsFrom(X)) -> natsFrom(proper(X))
[224] proper(s(X)) -> s(proper(X))
[225] proper(U171(X1,X2,X3)) -> U171(proper(X1),proper(X2),proper(X3))
[226] proper(head(X)) -> head(proper(X))
[227] proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2))
[228] proper(U181(X1,X2)) -> U181(proper(X1),proper(X2))
[229] proper(U191(X1,X2)) -> U191(proper(X1),proper(X2))
[230] proper(pair(X1,X2)) -> pair(proper(X1),proper(X2))
[231] proper(nil) -> ok(nil)
[232] proper(U201(X1,X2,X3,X4)) ->
 U201(proper(X1),proper(X2),proper(X3),proper(X4))
[233] proper(U202(X1,X2)) -> U202(proper(X1),proper(X2))
[234] proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
[235] proper(U211(X1,X2)) -> U211(proper(X1),proper(X2))
[236] proper(U221(X1,X2,X3)) -> U221(proper(X1),proper(X2),proper(X3))
[237] proper(fst(X)) -> fst(proper(X))
[238] proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
[239] proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
[240] proper(U42(X1,X2)) -> U42(proper(X1),proper(X2))
[241] proper(U43(X)) -> U43(proper(X))
[242] proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
[243] proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
[244] proper(U53(X)) -> U53(proper(X))
[245] proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
[246] proper(U62(X)) -> U62(proper(X))
[247] proper(isPLNat(X)) -> isPLNat(proper(X))
[248] proper(U71(X1,X2)) -> U71(proper(X1),proper(X2))
[249] proper(U72(X)) -> U72(proper(X))
[250] proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
[251] proper(U82(X)) -> U82(proper(X))
[252] proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
[253] proper(U92(X)) -> U92(proper(X))
[254] proper(and(X1,X2)) -> and(proper(X1),proper(X2))
[255] proper(isNaturalKind(X)) -> isNaturalKind(proper(X))
[256] proper(isLNatKind(X)) -> isLNatKind(proper(X))
[257] proper(isPLNatKind(X)) -> isPLNatKind(proper(X))
[258] proper(tail(X)) -> tail(proper(X))
[259] proper(take(X1,X2)) -> take(proper(X1),proper(X2))
[260] proper(0) -> ok(0)
[261] proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
[262] U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
[263] U102(ok(X1),ok(X2)) -> ok(U102(X1,X2))
[264] isNatural(ok(X)) -> ok(isNatural(X))
[265] U103(ok(X)) -> ok(U103(X))
[266] isLNat(ok(X)) -> ok(isLNat(X))
[267] U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
[268] snd(ok(X)) -> ok(snd(X))
[269] splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2))
[270] U111(ok(X1),ok(X2)) -> ok(U111(X1,X2))
[271] U112(ok(X)) -> ok(U112(X))
[272] U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
[273] U122(ok(X)) -> ok(U122(X))
[274] U131(ok(X1),ok(X2),ok(X3)) -> ok(U131(X1,X2,X3))
[275] U132(ok(X1),ok(X2)) -> ok(U132(X1,X2))
[276] U133(ok(X)) -> ok(U133(X))
[277] U141(ok(X1),ok(X2),ok(X3)) -> ok(U141(X1,X2,X3))
[278] U142(ok(X1),ok(X2)) -> ok(U142(X1,X2))
[279] U143(ok(X)) -> ok(U143(X))
[280] U151(ok(X1),ok(X2),ok(X3)) -> ok(U151(X1,X2,X3))
[281] U152(ok(X1),ok(X2)) -> ok(U152(X1,X2))
[282] U153(ok(X)) -> ok(U153(X))
[283] U161(ok(X1),ok(X2)) -> ok(U161(X1,X2))
[284] cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
[285] natsFrom(ok(X)) -> ok(natsFrom(X))
[286] s(ok(X)) -> ok(s(X))
[287] U171(ok(X1),ok(X2),ok(X3)) -> ok(U171(X1,X2,X3))
[288] head(ok(X)) -> ok(head(X))
[289] afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2))
[290] U181(ok(X1),ok(X2)) -> ok(U181(X1,X2))
[291] U191(ok(X1),ok(X2)) -> ok(U191(X1,X2))
[292] pair(ok(X1),ok(X2)) -> ok(pair(X1,X2))
[293] U201(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U201(X1,X2,X3,X4))
[294] U202(ok(X1),ok(X2)) -> ok(U202(X1,X2))
[295] U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
[296] U211(ok(X1),ok(X2)) -> ok(U211(X1,X2))
[297] U221(ok(X1),ok(X2),ok(X3)) -> ok(U221(X1,X2,X3))
[298] fst(ok(X)) -> ok(fst(X))
[299] U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
[300] U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
[301] U42(ok(X1),ok(X2)) -> ok(U42(X1,X2))
[302] U43(ok(X)) -> ok(U43(X))
[303] U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
[304] U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
[305] U53(ok(X)) -> ok(U53(X))
[306] U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
[307] U62(ok(X)) -> ok(U62(X))
[308] isPLNat(ok(X)) -> ok(isPLNat(X))
[309] U71(ok(X1),ok(X2)) -> ok(U71(X1,X2))
[310] U72(ok(X)) -> ok(U72(X))
[311] U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
[312] U82(ok(X)) -> ok(U82(X))
[313] U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
[314] U92(ok(X)) -> ok(U92(X))
[315] and(ok(X1),ok(X2)) -> ok(and(X1,X2))
[316] isNaturalKind(ok(X)) -> ok(isNaturalKind(X))
[317] isLNatKind(ok(X)) -> ok(isLNatKind(X))
[318] isPLNatKind(ok(X)) -> ok(isPLNatKind(X))
[319] tail(ok(X)) -> ok(tail(X))
[320] take(ok(X1),ok(X2)) -> ok(take(X1,X2))
[321] sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
[322] top(mark(X)) -> top(proper(X))
[323] top(ok(X)) -> top(active(X))


Sub problem: 
guided: 

DP termination of:
<Marked_active(U101(tt,V1,V2)) , Marked_U102(isNatural(V1),V2)>
<Marked_active(U101(tt,V1,V2)) , Marked_isNatural(V1)>
<Marked_active(U102(tt,V2)) , Marked_U103(isLNat(V2))>
<Marked_active(U102(tt,V2)) , Marked_isLNat(V2)>
<Marked_active(U11(tt,N,XS)) , Marked_snd(splitAt(N,XS))>
<Marked_active(U11(tt,N,XS)) , Marked_splitAt(N,XS)>
<Marked_active(U111(tt,V1)) , Marked_U112(isLNat(V1))>
<Marked_active(U111(tt,V1)) , Marked_isLNat(V1)>
<Marked_active(U121(tt,V1)) , Marked_U122(isNatural(V1))>
<Marked_active(U121(tt,V1)) , Marked_isNatural(V1)>
<Marked_active(U131(tt,V1,V2)) , Marked_U132(isNatural(V1),V2)>
<Marked_active(U131(tt,V1,V2)) , Marked_isNatural(V1)>
<Marked_active(U132(tt,V2)) , Marked_U133(isLNat(V2))>
<Marked_active(U132(tt,V2)) , Marked_isLNat(V2)>
<Marked_active(U141(tt,V1,V2)) , Marked_U142(isLNat(V1),V2)>
<Marked_active(U141(tt,V1,V2)) , Marked_isLNat(V1)>
<Marked_active(U142(tt,V2)) , Marked_U143(isLNat(V2))>
<Marked_active(U142(tt,V2)) , Marked_isLNat(V2)>
<Marked_active(U151(tt,V1,V2)) , Marked_U152(isNatural(V1),V2)>
<Marked_active(U151(tt,V1,V2)) , Marked_isNatural(V1)>
<Marked_active(U152(tt,V2)) , Marked_U153(isLNat(V2))>
<Marked_active(U152(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_head(afterNth(N,XS))>
<Marked_active(U171(tt,N,XS)) , Marked_afterNth(N,XS)>
<Marked_active(U191(tt,XS)) , Marked_pair(nil,XS)>
<Marked_active(U201(tt,N,X,XS)) , Marked_U202(splitAt(N,XS),X)>
<Marked_active(U201(tt,N,X,XS)) , Marked_splitAt(N,XS)>
<Marked_active(U202(pair(YS,ZS),X)) , Marked_pair(cons(X,YS),ZS)>
<Marked_active(U202(pair(YS,ZS),X)) , Marked_cons(X,YS)>
<Marked_active(U221(tt,N,XS)) , Marked_fst(splitAt(N,XS))>
<Marked_active(U221(tt,N,XS)) , Marked_splitAt(N,XS)>
<Marked_active(U41(tt,V1,V2)) , Marked_U42(isNatural(V1),V2)>
<Marked_active(U41(tt,V1,V2)) , Marked_isNatural(V1)>
<Marked_active(U42(tt,V2)) , Marked_U43(isLNat(V2))>
<Marked_active(U42(tt,V2)) , Marked_isLNat(V2)>
<Marked_active(U51(tt,V1,V2)) , Marked_U52(isNatural(V1),V2)>
<Marked_active(U51(tt,V1,V2)) , Marked_isNatural(V1)>
<Marked_active(U52(tt,V2)) , Marked_U53(isLNat(V2))>
<Marked_active(U52(tt,V2)) , Marked_isLNat(V2)>
<Marked_active(U61(tt,V1)) , Marked_U62(isPLNat(V1))>
<Marked_active(U61(tt,V1)) , Marked_isPLNat(V1)>
<Marked_active(U71(tt,V1)) , Marked_U72(isNatural(V1))>
<Marked_active(U71(tt,V1)) , Marked_isNatural(V1)>
<Marked_active(U81(tt,V1)) , Marked_U82(isPLNat(V1))>
<Marked_active(U81(tt,V1)) , Marked_isPLNat(V1)>
<Marked_active(U91(tt,V1)) , Marked_U92(isLNat(V1))>
<Marked_active(U91(tt,V1)) , Marked_isLNat(V1)>
<Marked_active(afterNth(N,XS)) , Marked_U11(and(and(isNatural(N),
                                                 isNaturalKind(N)),
                                             and(isLNat(XS),isLNatKind(XS))),
                                  N,XS)>
<Marked_active(afterNth(N,XS)) , Marked_and(and(isNatural(N),isNaturalKind(N)),
                                  and(isLNat(XS),isLNatKind(XS)))>
<Marked_active(afterNth(N,XS)) , Marked_and(isNatural(N),isNaturalKind(N))>
<Marked_active(afterNth(N,XS)) , Marked_isNatural(N)>
<Marked_active(afterNth(N,XS)) , Marked_isNaturalKind(N)>
<Marked_active(afterNth(N,XS)) , Marked_and(isLNat(XS),isLNatKind(XS))>
<Marked_active(afterNth(N,XS)) , Marked_isLNat(XS)>
<Marked_active(afterNth(N,XS)) , Marked_isLNatKind(XS)>
<Marked_active(fst(pair(X,Y))) , Marked_U21(and(and(isLNat(X),isLNatKind(X)),
                                             and(isLNat(Y),isLNatKind(Y))),
                                  X)>
<Marked_active(fst(pair(X,Y))) , Marked_and(and(isLNat(X),isLNatKind(X)),
                                  and(isLNat(Y),isLNatKind(Y)))>
<Marked_active(fst(pair(X,Y))) , Marked_and(isLNat(X),isLNatKind(X))>
<Marked_active(fst(pair(X,Y))) , Marked_isLNat(X)>
<Marked_active(fst(pair(X,Y))) , Marked_isLNatKind(X)>
<Marked_active(fst(pair(X,Y))) , Marked_and(isLNat(Y),isLNatKind(Y))>
<Marked_active(fst(pair(X,Y))) , Marked_isLNat(Y)>
<Marked_active(fst(pair(X,Y))) , Marked_isLNatKind(Y)>
<Marked_active(head(cons(N,XS))) , Marked_U31(and(and(isNatural(N),
                                                   isNaturalKind(N)),
                                               and(isLNat(XS),isLNatKind(XS))),
                                    N)>
<Marked_active(head(cons(N,XS))) , Marked_and(and(isNatural(N),
                                               isNaturalKind(N)),
                                    and(isLNat(XS),isLNatKind(XS)))>
<Marked_active(head(cons(N,XS))) , Marked_and(isNatural(N),isNaturalKind(N))>
<Marked_active(head(cons(N,XS))) , Marked_isNatural(N)>
<Marked_active(head(cons(N,XS))) , Marked_isNaturalKind(N)>
<Marked_active(head(cons(N,XS))) , Marked_and(isLNat(XS),isLNatKind(XS))>
<Marked_active(head(cons(N,XS))) , Marked_isLNat(XS)>
<Marked_active(head(cons(N,XS))) , Marked_isLNatKind(XS)>
<Marked_active(isLNat(afterNth(V1,V2))) , Marked_U41(and(isNaturalKind(V1),
                                                      isLNatKind(V2)),
                                           V1,V2)>
<Marked_active(isLNat(afterNth(V1,V2))) , Marked_and(isNaturalKind(V1),
                                           isLNatKind(V2))>
<Marked_active(isLNat(afterNth(V1,V2))) , Marked_isNaturalKind(V1)>
<Marked_active(isLNat(afterNth(V1,V2))) , Marked_isLNatKind(V2)>
<Marked_active(isLNat(cons(V1,V2))) , Marked_U51(and(isNaturalKind(V1),
                                                  isLNatKind(V2)),V1,
                                       V2)>
<Marked_active(isLNat(cons(V1,V2))) , Marked_and(isNaturalKind(V1),
                                       isLNatKind(V2))>
<Marked_active(isLNat(cons(V1,V2))) , Marked_isNaturalKind(V1)>
<Marked_active(isLNat(cons(V1,V2))) , Marked_isLNatKind(V2)>
<Marked_active(isLNat(fst(V1))) , Marked_U61(isPLNatKind(V1),V1)>
<Marked_active(isLNat(fst(V1))) , Marked_isPLNatKind(V1)>
<Marked_active(isLNat(natsFrom(V1))) , Marked_U71(isNaturalKind(V1),V1)>
<Marked_active(isLNat(natsFrom(V1))) , Marked_isNaturalKind(V1)>
<Marked_active(isLNat(snd(V1))) , Marked_U81(isPLNatKind(V1),V1)>
<Marked_active(isLNat(snd(V1))) , Marked_isPLNatKind(V1)>
<Marked_active(isLNat(tail(V1))) , Marked_U91(isLNatKind(V1),V1)>
<Marked_active(isLNat(tail(V1))) , Marked_isLNatKind(V1)>
<Marked_active(isLNat(take(V1,V2))) , Marked_U101(and(isNaturalKind(V1),
                                                   isLNatKind(V2)),V1,
                                       V2)>
<Marked_active(isLNat(take(V1,V2))) , Marked_and(isNaturalKind(V1),
                                       isLNatKind(V2))>
<Marked_active(isLNat(take(V1,V2))) , Marked_isNaturalKind(V1)>
<Marked_active(isLNat(take(V1,V2))) , Marked_isLNatKind(V2)>
<Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_and(isNaturalKind(V1),
                                               isLNatKind(V2))>
<Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_isNaturalKind(V1)>
<Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_isLNatKind(V2)>
<Marked_active(isLNatKind(cons(V1,V2))) , Marked_and(isNaturalKind(V1),
                                           isLNatKind(V2))>
<Marked_active(isLNatKind(cons(V1,V2))) , Marked_isNaturalKind(V1)>
<Marked_active(isLNatKind(cons(V1,V2))) , Marked_isLNatKind(V2)>
<Marked_active(isLNatKind(fst(V1))) , Marked_isPLNatKind(V1)>
<Marked_active(isLNatKind(natsFrom(V1))) , Marked_isNaturalKind(V1)>
<Marked_active(isLNatKind(snd(V1))) , Marked_isPLNatKind(V1)>
<Marked_active(isLNatKind(tail(V1))) , Marked_isLNatKind(V1)>
<Marked_active(isLNatKind(take(V1,V2))) , Marked_and(isNaturalKind(V1),
                                           isLNatKind(V2))>
<Marked_active(isLNatKind(take(V1,V2))) , Marked_isNaturalKind(V1)>
<Marked_active(isLNatKind(take(V1,V2))) , Marked_isLNatKind(V2)>
<Marked_active(isNatural(head(V1))) , Marked_U111(isLNatKind(V1),V1)>
<Marked_active(isNatural(head(V1))) , Marked_isLNatKind(V1)>
<Marked_active(isNatural(s(V1))) , Marked_U121(isNaturalKind(V1),V1)>
<Marked_active(isNatural(s(V1))) , Marked_isNaturalKind(V1)>
<Marked_active(isNatural(sel(V1,V2))) , Marked_U131(and(isNaturalKind(V1),
                                                     isLNatKind(V2)),
                                         V1,V2)>
<Marked_active(isNatural(sel(V1,V2))) , Marked_and(isNaturalKind(V1),
                                         isLNatKind(V2))>
<Marked_active(isNatural(sel(V1,V2))) , Marked_isNaturalKind(V1)>
<Marked_active(isNatural(sel(V1,V2))) , Marked_isLNatKind(V2)>
<Marked_active(isNaturalKind(head(V1))) , Marked_isLNatKind(V1)>
<Marked_active(isNaturalKind(s(V1))) , Marked_isNaturalKind(V1)>
<Marked_active(isNaturalKind(sel(V1,V2))) , Marked_and(isNaturalKind(V1),
                                             isLNatKind(V2))>
<Marked_active(isNaturalKind(sel(V1,V2))) , Marked_isNaturalKind(V1)>
<Marked_active(isNaturalKind(sel(V1,V2))) , Marked_isLNatKind(V2)>
<Marked_active(isPLNat(pair(V1,V2))) , Marked_U141(and(isLNatKind(V1),
                                                    isLNatKind(V2)),V1,
                                        V2)>
<Marked_active(isPLNat(pair(V1,V2))) , Marked_and(isLNatKind(V1),
                                        isLNatKind(V2))>
<Marked_active(isPLNat(pair(V1,V2))) , Marked_isLNatKind(V1)>
<Marked_active(isPLNat(pair(V1,V2))) , Marked_isLNatKind(V2)>
<Marked_active(isPLNat(splitAt(V1,V2))) , Marked_U151(and(isNaturalKind(V1),
                                                       isLNatKind(V2)),
                                           V1,V2)>
<Marked_active(isPLNat(splitAt(V1,V2))) , Marked_and(isNaturalKind(V1),
                                           isLNatKind(V2))>
<Marked_active(isPLNat(splitAt(V1,V2))) , Marked_isNaturalKind(V1)>
<Marked_active(isPLNat(splitAt(V1,V2))) , Marked_isLNatKind(V2)>
<Marked_active(isPLNatKind(pair(V1,V2))) , Marked_and(isLNatKind(V1),
                                            isLNatKind(V2))>
<Marked_active(isPLNatKind(pair(V1,V2))) , Marked_isLNatKind(V1)>
<Marked_active(isPLNatKind(pair(V1,V2))) , Marked_isLNatKind(V2)>
<Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_and(isNaturalKind(V1),
                                               isLNatKind(V2))>
<Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_isNaturalKind(V1)>
<Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_isLNatKind(V2)>
<Marked_active(natsFrom(N)) , Marked_U161(and(isNatural(N),isNaturalKind(N)),N)>
<Marked_active(natsFrom(N)) , Marked_and(isNatural(N),isNaturalKind(N))>
<Marked_active(natsFrom(N)) , Marked_isNatural(N)>
<Marked_active(natsFrom(N)) , Marked_isNaturalKind(N)>
<Marked_active(sel(N,XS)) , Marked_U171(and(and(isNatural(N),isNaturalKind(N)),
                                         and(isLNat(XS),isLNatKind(XS))),
                             N,XS)>
<Marked_active(sel(N,XS)) , Marked_and(and(isNatural(N),isNaturalKind(N)),
                             and(isLNat(XS),isLNatKind(XS)))>
<Marked_active(sel(N,XS)) , Marked_and(isNatural(N),isNaturalKind(N))>
<Marked_active(sel(N,XS)) , Marked_isNatural(N)>
<Marked_active(sel(N,XS)) , Marked_isNaturalKind(N)>
<Marked_active(sel(N,XS)) , Marked_and(isLNat(XS),isLNatKind(XS))>
<Marked_active(sel(N,XS)) , Marked_isLNat(XS)>
<Marked_active(sel(N,XS)) , Marked_isLNatKind(XS)>
<Marked_active(snd(pair(X,Y))) , Marked_U181(and(and(isLNat(X),isLNatKind(X)),
                                              and(isLNat(Y),isLNatKind(Y))),
                                  Y)>
<Marked_active(snd(pair(X,Y))) , Marked_and(and(isLNat(X),isLNatKind(X)),
                                  and(isLNat(Y),isLNatKind(Y)))>
<Marked_active(snd(pair(X,Y))) , Marked_and(isLNat(X),isLNatKind(X))>
<Marked_active(snd(pair(X,Y))) , Marked_isLNat(X)>
<Marked_active(snd(pair(X,Y))) , Marked_isLNatKind(X)>
<Marked_active(snd(pair(X,Y))) , Marked_and(isLNat(Y),isLNatKind(Y))>
<Marked_active(snd(pair(X,Y))) , Marked_isLNat(Y)>
<Marked_active(snd(pair(X,Y))) , Marked_isLNatKind(Y)>
<Marked_active(splitAt(0,XS)) , Marked_U191(and(isLNat(XS),isLNatKind(XS)),XS)>
<Marked_active(splitAt(0,XS)) , Marked_and(isLNat(XS),isLNatKind(XS))>
<Marked_active(splitAt(0,XS)) , Marked_isLNat(XS)>
<Marked_active(splitAt(0,XS)) , Marked_isLNatKind(XS)>
<Marked_active(splitAt(s(N),cons(X,XS))) , Marked_U201(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(and(isNatural(X),
                                                             isNaturalKind(X)),
                                                         and(isLNat(XS),
                                                          isLNatKind(XS)))),
                                            N,X,XS)>
<Marked_active(splitAt(s(N),cons(X,XS))) , Marked_and(and(isNatural(N),
                                                       isNaturalKind(N)),
                                            and(and(isNatural(X),
                                                 isNaturalKind(X)),
                                             and(isLNat(XS),isLNatKind(XS))))>
<Marked_active(splitAt(s(N),cons(X,XS))) , Marked_and(isNatural(N),
                                            isNaturalKind(N))>
<Marked_active(splitAt(s(N),cons(X,XS))) , Marked_isNatural(N)>
<Marked_active(splitAt(s(N),cons(X,XS))) , Marked_isNaturalKind(N)>
<Marked_active(splitAt(s(N),cons(X,XS))) , Marked_and(and(isNatural(X),
                                                       isNaturalKind(X)),
                                            and(isLNat(XS),isLNatKind(XS)))>
<Marked_active(splitAt(s(N),cons(X,XS))) , Marked_and(isNatural(X),
                                            isNaturalKind(X))>
<Marked_active(splitAt(s(N),cons(X,XS))) , Marked_isNatural(X)>
<Marked_active(splitAt(s(N),cons(X,XS))) , Marked_isNaturalKind(X)>
<Marked_active(splitAt(s(N),cons(X,XS))) , Marked_and(isLNat(XS),
                                            isLNatKind(XS))>
<Marked_active(splitAt(s(N),cons(X,XS))) , Marked_isLNat(XS)>
<Marked_active(splitAt(s(N),cons(X,XS))) , Marked_isLNatKind(XS)>
<Marked_active(tail(cons(N,XS))) , Marked_U211(and(and(isNatural(N),
                                                    isNaturalKind(N)),
                                                and(isLNat(XS),isLNatKind(XS))),
                                    XS)>
<Marked_active(tail(cons(N,XS))) , Marked_and(and(isNatural(N),
                                               isNaturalKind(N)),
                                    and(isLNat(XS),isLNatKind(XS)))>
<Marked_active(tail(cons(N,XS))) , Marked_and(isNatural(N),isNaturalKind(N))>
<Marked_active(tail(cons(N,XS))) , Marked_isNatural(N)>
<Marked_active(tail(cons(N,XS))) , Marked_isNaturalKind(N)>
<Marked_active(tail(cons(N,XS))) , Marked_and(isLNat(XS),isLNatKind(XS))>
<Marked_active(tail(cons(N,XS))) , Marked_isLNat(XS)>
<Marked_active(tail(cons(N,XS))) , Marked_isLNatKind(XS)>
<Marked_active(take(N,XS)) , Marked_U221(and(and(isNatural(N),isNaturalKind(N)),
                                          and(isLNat(XS),isLNatKind(XS))),
                              N,XS)>
<Marked_active(take(N,XS)) , Marked_and(and(isNatural(N),isNaturalKind(N)),
                              and(isLNat(XS),isLNatKind(XS)))>
<Marked_active(take(N,XS)) , Marked_and(isNatural(N),isNaturalKind(N))>
<Marked_active(take(N,XS)) , Marked_isNatural(N)>
<Marked_active(take(N,XS)) , Marked_isNaturalKind(N)>
<Marked_active(take(N,XS)) , Marked_and(isLNat(XS),isLNatKind(XS))>
<Marked_active(take(N,XS)) , Marked_isLNat(XS)>
<Marked_active(take(N,XS)) , Marked_isLNatKind(XS)>
<Marked_active(U101(X1,X2,X3)) , Marked_U101(active(X1),X2,X3)>
<Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
<Marked_active(U102(X1,X2)) , Marked_U102(active(X1),X2)>
<Marked_active(U102(X1,X2)) , Marked_active(X1)>
<Marked_active(U103(X)) , Marked_U103(active(X))>
<Marked_active(U103(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(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(U111(X1,X2)) , Marked_U111(active(X1),X2)>
<Marked_active(U111(X1,X2)) , Marked_active(X1)>
<Marked_active(U112(X)) , Marked_U112(active(X))>
<Marked_active(U112(X)) , Marked_active(X)>
<Marked_active(U121(X1,X2)) , Marked_U121(active(X1),X2)>
<Marked_active(U121(X1,X2)) , Marked_active(X1)>
<Marked_active(U122(X)) , Marked_U122(active(X))>
<Marked_active(U122(X)) , Marked_active(X)>
<Marked_active(U131(X1,X2,X3)) , Marked_U131(active(X1),X2,X3)>
<Marked_active(U131(X1,X2,X3)) , Marked_active(X1)>
<Marked_active(U132(X1,X2)) , Marked_U132(active(X1),X2)>
<Marked_active(U132(X1,X2)) , Marked_active(X1)>
<Marked_active(U133(X)) , Marked_U133(active(X))>
<Marked_active(U133(X)) , Marked_active(X)>
<Marked_active(U141(X1,X2,X3)) , Marked_U141(active(X1),X2,X3)>
<Marked_active(U141(X1,X2,X3)) , Marked_active(X1)>
<Marked_active(U142(X1,X2)) , Marked_U142(active(X1),X2)>
<Marked_active(U142(X1,X2)) , Marked_active(X1)>
<Marked_active(U143(X)) , Marked_U143(active(X))>
<Marked_active(U143(X)) , Marked_active(X)>
<Marked_active(U151(X1,X2,X3)) , Marked_U151(active(X1),X2,X3)>
<Marked_active(U151(X1,X2,X3)) , Marked_active(X1)>
<Marked_active(U152(X1,X2)) , Marked_U152(active(X1),X2)>
<Marked_active(U152(X1,X2)) , Marked_active(X1)>
<Marked_active(U153(X)) , Marked_U153(active(X))>
<Marked_active(U153(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(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(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)) , Marked_U202(active(X1),X2)>
<Marked_active(U202(X1,X2)) , Marked_active(X1)>
<Marked_active(U21(X1,X2)) , Marked_U21(active(X1),X2)>
<Marked_active(U21(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(U221(X1,X2,X3)) , Marked_U221(active(X1),X2,X3)>
<Marked_active(U221(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)) , Marked_U31(active(X1),X2)>
<Marked_active(U31(X1,X2)) , Marked_active(X1)>
<Marked_active(U41(X1,X2,X3)) , Marked_U41(active(X1),X2,X3)>
<Marked_active(U41(X1,X2,X3)) , Marked_active(X1)>
<Marked_active(U42(X1,X2)) , Marked_U42(active(X1),X2)>
<Marked_active(U42(X1,X2)) , Marked_active(X1)>
<Marked_active(U43(X)) , Marked_U43(active(X))>
<Marked_active(U43(X)) , Marked_active(X)>
<Marked_active(U51(X1,X2,X3)) , Marked_U51(active(X1),X2,X3)>
<Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
<Marked_active(U52(X1,X2)) , Marked_U52(active(X1),X2)>
<Marked_active(U52(X1,X2)) , Marked_active(X1)>
<Marked_active(U53(X)) , Marked_U53(active(X))>
<Marked_active(U53(X)) , Marked_active(X)>
<Marked_active(U61(X1,X2)) , Marked_U61(active(X1),X2)>
<Marked_active(U61(X1,X2)) , Marked_active(X1)>
<Marked_active(U62(X)) , Marked_U62(active(X))>
<Marked_active(U62(X)) , Marked_active(X)>
<Marked_active(U71(X1,X2)) , Marked_U71(active(X1),X2)>
<Marked_active(U71(X1,X2)) , Marked_active(X1)>
<Marked_active(U72(X)) , Marked_U72(active(X))>
<Marked_active(U72(X)) , Marked_active(X)>
<Marked_active(U81(X1,X2)) , Marked_U81(active(X1),X2)>
<Marked_active(U81(X1,X2)) , Marked_active(X1)>
<Marked_active(U82(X)) , Marked_U82(active(X))>
<Marked_active(U82(X)) , Marked_active(X)>
<Marked_active(U91(X1,X2)) , Marked_U91(active(X1),X2)>
<Marked_active(U91(X1,X2)) , Marked_active(X1)>
<Marked_active(U92(X)) , Marked_U92(active(X))>
<Marked_active(U92(X)) , Marked_active(X)>
<Marked_active(and(X1,X2)) , Marked_and(active(X1),X2)>
<Marked_active(and(X1,X2)) , Marked_active(X1)>
<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,X3) , Marked_U101(X1,X2,X3)>
<Marked_U102(mark(X1),X2) , Marked_U102(X1,X2)>
<Marked_U103(mark(X)) , Marked_U103(X)>
<Marked_U11(mark(X1),X2,X3) , Marked_U11(X1,X2,X3)>
<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_U111(mark(X1),X2) , Marked_U111(X1,X2)>
<Marked_U112(mark(X)) , Marked_U112(X)>
<Marked_U121(mark(X1),X2) , Marked_U121(X1,X2)>
<Marked_U122(mark(X)) , Marked_U122(X)>
<Marked_U131(mark(X1),X2,X3) , Marked_U131(X1,X2,X3)>
<Marked_U132(mark(X1),X2) , Marked_U132(X1,X2)>
<Marked_U133(mark(X)) , Marked_U133(X)>
<Marked_U141(mark(X1),X2,X3) , Marked_U141(X1,X2,X3)>
<Marked_U142(mark(X1),X2) , Marked_U142(X1,X2)>
<Marked_U143(mark(X)) , Marked_U143(X)>
<Marked_U151(mark(X1),X2,X3) , Marked_U151(X1,X2,X3)>
<Marked_U152(mark(X1),X2) , Marked_U152(X1,X2)>
<Marked_U153(mark(X)) , Marked_U153(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_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_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) , Marked_U202(X1,X2)>
<Marked_U21(mark(X1),X2) , Marked_U21(X1,X2)>
<Marked_U211(mark(X1),X2) , Marked_U211(X1,X2)>
<Marked_U221(mark(X1),X2,X3) , Marked_U221(X1,X2,X3)>
<Marked_fst(mark(X)) , Marked_fst(X)>
<Marked_U31(mark(X1),X2) , Marked_U31(X1,X2)>
<Marked_U41(mark(X1),X2,X3) , Marked_U41(X1,X2,X3)>
<Marked_U42(mark(X1),X2) , Marked_U42(X1,X2)>
<Marked_U43(mark(X)) , Marked_U43(X)>
<Marked_U51(mark(X1),X2,X3) , Marked_U51(X1,X2,X3)>
<Marked_U52(mark(X1),X2) , Marked_U52(X1,X2)>
<Marked_U53(mark(X)) , Marked_U53(X)>
<Marked_U61(mark(X1),X2) , Marked_U61(X1,X2)>
<Marked_U62(mark(X)) , Marked_U62(X)>
<Marked_U71(mark(X1),X2) , Marked_U71(X1,X2)>
<Marked_U72(mark(X)) , Marked_U72(X)>
<Marked_U81(mark(X1),X2) , Marked_U81(X1,X2)>
<Marked_U82(mark(X)) , Marked_U82(X)>
<Marked_U91(mark(X1),X2) , Marked_U91(X1,X2)>
<Marked_U92(mark(X)) , Marked_U92(X)>
<Marked_and(mark(X1),X2) , Marked_and(X1,X2)>
<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,X3)) , Marked_U101(proper(X1),proper(X2),proper(X3))>
<Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
<Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
<Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
<Marked_proper(U102(X1,X2)) , Marked_U102(proper(X1),proper(X2))>
<Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
<Marked_proper(isNatural(X)) , Marked_isNatural(proper(X))>
<Marked_proper(isNatural(X)) , Marked_proper(X)>
<Marked_proper(U103(X)) , Marked_U103(proper(X))>
<Marked_proper(U103(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(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(U111(X1,X2)) , Marked_U111(proper(X1),proper(X2))>
<Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U112(X)) , Marked_U112(proper(X))>
<Marked_proper(U112(X)) , Marked_proper(X)>
<Marked_proper(U121(X1,X2)) , Marked_U121(proper(X1),proper(X2))>
<Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U122(X)) , Marked_U122(proper(X))>
<Marked_proper(U122(X)) , Marked_proper(X)>
<Marked_proper(U131(X1,X2,X3)) , Marked_U131(proper(X1),proper(X2),proper(X3))>
<Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
<Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
<Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
<Marked_proper(U132(X1,X2)) , Marked_U132(proper(X1),proper(X2))>
<Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U133(X)) , Marked_U133(proper(X))>
<Marked_proper(U133(X)) , Marked_proper(X)>
<Marked_proper(U141(X1,X2,X3)) , Marked_U141(proper(X1),proper(X2),proper(X3))>
<Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
<Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
<Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
<Marked_proper(U142(X1,X2)) , Marked_U142(proper(X1),proper(X2))>
<Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U143(X)) , Marked_U143(proper(X))>
<Marked_proper(U143(X)) , Marked_proper(X)>
<Marked_proper(U151(X1,X2,X3)) , Marked_U151(proper(X1),proper(X2),proper(X3))>
<Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
<Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
<Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
<Marked_proper(U152(X1,X2)) , Marked_U152(proper(X1),proper(X2))>
<Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U153(X)) , Marked_U153(proper(X))>
<Marked_proper(U153(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(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(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)) , Marked_U202(proper(X1),proper(X2))>
<Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U21(X1,X2)) , Marked_U21(proper(X1),proper(X2))>
<Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U21(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(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(fst(X)) , Marked_fst(proper(X))>
<Marked_proper(fst(X)) , Marked_proper(X)>
<Marked_proper(U31(X1,X2)) , Marked_U31(proper(X1),proper(X2))>
<Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U41(X1,X2,X3)) , Marked_U41(proper(X1),proper(X2),proper(X3))>
<Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
<Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
<Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
<Marked_proper(U42(X1,X2)) , Marked_U42(proper(X1),proper(X2))>
<Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U43(X)) , Marked_U43(proper(X))>
<Marked_proper(U43(X)) , Marked_proper(X)>
<Marked_proper(U51(X1,X2,X3)) , Marked_U51(proper(X1),proper(X2),proper(X3))>
<Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
<Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
<Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
<Marked_proper(U52(X1,X2)) , Marked_U52(proper(X1),proper(X2))>
<Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U53(X)) , Marked_U53(proper(X))>
<Marked_proper(U53(X)) , Marked_proper(X)>
<Marked_proper(U61(X1,X2)) , Marked_U61(proper(X1),proper(X2))>
<Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U62(X)) , Marked_U62(proper(X))>
<Marked_proper(U62(X)) , Marked_proper(X)>
<Marked_proper(isPLNat(X)) , Marked_isPLNat(proper(X))>
<Marked_proper(isPLNat(X)) , Marked_proper(X)>
<Marked_proper(U71(X1,X2)) , Marked_U71(proper(X1),proper(X2))>
<Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U72(X)) , Marked_U72(proper(X))>
<Marked_proper(U72(X)) , Marked_proper(X)>
<Marked_proper(U81(X1,X2)) , Marked_U81(proper(X1),proper(X2))>
<Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U82(X)) , Marked_U82(proper(X))>
<Marked_proper(U82(X)) , Marked_proper(X)>
<Marked_proper(U91(X1,X2)) , Marked_U91(proper(X1),proper(X2))>
<Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U92(X)) , Marked_U92(proper(X))>
<Marked_proper(U92(X)) , Marked_proper(X)>
<Marked_proper(and(X1,X2)) , Marked_and(proper(X1),proper(X2))>
<Marked_proper(and(X1,X2)) , Marked_proper(X1)>
<Marked_proper(and(X1,X2)) , Marked_proper(X2)>
<Marked_proper(isNaturalKind(X)) , Marked_isNaturalKind(proper(X))>
<Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
<Marked_proper(isLNatKind(X)) , Marked_isLNatKind(proper(X))>
<Marked_proper(isLNatKind(X)) , Marked_proper(X)>
<Marked_proper(isPLNatKind(X)) , Marked_isPLNatKind(proper(X))>
<Marked_proper(isPLNatKind(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),ok(X3)) , Marked_U101(X1,X2,X3)>
<Marked_U102(ok(X1),ok(X2)) , Marked_U102(X1,X2)>
<Marked_isNatural(ok(X)) , Marked_isNatural(X)>
<Marked_U103(ok(X)) , Marked_U103(X)>
<Marked_isLNat(ok(X)) , Marked_isLNat(X)>
<Marked_U11(ok(X1),ok(X2),ok(X3)) , Marked_U11(X1,X2,X3)>
<Marked_snd(ok(X)) , Marked_snd(X)>
<Marked_splitAt(ok(X1),ok(X2)) , Marked_splitAt(X1,X2)>
<Marked_U111(ok(X1),ok(X2)) , Marked_U111(X1,X2)>
<Marked_U112(ok(X)) , Marked_U112(X)>
<Marked_U121(ok(X1),ok(X2)) , Marked_U121(X1,X2)>
<Marked_U122(ok(X)) , Marked_U122(X)>
<Marked_U131(ok(X1),ok(X2),ok(X3)) , Marked_U131(X1,X2,X3)>
<Marked_U132(ok(X1),ok(X2)) , Marked_U132(X1,X2)>
<Marked_U133(ok(X)) , Marked_U133(X)>
<Marked_U141(ok(X1),ok(X2),ok(X3)) , Marked_U141(X1,X2,X3)>
<Marked_U142(ok(X1),ok(X2)) , Marked_U142(X1,X2)>
<Marked_U143(ok(X)) , Marked_U143(X)>
<Marked_U151(ok(X1),ok(X2),ok(X3)) , Marked_U151(X1,X2,X3)>
<Marked_U152(ok(X1),ok(X2)) , Marked_U152(X1,X2)>
<Marked_U153(ok(X)) , Marked_U153(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_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_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)) , Marked_U202(X1,X2)>
<Marked_U21(ok(X1),ok(X2)) , Marked_U21(X1,X2)>
<Marked_U211(ok(X1),ok(X2)) , Marked_U211(X1,X2)>
<Marked_U221(ok(X1),ok(X2),ok(X3)) , Marked_U221(X1,X2,X3)>
<Marked_fst(ok(X)) , Marked_fst(X)>
<Marked_U31(ok(X1),ok(X2)) , Marked_U31(X1,X2)>
<Marked_U41(ok(X1),ok(X2),ok(X3)) , Marked_U41(X1,X2,X3)>
<Marked_U42(ok(X1),ok(X2)) , Marked_U42(X1,X2)>
<Marked_U43(ok(X)) , Marked_U43(X)>
<Marked_U51(ok(X1),ok(X2),ok(X3)) , Marked_U51(X1,X2,X3)>
<Marked_U52(ok(X1),ok(X2)) , Marked_U52(X1,X2)>
<Marked_U53(ok(X)) , Marked_U53(X)>
<Marked_U61(ok(X1),ok(X2)) , Marked_U61(X1,X2)>
<Marked_U62(ok(X)) , Marked_U62(X)>
<Marked_isPLNat(ok(X)) , Marked_isPLNat(X)>
<Marked_U71(ok(X1),ok(X2)) , Marked_U71(X1,X2)>
<Marked_U72(ok(X)) , Marked_U72(X)>
<Marked_U81(ok(X1),ok(X2)) , Marked_U81(X1,X2)>
<Marked_U82(ok(X)) , Marked_U82(X)>
<Marked_U91(ok(X1),ok(X2)) , Marked_U91(X1,X2)>
<Marked_U92(ok(X)) , Marked_U92(X)>
<Marked_and(ok(X1),ok(X2)) , Marked_and(X1,X2)>
<Marked_isNaturalKind(ok(X)) , Marked_isNaturalKind(X)>
<Marked_isLNatKind(ok(X)) , Marked_isLNatKind(X)>
<Marked_isPLNatKind(ok(X)) , Marked_isPLNatKind(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 63 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <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(U62(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(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(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <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(U62(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(X)) , Marked_proper(X)>
  <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(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <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(U62(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(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(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <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(U62(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(X)) , Marked_proper(X)>
  <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(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isPLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isLNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNaturalKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U92(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U82(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U72(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U62(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <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(U62(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(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(X3)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <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(U62(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(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(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <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(U62(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(X)) , Marked_proper(X)>
  <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(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <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(U62(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(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(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <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(U62(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(X)) , Marked_proper(X)>
  <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(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U211(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U202(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <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(U62(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(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(X4)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <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(U62(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(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(X3)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <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(U62(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(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(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <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(U62(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(X)) , Marked_proper(X)>
  <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(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <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(U62(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(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(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <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(U62(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(X)) , Marked_proper(X)>
  <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(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <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(U62(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(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(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <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(U62(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(X)) , Marked_proper(X)>
  <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(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U191(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <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(U62(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(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(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <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(U62(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(X)) , Marked_proper(X)>
  <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(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U181(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <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(U62(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(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(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <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(U62(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(X)) , Marked_proper(X)>
  <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(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <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(U62(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(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(X3)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <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(U62(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(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(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <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(U62(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(X)) , Marked_proper(X)>
  <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(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <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(U62(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(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(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <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(U62(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(X)) , Marked_proper(X)>
  <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(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <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(U62(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(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(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , 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(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <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(U62(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , 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(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(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(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , 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(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(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(U153(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <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(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(U103(X)) , Marked_proper(X)>
  <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(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U161(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U153(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U152(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U143(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U142(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U133(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U153(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U152(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U151(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U143(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U142(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U141(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U133(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U132(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U122(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U121(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U112(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U111(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U103(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U102(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U132(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isPLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isLNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNaturalKind(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U92(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U82(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U72(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U62(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U221(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U211(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U202(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U201(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U191(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U181(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U171(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U131(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U161(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U131(X1,X2,X3)) ,