- : 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] mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
[82] mark(tt) -> active(tt)
[83] mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
[84] mark(isNatural(X)) -> active(isNatural(X))
[85] mark(U103(X)) -> active(U103(mark(X)))
[86] mark(isLNat(X)) -> active(isLNat(X))
[87] mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
[88] mark(snd(X)) -> active(snd(mark(X)))
[89] mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
[90] mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
[91] mark(U112(X)) -> active(U112(mark(X)))
[92] mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
[93] mark(U122(X)) -> active(U122(mark(X)))
[94] mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
[95] mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
[96] mark(U133(X)) -> active(U133(mark(X)))
[97] mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
[98] mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
[99] mark(U143(X)) -> active(U143(mark(X)))
[100] mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
[101] mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
[102] mark(U153(X)) -> active(U153(mark(X)))
[103] mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
[104] mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
[105] mark(natsFrom(X)) -> active(natsFrom(mark(X)))
[106] mark(s(X)) -> active(s(mark(X)))
[107] mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
[108] mark(head(X)) -> active(head(mark(X)))
[109] mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
[110] mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
[111] mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
[112] mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
[113] mark(nil) -> active(nil)
[114] mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
[115] mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
[116] mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
[117] mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
[118] mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
[119] mark(fst(X)) -> active(fst(mark(X)))
[120] mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
[121] mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
[122] mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
[123] mark(U43(X)) -> active(U43(mark(X)))
[124] mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
[125] mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
[126] mark(U53(X)) -> active(U53(mark(X)))
[127] mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
[128] mark(U62(X)) -> active(U62(mark(X)))
[129] mark(isPLNat(X)) -> active(isPLNat(X))
[130] mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
[131] mark(U72(X)) -> active(U72(mark(X)))
[132] mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
[133] mark(U82(X)) -> active(U82(mark(X)))
[134] mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
[135] mark(U92(X)) -> active(U92(mark(X)))
[136] mark(and(X1,X2)) -> active(and(mark(X1),X2))
[137] mark(isNaturalKind(X)) -> active(isNaturalKind(X))
[138] mark(isLNatKind(X)) -> active(isLNatKind(X))
[139] mark(isPLNatKind(X)) -> active(isPLNatKind(X))
[140] mark(tail(X)) -> active(tail(mark(X)))
[141] mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
[142] mark(0) -> active(0)
[143] mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
[144] U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
[145] U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
[146] U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
[147] U101(active(X1),X2,X3) -> U101(X1,X2,X3)
[148] U101(X1,active(X2),X3) -> U101(X1,X2,X3)
[149] U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
[150] U102(mark(X1),X2) -> U102(X1,X2)
[151] U102(X1,mark(X2)) -> U102(X1,X2)
[152] U102(active(X1),X2) -> U102(X1,X2)
[153] U102(X1,active(X2)) -> U102(X1,X2)
[154] isNatural(mark(X)) -> isNatural(X)
[155] isNatural(active(X)) -> isNatural(X)
[156] U103(mark(X)) -> U103(X)
[157] U103(active(X)) -> U103(X)
[158] isLNat(mark(X)) -> isLNat(X)
[159] isLNat(active(X)) -> isLNat(X)
[160] U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
[161] U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
[162] U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
[163] U11(active(X1),X2,X3) -> U11(X1,X2,X3)
[164] U11(X1,active(X2),X3) -> U11(X1,X2,X3)
[165] U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
[166] snd(mark(X)) -> snd(X)
[167] snd(active(X)) -> snd(X)
[168] splitAt(mark(X1),X2) -> splitAt(X1,X2)
[169] splitAt(X1,mark(X2)) -> splitAt(X1,X2)
[170] splitAt(active(X1),X2) -> splitAt(X1,X2)
[171] splitAt(X1,active(X2)) -> splitAt(X1,X2)
[172] U111(mark(X1),X2) -> U111(X1,X2)
[173] U111(X1,mark(X2)) -> U111(X1,X2)
[174] U111(active(X1),X2) -> U111(X1,X2)
[175] U111(X1,active(X2)) -> U111(X1,X2)
[176] U112(mark(X)) -> U112(X)
[177] U112(active(X)) -> U112(X)
[178] U121(mark(X1),X2) -> U121(X1,X2)
[179] U121(X1,mark(X2)) -> U121(X1,X2)
[180] U121(active(X1),X2) -> U121(X1,X2)
[181] U121(X1,active(X2)) -> U121(X1,X2)
[182] U122(mark(X)) -> U122(X)
[183] U122(active(X)) -> U122(X)
[184] U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
[185] U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
[186] U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
[187] U131(active(X1),X2,X3) -> U131(X1,X2,X3)
[188] U131(X1,active(X2),X3) -> U131(X1,X2,X3)
[189] U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
[190] U132(mark(X1),X2) -> U132(X1,X2)
[191] U132(X1,mark(X2)) -> U132(X1,X2)
[192] U132(active(X1),X2) -> U132(X1,X2)
[193] U132(X1,active(X2)) -> U132(X1,X2)
[194] U133(mark(X)) -> U133(X)
[195] U133(active(X)) -> U133(X)
[196] U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
[197] U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
[198] U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
[199] U141(active(X1),X2,X3) -> U141(X1,X2,X3)
[200] U141(X1,active(X2),X3) -> U141(X1,X2,X3)
[201] U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
[202] U142(mark(X1),X2) -> U142(X1,X2)
[203] U142(X1,mark(X2)) -> U142(X1,X2)
[204] U142(active(X1),X2) -> U142(X1,X2)
[205] U142(X1,active(X2)) -> U142(X1,X2)
[206] U143(mark(X)) -> U143(X)
[207] U143(active(X)) -> U143(X)
[208] U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
[209] U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
[210] U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
[211] U151(active(X1),X2,X3) -> U151(X1,X2,X3)
[212] U151(X1,active(X2),X3) -> U151(X1,X2,X3)
[213] U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
[214] U152(mark(X1),X2) -> U152(X1,X2)
[215] U152(X1,mark(X2)) -> U152(X1,X2)
[216] U152(active(X1),X2) -> U152(X1,X2)
[217] U152(X1,active(X2)) -> U152(X1,X2)
[218] U153(mark(X)) -> U153(X)
[219] U153(active(X)) -> U153(X)
[220] U161(mark(X1),X2) -> U161(X1,X2)
[221] U161(X1,mark(X2)) -> U161(X1,X2)
[222] U161(active(X1),X2) -> U161(X1,X2)
[223] U161(X1,active(X2)) -> U161(X1,X2)
[224] cons(mark(X1),X2) -> cons(X1,X2)
[225] cons(X1,mark(X2)) -> cons(X1,X2)
[226] cons(active(X1),X2) -> cons(X1,X2)
[227] cons(X1,active(X2)) -> cons(X1,X2)
[228] natsFrom(mark(X)) -> natsFrom(X)
[229] natsFrom(active(X)) -> natsFrom(X)
[230] s(mark(X)) -> s(X)
[231] s(active(X)) -> s(X)
[232] U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
[233] U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
[234] U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
[235] U171(active(X1),X2,X3) -> U171(X1,X2,X3)
[236] U171(X1,active(X2),X3) -> U171(X1,X2,X3)
[237] U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
[238] head(mark(X)) -> head(X)
[239] head(active(X)) -> head(X)
[240] afterNth(mark(X1),X2) -> afterNth(X1,X2)
[241] afterNth(X1,mark(X2)) -> afterNth(X1,X2)
[242] afterNth(active(X1),X2) -> afterNth(X1,X2)
[243] afterNth(X1,active(X2)) -> afterNth(X1,X2)
[244] U181(mark(X1),X2) -> U181(X1,X2)
[245] U181(X1,mark(X2)) -> U181(X1,X2)
[246] U181(active(X1),X2) -> U181(X1,X2)
[247] U181(X1,active(X2)) -> U181(X1,X2)
[248] U191(mark(X1),X2) -> U191(X1,X2)
[249] U191(X1,mark(X2)) -> U191(X1,X2)
[250] U191(active(X1),X2) -> U191(X1,X2)
[251] U191(X1,active(X2)) -> U191(X1,X2)
[252] pair(mark(X1),X2) -> pair(X1,X2)
[253] pair(X1,mark(X2)) -> pair(X1,X2)
[254] pair(active(X1),X2) -> pair(X1,X2)
[255] pair(X1,active(X2)) -> pair(X1,X2)
[256] U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
[257] U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
[258] U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
[259] U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
[260] U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
[261] U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
[262] U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
[263] U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
[264] U202(mark(X1),X2) -> U202(X1,X2)
[265] U202(X1,mark(X2)) -> U202(X1,X2)
[266] U202(active(X1),X2) -> U202(X1,X2)
[267] U202(X1,active(X2)) -> U202(X1,X2)
[268] U21(mark(X1),X2) -> U21(X1,X2)
[269] U21(X1,mark(X2)) -> U21(X1,X2)
[270] U21(active(X1),X2) -> U21(X1,X2)
[271] U21(X1,active(X2)) -> U21(X1,X2)
[272] U211(mark(X1),X2) -> U211(X1,X2)
[273] U211(X1,mark(X2)) -> U211(X1,X2)
[274] U211(active(X1),X2) -> U211(X1,X2)
[275] U211(X1,active(X2)) -> U211(X1,X2)
[276] U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
[277] U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
[278] U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
[279] U221(active(X1),X2,X3) -> U221(X1,X2,X3)
[280] U221(X1,active(X2),X3) -> U221(X1,X2,X3)
[281] U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
[282] fst(mark(X)) -> fst(X)
[283] fst(active(X)) -> fst(X)
[284] U31(mark(X1),X2) -> U31(X1,X2)
[285] U31(X1,mark(X2)) -> U31(X1,X2)
[286] U31(active(X1),X2) -> U31(X1,X2)
[287] U31(X1,active(X2)) -> U31(X1,X2)
[288] U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
[289] U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
[290] U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
[291] U41(active(X1),X2,X3) -> U41(X1,X2,X3)
[292] U41(X1,active(X2),X3) -> U41(X1,X2,X3)
[293] U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
[294] U42(mark(X1),X2) -> U42(X1,X2)
[295] U42(X1,mark(X2)) -> U42(X1,X2)
[296] U42(active(X1),X2) -> U42(X1,X2)
[297] U42(X1,active(X2)) -> U42(X1,X2)
[298] U43(mark(X)) -> U43(X)
[299] U43(active(X)) -> U43(X)
[300] U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
[301] U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
[302] U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
[303] U51(active(X1),X2,X3) -> U51(X1,X2,X3)
[304] U51(X1,active(X2),X3) -> U51(X1,X2,X3)
[305] U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
[306] U52(mark(X1),X2) -> U52(X1,X2)
[307] U52(X1,mark(X2)) -> U52(X1,X2)
[308] U52(active(X1),X2) -> U52(X1,X2)
[309] U52(X1,active(X2)) -> U52(X1,X2)
[310] U53(mark(X)) -> U53(X)
[311] U53(active(X)) -> U53(X)
[312] U61(mark(X1),X2) -> U61(X1,X2)
[313] U61(X1,mark(X2)) -> U61(X1,X2)
[314] U61(active(X1),X2) -> U61(X1,X2)
[315] U61(X1,active(X2)) -> U61(X1,X2)
[316] U62(mark(X)) -> U62(X)
[317] U62(active(X)) -> U62(X)
[318] isPLNat(mark(X)) -> isPLNat(X)
[319] isPLNat(active(X)) -> isPLNat(X)
[320] U71(mark(X1),X2) -> U71(X1,X2)
[321] U71(X1,mark(X2)) -> U71(X1,X2)
[322] U71(active(X1),X2) -> U71(X1,X2)
[323] U71(X1,active(X2)) -> U71(X1,X2)
[324] U72(mark(X)) -> U72(X)
[325] U72(active(X)) -> U72(X)
[326] U81(mark(X1),X2) -> U81(X1,X2)
[327] U81(X1,mark(X2)) -> U81(X1,X2)
[328] U81(active(X1),X2) -> U81(X1,X2)
[329] U81(X1,active(X2)) -> U81(X1,X2)
[330] U82(mark(X)) -> U82(X)
[331] U82(active(X)) -> U82(X)
[332] U91(mark(X1),X2) -> U91(X1,X2)
[333] U91(X1,mark(X2)) -> U91(X1,X2)
[334] U91(active(X1),X2) -> U91(X1,X2)
[335] U91(X1,active(X2)) -> U91(X1,X2)
[336] U92(mark(X)) -> U92(X)
[337] U92(active(X)) -> U92(X)
[338] and(mark(X1),X2) -> and(X1,X2)
[339] and(X1,mark(X2)) -> and(X1,X2)
[340] and(active(X1),X2) -> and(X1,X2)
[341] and(X1,active(X2)) -> and(X1,X2)
[342] isNaturalKind(mark(X)) -> isNaturalKind(X)
[343] isNaturalKind(active(X)) -> isNaturalKind(X)
[344] isLNatKind(mark(X)) -> isLNatKind(X)
[345] isLNatKind(active(X)) -> isLNatKind(X)
[346] isPLNatKind(mark(X)) -> isPLNatKind(X)
[347] isPLNatKind(active(X)) -> isPLNatKind(X)
[348] tail(mark(X)) -> tail(X)
[349] tail(active(X)) -> tail(X)
[350] take(mark(X1),X2) -> take(X1,X2)
[351] take(X1,mark(X2)) -> take(X1,X2)
[352] take(active(X1),X2) -> take(X1,X2)
[353] take(X1,active(X2)) -> take(X1,X2)
[354] sel(mark(X1),X2) -> sel(X1,X2)
[355] sel(X1,mark(X2)) -> sel(X1,X2)
[356] sel(active(X1),X2) -> sel(X1,X2)
[357] sel(X1,active(X2)) -> sel(X1,X2)


Sub problem: 
guided: 

DP termination of:
<Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
<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_mark(U103(isLNat(V2)))>
<Marked_active(U102(tt,V2)) , Marked_U103(isLNat(V2))>
<Marked_active(U102(tt,V2)) , Marked_isLNat(V2)>
<Marked_active(U103(tt)) , Marked_mark(tt)>
<Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
<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_mark(U112(isLNat(V1)))>
<Marked_active(U111(tt,V1)) , Marked_U112(isLNat(V1))>
<Marked_active(U111(tt,V1)) , Marked_isLNat(V1)>
<Marked_active(U112(tt)) , Marked_mark(tt)>
<Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
<Marked_active(U121(tt,V1)) , Marked_U122(isNatural(V1))>
<Marked_active(U121(tt,V1)) , Marked_isNatural(V1)>
<Marked_active(U122(tt)) , Marked_mark(tt)>
<Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
<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_mark(U133(isLNat(V2)))>
<Marked_active(U132(tt,V2)) , Marked_U133(isLNat(V2))>
<Marked_active(U132(tt,V2)) , Marked_isLNat(V2)>
<Marked_active(U133(tt)) , Marked_mark(tt)>
<Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),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_mark(U143(isLNat(V2)))>
<Marked_active(U142(tt,V2)) , Marked_U143(isLNat(V2))>
<Marked_active(U142(tt,V2)) , Marked_isLNat(V2)>
<Marked_active(U143(tt)) , Marked_mark(tt)>
<Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),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_mark(U153(isLNat(V2)))>
<Marked_active(U152(tt,V2)) , Marked_U153(isLNat(V2))>
<Marked_active(U152(tt,V2)) , Marked_isLNat(V2)>
<Marked_active(U153(tt)) , Marked_mark(tt)>
<Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
<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_mark(head(afterNth(N,XS)))>
<Marked_active(U171(tt,N,XS)) , Marked_head(afterNth(N,XS))>
<Marked_active(U171(tt,N,XS)) , Marked_afterNth(N,XS)>
<Marked_active(U181(tt,Y)) , Marked_mark(Y)>
<Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
<Marked_active(U191(tt,XS)) , Marked_pair(nil,XS)>
<Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
<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_mark(pair(cons(X,YS),ZS))>
<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(U21(tt,X)) , Marked_mark(X)>
<Marked_active(U211(tt,XS)) , Marked_mark(XS)>
<Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
<Marked_active(U221(tt,N,XS)) , Marked_fst(splitAt(N,XS))>
<Marked_active(U221(tt,N,XS)) , Marked_splitAt(N,XS)>
<Marked_active(U31(tt,N)) , Marked_mark(N)>
<Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
<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_mark(U43(isLNat(V2)))>
<Marked_active(U42(tt,V2)) , Marked_U43(isLNat(V2))>
<Marked_active(U42(tt,V2)) , Marked_isLNat(V2)>
<Marked_active(U43(tt)) , Marked_mark(tt)>
<Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),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_mark(U53(isLNat(V2)))>
<Marked_active(U52(tt,V2)) , Marked_U53(isLNat(V2))>
<Marked_active(U52(tt,V2)) , Marked_isLNat(V2)>
<Marked_active(U53(tt)) , Marked_mark(tt)>
<Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
<Marked_active(U61(tt,V1)) , Marked_U62(isPLNat(V1))>
<Marked_active(U61(tt,V1)) , Marked_isPLNat(V1)>
<Marked_active(U62(tt)) , Marked_mark(tt)>
<Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
<Marked_active(U71(tt,V1)) , Marked_U72(isNatural(V1))>
<Marked_active(U71(tt,V1)) , Marked_isNatural(V1)>
<Marked_active(U72(tt)) , Marked_mark(tt)>
<Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
<Marked_active(U81(tt,V1)) , Marked_U82(isPLNat(V1))>
<Marked_active(U81(tt,V1)) , Marked_isPLNat(V1)>
<Marked_active(U82(tt)) , Marked_mark(tt)>
<Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
<Marked_active(U91(tt,V1)) , Marked_U92(isLNat(V1))>
<Marked_active(U91(tt,V1)) , Marked_isLNat(V1)>
<Marked_active(U92(tt)) , Marked_mark(tt)>
<Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                      isNaturalKind(N)),
                                                  and(isLNat(XS),
                                                   isLNatKind(XS))),N,
                                              XS))>
<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(and(tt,X)) , Marked_mark(X)>
<Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                      isLNatKind(X)),
                                                  and(isLNat(Y),isLNatKind(Y))),
                                              X))>
<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_mark(U31(and(and(isNatural(N),
                                                        isNaturalKind(N)),
                                                    and(isLNat(XS),
                                                     isLNatKind(XS))),
                                                N))>
<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(nil)) , Marked_mark(tt)>
<Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(isNaturalKind(V1),
                                                           isLNatKind(V2)),
                                                       V1,V2))>
<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_mark(U51(and(isNaturalKind(V1),
                                                       isLNatKind(V2)),
                                                   V1,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_mark(U61(isPLNatKind(V1),V1))>
<Marked_active(isLNat(fst(V1))) , Marked_U61(isPLNatKind(V1),V1)>
<Marked_active(isLNat(fst(V1))) , Marked_isPLNatKind(V1)>
<Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(V1),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_mark(U81(isPLNatKind(V1),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_mark(U91(isLNatKind(V1),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_mark(U101(and(isNaturalKind(V1),
                                                        isLNatKind(V2)),
                                                   V1,V2))>
<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(nil)) , Marked_mark(tt)>
<Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(isNaturalKind(V1),
                                                           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_mark(and(isNaturalKind(V1),
                                                       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_mark(isPLNatKind(V1))>
<Marked_active(isLNatKind(fst(V1))) , Marked_isPLNatKind(V1)>
<Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(V1))>
<Marked_active(isLNatKind(natsFrom(V1))) , Marked_isNaturalKind(V1)>
<Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
<Marked_active(isLNatKind(snd(V1))) , Marked_isPLNatKind(V1)>
<Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
<Marked_active(isLNatKind(tail(V1))) , Marked_isLNatKind(V1)>
<Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(V1),
                                                       isLNatKind(V2)))>
<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(0)) , Marked_mark(tt)>
<Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),V1))>
<Marked_active(isNatural(head(V1))) , Marked_U111(isLNatKind(V1),V1)>
<Marked_active(isNatural(head(V1))) , Marked_isLNatKind(V1)>
<Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),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_mark(U131(and(isNaturalKind(V1),
                                                          isLNatKind(V2)),
                                                     V1,V2))>
<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(0)) , Marked_mark(tt)>
<Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
<Marked_active(isNaturalKind(head(V1))) , Marked_isLNatKind(V1)>
<Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
<Marked_active(isNaturalKind(s(V1))) , Marked_isNaturalKind(V1)>
<Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(isNaturalKind(V1),
                                                         isLNatKind(V2)))>
<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_mark(U141(and(isLNatKind(V1),
                                                         isLNatKind(V2)),
                                                    V1,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_mark(U151(and(isNaturalKind(
                                                                V1),
                                                            isLNatKind(V2)),
                                                       V1,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_mark(and(isLNatKind(V1),
                                                        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_mark(and(isNaturalKind(V1),
                                                           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_mark(U161(and(isNatural(N),
                                                isNaturalKind(N)),N))>
<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_mark(U171(and(and(isNatural(N),
                                                  isNaturalKind(N)),
                                              and(isLNat(XS),isLNatKind(XS))),
                                         N,XS))>
<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_mark(U181(and(and(isLNat(X),
                                                       isLNatKind(X)),
                                                   and(isLNat(Y),isLNatKind(Y))),
                                              Y))>
<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_mark(U191(and(isLNat(XS),isLNatKind(XS)),
                                             XS))>
<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_mark(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_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_mark(U211(and(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                     and(isLNat(XS),
                                                      isLNatKind(XS))),
                                                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_mark(U221(and(and(isNatural(N),
                                                   isNaturalKind(N)),
                                               and(isLNat(XS),isLNatKind(XS))),
                                          N,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_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
<Marked_mark(U101(X1,X2,X3)) , Marked_U101(mark(X1),X2,X3)>
<Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(tt) , Marked_active(tt)>
<Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
<Marked_mark(U102(X1,X2)) , Marked_U102(mark(X1),X2)>
<Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
<Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
<Marked_mark(U103(X)) , Marked_U103(mark(X))>
<Marked_mark(U103(X)) , Marked_mark(X)>
<Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
<Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
<Marked_mark(U11(X1,X2,X3)) , Marked_U11(mark(X1),X2,X3)>
<Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
<Marked_mark(snd(X)) , Marked_snd(mark(X))>
<Marked_mark(snd(X)) , Marked_mark(X)>
<Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),mark(X2)))>
<Marked_mark(splitAt(X1,X2)) , Marked_splitAt(mark(X1),mark(X2))>
<Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
<Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
<Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
<Marked_mark(U111(X1,X2)) , Marked_U111(mark(X1),X2)>
<Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
<Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
<Marked_mark(U112(X)) , Marked_U112(mark(X))>
<Marked_mark(U112(X)) , Marked_mark(X)>
<Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
<Marked_mark(U121(X1,X2)) , Marked_U121(mark(X1),X2)>
<Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
<Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
<Marked_mark(U122(X)) , Marked_U122(mark(X))>
<Marked_mark(U122(X)) , Marked_mark(X)>
<Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
<Marked_mark(U131(X1,X2,X3)) , Marked_U131(mark(X1),X2,X3)>
<Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
<Marked_mark(U132(X1,X2)) , Marked_U132(mark(X1),X2)>
<Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
<Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
<Marked_mark(U133(X)) , Marked_U133(mark(X))>
<Marked_mark(U133(X)) , Marked_mark(X)>
<Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
<Marked_mark(U141(X1,X2,X3)) , Marked_U141(mark(X1),X2,X3)>
<Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
<Marked_mark(U142(X1,X2)) , Marked_U142(mark(X1),X2)>
<Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
<Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
<Marked_mark(U143(X)) , Marked_U143(mark(X))>
<Marked_mark(U143(X)) , Marked_mark(X)>
<Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
<Marked_mark(U151(X1,X2,X3)) , Marked_U151(mark(X1),X2,X3)>
<Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
<Marked_mark(U152(X1,X2)) , Marked_U152(mark(X1),X2)>
<Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
<Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
<Marked_mark(U153(X)) , Marked_U153(mark(X))>
<Marked_mark(U153(X)) , Marked_mark(X)>
<Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
<Marked_mark(U161(X1,X2)) , Marked_U161(mark(X1),X2)>
<Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
<Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
<Marked_mark(cons(X1,X2)) , Marked_cons(mark(X1),X2)>
<Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
<Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
<Marked_mark(natsFrom(X)) , Marked_natsFrom(mark(X))>
<Marked_mark(natsFrom(X)) , Marked_mark(X)>
<Marked_mark(s(X)) , Marked_active(s(mark(X)))>
<Marked_mark(s(X)) , Marked_s(mark(X))>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
<Marked_mark(U171(X1,X2,X3)) , Marked_U171(mark(X1),X2,X3)>
<Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(head(X)) , Marked_active(head(mark(X)))>
<Marked_mark(head(X)) , Marked_head(mark(X))>
<Marked_mark(head(X)) , Marked_mark(X)>
<Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))>
<Marked_mark(afterNth(X1,X2)) , Marked_afterNth(mark(X1),mark(X2))>
<Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
<Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
<Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
<Marked_mark(U181(X1,X2)) , Marked_U181(mark(X1),X2)>
<Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
<Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
<Marked_mark(U191(X1,X2)) , Marked_U191(mark(X1),X2)>
<Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
<Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
<Marked_mark(pair(X1,X2)) , Marked_pair(mark(X1),mark(X2))>
<Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
<Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
<Marked_mark(nil) , Marked_active(nil)>
<Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))>
<Marked_mark(U201(X1,X2,X3,X4)) , Marked_U201(mark(X1),X2,X3,X4)>
<Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
<Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
<Marked_mark(U202(X1,X2)) , Marked_U202(mark(X1),X2)>
<Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
<Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
<Marked_mark(U21(X1,X2)) , Marked_U21(mark(X1),X2)>
<Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
<Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
<Marked_mark(U211(X1,X2)) , Marked_U211(mark(X1),X2)>
<Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
<Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
<Marked_mark(U221(X1,X2,X3)) , Marked_U221(mark(X1),X2,X3)>
<Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
<Marked_mark(fst(X)) , Marked_fst(mark(X))>
<Marked_mark(fst(X)) , Marked_mark(X)>
<Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
<Marked_mark(U31(X1,X2)) , Marked_U31(mark(X1),X2)>
<Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
<Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
<Marked_mark(U41(X1,X2,X3)) , Marked_U41(mark(X1),X2,X3)>
<Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
<Marked_mark(U42(X1,X2)) , Marked_U42(mark(X1),X2)>
<Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
<Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
<Marked_mark(U43(X)) , Marked_U43(mark(X))>
<Marked_mark(U43(X)) , Marked_mark(X)>
<Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
<Marked_mark(U51(X1,X2,X3)) , Marked_U51(mark(X1),X2,X3)>
<Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
<Marked_mark(U52(X1,X2)) , Marked_U52(mark(X1),X2)>
<Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
<Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
<Marked_mark(U53(X)) , Marked_U53(mark(X))>
<Marked_mark(U53(X)) , Marked_mark(X)>
<Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
<Marked_mark(U61(X1,X2)) , Marked_U61(mark(X1),X2)>
<Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
<Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
<Marked_mark(U62(X)) , Marked_U62(mark(X))>
<Marked_mark(U62(X)) , Marked_mark(X)>
<Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
<Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
<Marked_mark(U71(X1,X2)) , Marked_U71(mark(X1),X2)>
<Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
<Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
<Marked_mark(U72(X)) , Marked_U72(mark(X))>
<Marked_mark(U72(X)) , Marked_mark(X)>
<Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
<Marked_mark(U81(X1,X2)) , Marked_U81(mark(X1),X2)>
<Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
<Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
<Marked_mark(U82(X)) , Marked_U82(mark(X))>
<Marked_mark(U82(X)) , Marked_mark(X)>
<Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
<Marked_mark(U91(X1,X2)) , Marked_U91(mark(X1),X2)>
<Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
<Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
<Marked_mark(U92(X)) , Marked_U92(mark(X))>
<Marked_mark(U92(X)) , Marked_mark(X)>
<Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
<Marked_mark(and(X1,X2)) , Marked_and(mark(X1),X2)>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
<Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
<Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
<Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
<Marked_mark(tail(X)) , Marked_tail(mark(X))>
<Marked_mark(tail(X)) , Marked_mark(X)>
<Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
<Marked_mark(take(X1,X2)) , Marked_take(mark(X1),mark(X2))>
<Marked_mark(take(X1,X2)) , Marked_mark(X1)>
<Marked_mark(take(X1,X2)) , Marked_mark(X2)>
<Marked_mark(0) , Marked_active(0)>
<Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
<Marked_mark(sel(X1,X2)) , Marked_sel(mark(X1),mark(X2))>
<Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
<Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
<Marked_U101(mark(X1),X2,X3) , Marked_U101(X1,X2,X3)>
<Marked_U101(X1,mark(X2),X3) , Marked_U101(X1,X2,X3)>
<Marked_U101(X1,X2,mark(X3)) , Marked_U101(X1,X2,X3)>
<Marked_U101(active(X1),X2,X3) , Marked_U101(X1,X2,X3)>
<Marked_U101(X1,active(X2),X3) , Marked_U101(X1,X2,X3)>
<Marked_U101(X1,X2,active(X3)) , Marked_U101(X1,X2,X3)>
<Marked_U102(mark(X1),X2) , Marked_U102(X1,X2)>
<Marked_U102(X1,mark(X2)) , Marked_U102(X1,X2)>
<Marked_U102(active(X1),X2) , Marked_U102(X1,X2)>
<Marked_U102(X1,active(X2)) , Marked_U102(X1,X2)>
<Marked_isNatural(mark(X)) , Marked_isNatural(X)>
<Marked_isNatural(active(X)) , Marked_isNatural(X)>
<Marked_U103(mark(X)) , Marked_U103(X)>
<Marked_U103(active(X)) , Marked_U103(X)>
<Marked_isLNat(mark(X)) , Marked_isLNat(X)>
<Marked_isLNat(active(X)) , Marked_isLNat(X)>
<Marked_U11(mark(X1),X2,X3) , Marked_U11(X1,X2,X3)>
<Marked_U11(X1,mark(X2),X3) , Marked_U11(X1,X2,X3)>
<Marked_U11(X1,X2,mark(X3)) , Marked_U11(X1,X2,X3)>
<Marked_U11(active(X1),X2,X3) , Marked_U11(X1,X2,X3)>
<Marked_U11(X1,active(X2),X3) , Marked_U11(X1,X2,X3)>
<Marked_U11(X1,X2,active(X3)) , Marked_U11(X1,X2,X3)>
<Marked_snd(mark(X)) , Marked_snd(X)>
<Marked_snd(active(X)) , Marked_snd(X)>
<Marked_splitAt(mark(X1),X2) , Marked_splitAt(X1,X2)>
<Marked_splitAt(X1,mark(X2)) , Marked_splitAt(X1,X2)>
<Marked_splitAt(active(X1),X2) , Marked_splitAt(X1,X2)>
<Marked_splitAt(X1,active(X2)) , Marked_splitAt(X1,X2)>
<Marked_U111(mark(X1),X2) , Marked_U111(X1,X2)>
<Marked_U111(X1,mark(X2)) , Marked_U111(X1,X2)>
<Marked_U111(active(X1),X2) , Marked_U111(X1,X2)>
<Marked_U111(X1,active(X2)) , Marked_U111(X1,X2)>
<Marked_U112(mark(X)) , Marked_U112(X)>
<Marked_U112(active(X)) , Marked_U112(X)>
<Marked_U121(mark(X1),X2) , Marked_U121(X1,X2)>
<Marked_U121(X1,mark(X2)) , Marked_U121(X1,X2)>
<Marked_U121(active(X1),X2) , Marked_U121(X1,X2)>
<Marked_U121(X1,active(X2)) , Marked_U121(X1,X2)>
<Marked_U122(mark(X)) , Marked_U122(X)>
<Marked_U122(active(X)) , Marked_U122(X)>
<Marked_U131(mark(X1),X2,X3) , Marked_U131(X1,X2,X3)>
<Marked_U131(X1,mark(X2),X3) , Marked_U131(X1,X2,X3)>
<Marked_U131(X1,X2,mark(X3)) , Marked_U131(X1,X2,X3)>
<Marked_U131(active(X1),X2,X3) , Marked_U131(X1,X2,X3)>
<Marked_U131(X1,active(X2),X3) , Marked_U131(X1,X2,X3)>
<Marked_U131(X1,X2,active(X3)) , Marked_U131(X1,X2,X3)>
<Marked_U132(mark(X1),X2) , Marked_U132(X1,X2)>
<Marked_U132(X1,mark(X2)) , Marked_U132(X1,X2)>
<Marked_U132(active(X1),X2) , Marked_U132(X1,X2)>
<Marked_U132(X1,active(X2)) , Marked_U132(X1,X2)>
<Marked_U133(mark(X)) , Marked_U133(X)>
<Marked_U133(active(X)) , Marked_U133(X)>
<Marked_U141(mark(X1),X2,X3) , Marked_U141(X1,X2,X3)>
<Marked_U141(X1,mark(X2),X3) , Marked_U141(X1,X2,X3)>
<Marked_U141(X1,X2,mark(X3)) , Marked_U141(X1,X2,X3)>
<Marked_U141(active(X1),X2,X3) , Marked_U141(X1,X2,X3)>
<Marked_U141(X1,active(X2),X3) , Marked_U141(X1,X2,X3)>
<Marked_U141(X1,X2,active(X3)) , Marked_U141(X1,X2,X3)>
<Marked_U142(mark(X1),X2) , Marked_U142(X1,X2)>
<Marked_U142(X1,mark(X2)) , Marked_U142(X1,X2)>
<Marked_U142(active(X1),X2) , Marked_U142(X1,X2)>
<Marked_U142(X1,active(X2)) , Marked_U142(X1,X2)>
<Marked_U143(mark(X)) , Marked_U143(X)>
<Marked_U143(active(X)) , Marked_U143(X)>
<Marked_U151(mark(X1),X2,X3) , Marked_U151(X1,X2,X3)>
<Marked_U151(X1,mark(X2),X3) , Marked_U151(X1,X2,X3)>
<Marked_U151(X1,X2,mark(X3)) , Marked_U151(X1,X2,X3)>
<Marked_U151(active(X1),X2,X3) , Marked_U151(X1,X2,X3)>
<Marked_U151(X1,active(X2),X3) , Marked_U151(X1,X2,X3)>
<Marked_U151(X1,X2,active(X3)) , Marked_U151(X1,X2,X3)>
<Marked_U152(mark(X1),X2) , Marked_U152(X1,X2)>
<Marked_U152(X1,mark(X2)) , Marked_U152(X1,X2)>
<Marked_U152(active(X1),X2) , Marked_U152(X1,X2)>
<Marked_U152(X1,active(X2)) , Marked_U152(X1,X2)>
<Marked_U153(mark(X)) , Marked_U153(X)>
<Marked_U153(active(X)) , Marked_U153(X)>
<Marked_U161(mark(X1),X2) , Marked_U161(X1,X2)>
<Marked_U161(X1,mark(X2)) , Marked_U161(X1,X2)>
<Marked_U161(active(X1),X2) , Marked_U161(X1,X2)>
<Marked_U161(X1,active(X2)) , Marked_U161(X1,X2)>
<Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
<Marked_cons(X1,mark(X2)) , Marked_cons(X1,X2)>
<Marked_cons(active(X1),X2) , Marked_cons(X1,X2)>
<Marked_cons(X1,active(X2)) , Marked_cons(X1,X2)>
<Marked_natsFrom(mark(X)) , Marked_natsFrom(X)>
<Marked_natsFrom(active(X)) , Marked_natsFrom(X)>
<Marked_s(mark(X)) , Marked_s(X)>
<Marked_s(active(X)) , Marked_s(X)>
<Marked_U171(mark(X1),X2,X3) , Marked_U171(X1,X2,X3)>
<Marked_U171(X1,mark(X2),X3) , Marked_U171(X1,X2,X3)>
<Marked_U171(X1,X2,mark(X3)) , Marked_U171(X1,X2,X3)>
<Marked_U171(active(X1),X2,X3) , Marked_U171(X1,X2,X3)>
<Marked_U171(X1,active(X2),X3) , Marked_U171(X1,X2,X3)>
<Marked_U171(X1,X2,active(X3)) , Marked_U171(X1,X2,X3)>
<Marked_head(mark(X)) , Marked_head(X)>
<Marked_head(active(X)) , Marked_head(X)>
<Marked_afterNth(mark(X1),X2) , Marked_afterNth(X1,X2)>
<Marked_afterNth(X1,mark(X2)) , Marked_afterNth(X1,X2)>
<Marked_afterNth(active(X1),X2) , Marked_afterNth(X1,X2)>
<Marked_afterNth(X1,active(X2)) , Marked_afterNth(X1,X2)>
<Marked_U181(mark(X1),X2) , Marked_U181(X1,X2)>
<Marked_U181(X1,mark(X2)) , Marked_U181(X1,X2)>
<Marked_U181(active(X1),X2) , Marked_U181(X1,X2)>
<Marked_U181(X1,active(X2)) , Marked_U181(X1,X2)>
<Marked_U191(mark(X1),X2) , Marked_U191(X1,X2)>
<Marked_U191(X1,mark(X2)) , Marked_U191(X1,X2)>
<Marked_U191(active(X1),X2) , Marked_U191(X1,X2)>
<Marked_U191(X1,active(X2)) , Marked_U191(X1,X2)>
<Marked_pair(mark(X1),X2) , Marked_pair(X1,X2)>
<Marked_pair(X1,mark(X2)) , Marked_pair(X1,X2)>
<Marked_pair(active(X1),X2) , Marked_pair(X1,X2)>
<Marked_pair(X1,active(X2)) , Marked_pair(X1,X2)>
<Marked_U201(mark(X1),X2,X3,X4) , Marked_U201(X1,X2,X3,X4)>
<Marked_U201(X1,mark(X2),X3,X4) , Marked_U201(X1,X2,X3,X4)>
<Marked_U201(X1,X2,mark(X3),X4) , Marked_U201(X1,X2,X3,X4)>
<Marked_U201(X1,X2,X3,mark(X4)) , Marked_U201(X1,X2,X3,X4)>
<Marked_U201(active(X1),X2,X3,X4) , Marked_U201(X1,X2,X3,X4)>
<Marked_U201(X1,active(X2),X3,X4) , Marked_U201(X1,X2,X3,X4)>
<Marked_U201(X1,X2,active(X3),X4) , Marked_U201(X1,X2,X3,X4)>
<Marked_U201(X1,X2,X3,active(X4)) , Marked_U201(X1,X2,X3,X4)>
<Marked_U202(mark(X1),X2) , Marked_U202(X1,X2)>
<Marked_U202(X1,mark(X2)) , Marked_U202(X1,X2)>
<Marked_U202(active(X1),X2) , Marked_U202(X1,X2)>
<Marked_U202(X1,active(X2)) , Marked_U202(X1,X2)>
<Marked_U21(mark(X1),X2) , Marked_U21(X1,X2)>
<Marked_U21(X1,mark(X2)) , Marked_U21(X1,X2)>
<Marked_U21(active(X1),X2) , Marked_U21(X1,X2)>
<Marked_U21(X1,active(X2)) , Marked_U21(X1,X2)>
<Marked_U211(mark(X1),X2) , Marked_U211(X1,X2)>
<Marked_U211(X1,mark(X2)) , Marked_U211(X1,X2)>
<Marked_U211(active(X1),X2) , Marked_U211(X1,X2)>
<Marked_U211(X1,active(X2)) , Marked_U211(X1,X2)>
<Marked_U221(mark(X1),X2,X3) , Marked_U221(X1,X2,X3)>
<Marked_U221(X1,mark(X2),X3) , Marked_U221(X1,X2,X3)>
<Marked_U221(X1,X2,mark(X3)) , Marked_U221(X1,X2,X3)>
<Marked_U221(active(X1),X2,X3) , Marked_U221(X1,X2,X3)>
<Marked_U221(X1,active(X2),X3) , Marked_U221(X1,X2,X3)>
<Marked_U221(X1,X2,active(X3)) , Marked_U221(X1,X2,X3)>
<Marked_fst(mark(X)) , Marked_fst(X)>
<Marked_fst(active(X)) , Marked_fst(X)>
<Marked_U31(mark(X1),X2) , Marked_U31(X1,X2)>
<Marked_U31(X1,mark(X2)) , Marked_U31(X1,X2)>
<Marked_U31(active(X1),X2) , Marked_U31(X1,X2)>
<Marked_U31(X1,active(X2)) , Marked_U31(X1,X2)>
<Marked_U41(mark(X1),X2,X3) , Marked_U41(X1,X2,X3)>
<Marked_U41(X1,mark(X2),X3) , Marked_U41(X1,X2,X3)>
<Marked_U41(X1,X2,mark(X3)) , Marked_U41(X1,X2,X3)>
<Marked_U41(active(X1),X2,X3) , Marked_U41(X1,X2,X3)>
<Marked_U41(X1,active(X2),X3) , Marked_U41(X1,X2,X3)>
<Marked_U41(X1,X2,active(X3)) , Marked_U41(X1,X2,X3)>
<Marked_U42(mark(X1),X2) , Marked_U42(X1,X2)>
<Marked_U42(X1,mark(X2)) , Marked_U42(X1,X2)>
<Marked_U42(active(X1),X2) , Marked_U42(X1,X2)>
<Marked_U42(X1,active(X2)) , Marked_U42(X1,X2)>
<Marked_U43(mark(X)) , Marked_U43(X)>
<Marked_U43(active(X)) , Marked_U43(X)>
<Marked_U51(mark(X1),X2,X3) , Marked_U51(X1,X2,X3)>
<Marked_U51(X1,mark(X2),X3) , Marked_U51(X1,X2,X3)>
<Marked_U51(X1,X2,mark(X3)) , Marked_U51(X1,X2,X3)>
<Marked_U51(active(X1),X2,X3) , Marked_U51(X1,X2,X3)>
<Marked_U51(X1,active(X2),X3) , Marked_U51(X1,X2,X3)>
<Marked_U51(X1,X2,active(X3)) , Marked_U51(X1,X2,X3)>
<Marked_U52(mark(X1),X2) , Marked_U52(X1,X2)>
<Marked_U52(X1,mark(X2)) , Marked_U52(X1,X2)>
<Marked_U52(active(X1),X2) , Marked_U52(X1,X2)>
<Marked_U52(X1,active(X2)) , Marked_U52(X1,X2)>
<Marked_U53(mark(X)) , Marked_U53(X)>
<Marked_U53(active(X)) , Marked_U53(X)>
<Marked_U61(mark(X1),X2) , Marked_U61(X1,X2)>
<Marked_U61(X1,mark(X2)) , Marked_U61(X1,X2)>
<Marked_U61(active(X1),X2) , Marked_U61(X1,X2)>
<Marked_U61(X1,active(X2)) , Marked_U61(X1,X2)>
<Marked_U62(mark(X)) , Marked_U62(X)>
<Marked_U62(active(X)) , Marked_U62(X)>
<Marked_isPLNat(mark(X)) , Marked_isPLNat(X)>
<Marked_isPLNat(active(X)) , Marked_isPLNat(X)>
<Marked_U71(mark(X1),X2) , Marked_U71(X1,X2)>
<Marked_U71(X1,mark(X2)) , Marked_U71(X1,X2)>
<Marked_U71(active(X1),X2) , Marked_U71(X1,X2)>
<Marked_U71(X1,active(X2)) , Marked_U71(X1,X2)>
<Marked_U72(mark(X)) , Marked_U72(X)>
<Marked_U72(active(X)) , Marked_U72(X)>
<Marked_U81(mark(X1),X2) , Marked_U81(X1,X2)>
<Marked_U81(X1,mark(X2)) , Marked_U81(X1,X2)>
<Marked_U81(active(X1),X2) , Marked_U81(X1,X2)>
<Marked_U81(X1,active(X2)) , Marked_U81(X1,X2)>
<Marked_U82(mark(X)) , Marked_U82(X)>
<Marked_U82(active(X)) , Marked_U82(X)>
<Marked_U91(mark(X1),X2) , Marked_U91(X1,X2)>
<Marked_U91(X1,mark(X2)) , Marked_U91(X1,X2)>
<Marked_U91(active(X1),X2) , Marked_U91(X1,X2)>
<Marked_U91(X1,active(X2)) , Marked_U91(X1,X2)>
<Marked_U92(mark(X)) , Marked_U92(X)>
<Marked_U92(active(X)) , Marked_U92(X)>
<Marked_and(mark(X1),X2) , Marked_and(X1,X2)>
<Marked_and(X1,mark(X2)) , Marked_and(X1,X2)>
<Marked_and(active(X1),X2) , Marked_and(X1,X2)>
<Marked_and(X1,active(X2)) , Marked_and(X1,X2)>
<Marked_isNaturalKind(mark(X)) , Marked_isNaturalKind(X)>
<Marked_isNaturalKind(active(X)) , Marked_isNaturalKind(X)>
<Marked_isLNatKind(mark(X)) , Marked_isLNatKind(X)>
<Marked_isLNatKind(active(X)) , Marked_isLNatKind(X)>
<Marked_isPLNatKind(mark(X)) , Marked_isPLNatKind(X)>
<Marked_isPLNatKind(active(X)) , Marked_isPLNatKind(X)>
<Marked_tail(mark(X)) , Marked_tail(X)>
<Marked_tail(active(X)) , Marked_tail(X)>
<Marked_take(mark(X1),X2) , Marked_take(X1,X2)>
<Marked_take(X1,mark(X2)) , Marked_take(X1,X2)>
<Marked_take(active(X1),X2) , Marked_take(X1,X2)>
<Marked_take(X1,active(X2)) , Marked_take(X1,X2)>
<Marked_sel(mark(X1),X2) , Marked_sel(X1,X2)>
<Marked_sel(X1,mark(X2)) , Marked_sel(X1,X2)>
<Marked_sel(active(X1),X2) , Marked_sel(X1,X2)>
<Marked_sel(X1,active(X2)) , Marked_sel(X1,X2)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 61 components:

{  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
      --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(sel(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(tail(X)) , Marked_mark(X)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U92(X)) , Marked_mark(X)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U91(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U82(X)) , Marked_mark(X)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U81(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U72(X)) , Marked_mark(X)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U71(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U62(X)) , Marked_mark(X)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U61(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U53(X)) , Marked_mark(X)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U52(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U43(X)) , Marked_mark(X)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(fst(X)) , Marked_mark(X)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U211(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U202(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),X2,X3,X4))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(pair(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U191(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U181(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U161(X1,X2)) , Marked_active(U161(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U153(X)) , Marked_active(U153(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U152(X1,X2)) , Marked_active(U152(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U151(X1,X2,X3)) , Marked_active(U151(mark(X1),X2,X3))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U143(X)) , Marked_active(U143(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U142(X1,X2)) , Marked_active(U142(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U141(X1,X2,X3)) , Marked_active(U141(mark(X1),X2,X3))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U133(X)) , Marked_active(U133(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U132(X1,X2)) , Marked_active(U132(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U131(X1,X2,X3)) , Marked_active(U131(mark(X1),X2,X3))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U122(X)) , Marked_active(U122(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U121(X1,X2)) , Marked_active(U121(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U112(X)) , Marked_active(U112(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U111(X1,X2)) , Marked_active(U111(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(splitAt(X1,X2)) , Marked_active(splitAt(mark(X1),
                                                       mark(X2)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(snd(X)) , Marked_active(snd(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_active(U11(mark(X1),X2,X3))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isLNat(X)) , Marked_active(isLNat(X))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U103(X)) , Marked_active(U103(mark(X)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNatural(X)) , Marked_active(isNatural(X))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U102(X1,X2)) , Marked_active(U102(mark(X1),X2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U101(X1,X2,X3)) , Marked_active(U101(mark(X1),X2,X3))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(take(N,XS)) , Marked_mark(U221(and(and(isNatural(N),
                                                            isNaturalKind(N)),
                                                        and(isLNat(XS),
                                                         isLNatKind(XS))),
                                                   N,XS))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(tail(cons(N,XS))) , Marked_mark(U211(and(and(
                                                                  isNatural(
                                                                   N),
                                                                  isNaturalKind(
                                                                   N)),
                                                              and(isLNat(XS),
                                                               isLNatKind(XS))),
                                                         XS))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(splitAt(s(N),cons(X,XS))) , Marked_mark(U201(
                                                                 and(
                                                                  and(
                                                                   isNatural(
                                                                    N),
                                                                   isNaturalKind(
                                                                    N)),
                                                                  and(
                                                                   and(
                                                                    isNatural(
                                                                    X),
                                                                    isNaturalKind(
                                                                    X)),
                                                                   and(
                                                                    isLNat(
                                                                    XS),
                                                                    isLNatKind(
                                                                    XS)))),
                                                                 N,X,
                                                                 XS))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(splitAt(0,XS)) , Marked_mark(U191(and(isLNat(XS),
                                                           isLNatKind(XS)),
                                                      XS))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(snd(pair(X,Y))) , Marked_mark(U181(and(and(isLNat(X),
                                                                isLNatKind(X)),
                                                            and(isLNat(Y),
                                                             isLNatKind(Y))),
                                                       Y))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(sel(N,XS)) , Marked_mark(U171(and(and(isNatural(N),
                                                           isNaturalKind(N)),
                                                       and(isLNat(XS),
                                                        isLNatKind(XS))),
                                                  N,XS))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(natsFrom(N)) , Marked_mark(U161(and(isNatural(N),
                                                         isNaturalKind(N)),
                                                    N))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(isPLNatKind(splitAt(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(isPLNatKind(pair(V1,V2))) , Marked_mark(and(isLNatKind(
                                                                    V1),
                                                                 isLNatKind(V2)))
                                                     >
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(isPLNat(splitAt(V1,V2))) , Marked_mark(U151(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(isPLNat(pair(V1,V2))) , Marked_mark(U141(and(
                                                                  isLNatKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)),
                                                             V1,V2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(isNaturalKind(sel(V1,V2))) , Marked_mark(and(
                                                                  isNaturalKind(
                                                                   V1),
                                                                  isLNatKind(
                                                                   V2)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(isNaturalKind(s(V1))) , Marked_mark(isNaturalKind(V1))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(isNaturalKind(head(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(isNatural(sel(V1,V2))) , Marked_mark(U131(and(
                                                                   isNaturalKind(
                                                                    V1),
                                                                   isLNatKind(
                                                                    V2)),
                                                              V1,V2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(isNatural(s(V1))) , Marked_mark(U121(isNaturalKind(V1),
                                                         V1))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(isNatural(head(V1))) , Marked_mark(U111(isLNatKind(V1),
                                                            V1))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNatKind(take(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNatKind(tail(V1))) , Marked_mark(isLNatKind(V1))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNatKind(snd(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNatKind(natsFrom(V1))) , Marked_mark(isNaturalKind(
                                                                 V1))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNatKind(fst(V1))) , Marked_mark(isPLNatKind(V1))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNatKind(cons(V1,V2))) , Marked_mark(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNatKind(afterNth(V1,V2))) , Marked_mark(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNat(take(V1,V2))) , Marked_mark(U101(and(isNaturalKind(
                                                                    V1),
                                                                 isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNat(tail(V1))) , Marked_mark(U91(isLNatKind(V1),V1))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNat(snd(V1))) , Marked_mark(U81(isPLNatKind(V1),V1))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNat(natsFrom(V1))) , Marked_mark(U71(isNaturalKind(
                                                                 V1),
                                                             V1))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNat(fst(V1))) , Marked_mark(U61(isPLNatKind(V1),V1))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNat(cons(V1,V2))) , Marked_mark(U51(and(isNaturalKind(
                                                                    V1),
                                                                isLNatKind(V2)),
                                                            V1,V2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(isLNat(afterNth(V1,V2))) , Marked_mark(U41(and(
                                                                    isNaturalKind(
                                                                    V1),
                                                                    isLNatKind(
                                                                    V2)),
                                                                V1,V2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(head(cons(N,XS))) , Marked_mark(U31(and(and(isNatural(
                                                                    N),
                                                                 isNaturalKind(
                                                                  N)),
                                                             and(isLNat(XS),
                                                              isLNatKind(XS))),
                                                         N))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(fst(pair(X,Y))) , Marked_mark(U21(and(and(isLNat(X),
                                                               isLNatKind(X)),
                                                           and(isLNat(Y),
                                                            isLNatKind(Y))),
                                                       X))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(afterNth(N,XS)) , Marked_mark(U11(and(and(isNatural(N),
                                                               isNaturalKind(N)),
                                                           and(isLNat(XS),
                                                            isLNatKind(XS))),
                                                       N,XS))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(U91(tt,V1)) , Marked_mark(U92(isLNat(V1)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(U81(tt,V1)) , Marked_mark(U82(isPLNat(V1)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(U71(tt,V1)) , Marked_mark(U72(isNatural(V1)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(U61(tt,V1)) , Marked_mark(U62(isPLNat(V1)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(U52(tt,V2)) , Marked_mark(U53(isLNat(V2)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(U51(tt,V1,V2)) , Marked_mark(U52(isNatural(V1),V2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(U42(tt,V2)) , Marked_mark(U43(isLNat(V2)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(U41(tt,V1,V2)) , Marked_mark(U42(isNatural(V1),V2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(U31(tt,N)) , Marked_mark(N)>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(U221(tt,N,XS)) , Marked_mark(fst(splitAt(N,XS)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(U211(tt,XS)) , Marked_mark(XS)>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(U21(tt,X)) , Marked_mark(X)>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(U202(pair(YS,ZS),X)) , Marked_mark(pair(cons(X,YS),ZS))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(U201(tt,N,X,XS)) , Marked_mark(U202(splitAt(N,XS),X))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(U191(tt,XS)) , Marked_mark(pair(nil,XS))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(U181(tt,Y)) , Marked_mark(Y)>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(U171(tt,N,XS)) , Marked_mark(head(afterNth(N,XS)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(U161(tt,N)) , Marked_mark(cons(N,natsFrom(s(N))))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(U152(tt,V2)) , Marked_mark(U153(isLNat(V2)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(U151(tt,V1,V2)) , Marked_mark(U152(isNatural(V1),V2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(U142(tt,V2)) , Marked_mark(U143(isLNat(V2)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(U141(tt,V1,V2)) , Marked_mark(U142(isLNat(V1),V2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(U132(tt,V2)) , Marked_mark(U133(isLNat(V2)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(U131(tt,V1,V2)) , Marked_mark(U132(isNatural(V1),V2))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(U121(tt,V1)) , Marked_mark(U122(isNatural(V1)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(U111(tt,V1)) , Marked_mark(U112(isLNat(V1)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(U11(tt,N,XS)) , Marked_mark(snd(splitAt(N,XS)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(U102(tt,V2)) , Marked_mark(U103(isLNat(V2)))>
  <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),mark(X2)))> 
     --> <Marked_active(U101(tt,V1,V2)) , Marked_mark(U102(isNatural(V1),V2))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(sel(X1,X2)) , Marked_active(sel(mark(X1),mark(X2)))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_active(take(mark(X1),mark(X2)))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(tail(X)) , Marked_mark(X)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(tail(X)) , Marked_active(tail(mark(X)))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(isPLNatKind(X)) , Marked_active(isPLNatKind(X))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(isLNatKind(X)) , Marked_active(isLNatKind(X))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(isNaturalKind(X)) , Marked_active(isNaturalKind(X))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U92(X)) , Marked_mark(X)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U92(X)) , Marked_active(U92(mark(X)))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U91(X1,X2)) , Marked_active(U91(mark(X1),X2))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U82(X)) , Marked_mark(X)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U82(X)) , Marked_active(U82(mark(X)))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U81(X1,X2)) , Marked_active(U81(mark(X1),X2))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U72(X)) , Marked_mark(X)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U72(X)) , Marked_active(U72(mark(X)))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U71(X1,X2)) , Marked_active(U71(mark(X1),X2))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(isPLNat(X)) , Marked_active(isPLNat(X))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U62(X)) , Marked_mark(X)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U62(X)) , Marked_active(U62(mark(X)))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U61(X1,X2)) , Marked_active(U61(mark(X1),X2))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U53(X)) , Marked_mark(X)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U53(X)) , Marked_active(U53(mark(X)))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U52(X1,X2)) , Marked_active(U52(mark(X1),X2))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U51(X1,X2,X3)) , Marked_active(U51(mark(X1),X2,X3))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U43(X)) , Marked_mark(X)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U43(X)) , Marked_active(U43(mark(X)))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U42(X1,X2)) , Marked_active(U42(mark(X1),X2))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_active(U41(mark(X1),X2,X3))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_active(U31(mark(X1),X2))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(fst(X)) , Marked_mark(X)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(fst(X)) , Marked_active(fst(mark(X)))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U221(X1,X2,X3)) , Marked_active(U221(mark(X1),X2,X3))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U211(X1,X2)) , Marked_active(U211(mark(X1),X2))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2)) , Marked_active(U21(mark(X1),X2))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U202(X1,X2)) , Marked_active(U202(mark(X1),X2))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_mark(X1)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U201(X1,X2,X3,X4)) , Marked_active(U201(mark(X1),
                                                          X2,X3,X4))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(pair(X1,X2)) , Marked_active(pair(mark(X1),mark(X2)))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U191(X1,X2)) , Marked_active(U191(mark(X1),X2))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U181(X1,X2)) , Marked_active(U181(mark(X1),X2))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(afterNth(X1,X2)) , Marked_active(afterNth(mark(X1),
                                                        mark(X2)))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(head(X)) , Marked_mark(X)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(head(X)) , Marked_active(head(mark(X)))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U171(X1,X2,X3)) , Marked_active(U171(mark(X1),X2,X3))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(natsFrom(X)) , Marked_mark(X)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(natsFrom(X)) , Marked_active(natsFrom(mark(X)))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(head(X)) , Marked_mark(X)> 
     --> <Marked_mark(U1