The TRS could not be proven terminating. The proof attempt took 60001 ms.
Problem 1 remains open; application of the following processors failed [DependencyGraph (24913ms), SubtermCriterion (2ms), DependencyGraph (23581ms), PolynomialLinearRange4iUR (timeout), DependencyGraph (timeout)].
| mark#(pair(X1, X2)) | → | mark#(X2) | a__U51#(tt, Y) | → | a__U52#(tt, Y) | |
| a__U82#(tt, N, XS) | → | mark#(XS) | a__snd#(pair(X, Y)) | → | a__U51#(tt, Y) | |
| a__U12#(tt, N, XS) | → | a__splitAt#(mark(N), mark(XS)) | mark#(U64(X1, X2)) | → | mark#(X1) | |
| mark#(U12(X1, X2, X3)) | → | a__U12#(mark(X1), X2, X3) | a__U41#(tt, N, XS) | → | a__U42#(tt, N, XS) | |
| a__U21#(tt, X) | → | a__U22#(tt, X) | mark#(s(X)) | → | mark#(X) | |
| mark#(sel(X1, X2)) | → | mark#(X1) | mark#(U72(X1, X2)) | → | mark#(X1) | |
| mark#(cons(X1, X2)) | → | mark#(X1) | mark#(U42(X1, X2, X3)) | → | mark#(X1) | |
| mark#(U82(X1, X2, X3)) | → | mark#(X1) | mark#(afterNth(X1, X2)) | → | mark#(X1) | |
| mark#(U61(X1, X2, X3, X4)) | → | a__U61#(mark(X1), X2, X3, X4) | mark#(pair(X1, X2)) | → | mark#(X1) | |
| a__afterNth#(N, XS) | → | a__U11#(tt, N, XS) | mark#(U41(X1, X2, X3)) | → | mark#(X1) | |
| mark#(tail(X)) | → | mark#(X) | mark#(U32(X1, X2)) | → | mark#(X1) | |
| a__U63#(tt, N, X, XS) | → | a__splitAt#(mark(N), mark(XS)) | mark#(afterNth(X1, X2)) | → | mark#(X2) | |
| a__U71#(tt, XS) | → | a__U72#(tt, XS) | mark#(U11(X1, X2, X3)) | → | mark#(X1) | |
| a__tail#(cons(N, XS)) | → | a__U71#(tt, XS) | a__U22#(tt, X) | → | mark#(X) | |
| a__U12#(tt, N, XS) | → | mark#(XS) | mark#(U41(X1, X2, X3)) | → | a__U41#(mark(X1), X2, X3) | |
| mark#(U64(X1, X2)) | → | a__U64#(mark(X1), X2) | mark#(U81(X1, X2, X3)) | → | mark#(X1) | |
| a__U72#(tt, XS) | → | mark#(XS) | a__U64#(pair(YS, ZS), X) | → | mark#(ZS) | |
| mark#(U22(X1, X2)) | → | mark#(X1) | mark#(head(X)) | → | mark#(X) | |
| mark#(splitAt(X1, X2)) | → | mark#(X1) | a__U31#(tt, N) | → | a__U32#(tt, N) | |
| mark#(head(X)) | → | a__head#(mark(X)) | mark#(U52(X1, X2)) | → | a__U52#(mark(X1), X2) | |
| mark#(fst(X)) | → | a__fst#(mark(X)) | a__head#(cons(N, XS)) | → | a__U31#(tt, N) | |
| a__U12#(tt, N, XS) | → | mark#(N) | mark#(fst(X)) | → | mark#(X) | |
| mark#(U51(X1, X2)) | → | a__U51#(mark(X1), X2) | mark#(U72(X1, X2)) | → | a__U72#(mark(X1), X2) | |
| mark#(snd(X)) | → | mark#(X) | mark#(natsFrom(X)) | → | mark#(X) | |
| a__U81#(tt, N, XS) | → | a__U82#(tt, N, XS) | a__U32#(tt, N) | → | mark#(N) | |
| a__U64#(pair(YS, ZS), X) | → | mark#(X) | a__U63#(tt, N, X, XS) | → | mark#(N) | |
| mark#(take(X1, X2)) | → | a__take#(mark(X1), mark(X2)) | mark#(splitAt(X1, X2)) | → | a__splitAt#(mark(X1), mark(X2)) | |
| a__splitAt#(0, XS) | → | mark#(XS) | mark#(U62(X1, X2, X3, X4)) | → | a__U62#(mark(X1), X2, X3, X4) | |
| a__U62#(tt, N, X, XS) | → | a__U63#(tt, N, X, XS) | a__take#(N, XS) | → | a__U81#(tt, N, XS) | |
| a__U12#(tt, N, XS) | → | a__snd#(a__splitAt(mark(N), mark(XS))) | mark#(take(X1, X2)) | → | mark#(X1) | |
| mark#(afterNth(X1, X2)) | → | a__afterNth#(mark(X1), mark(X2)) | a__U52#(tt, Y) | → | mark#(Y) | |
| mark#(U22(X1, X2)) | → | a__U22#(mark(X1), X2) | a__U82#(tt, N, XS) | → | a__splitAt#(mark(N), mark(XS)) | |
| mark#(U31(X1, X2)) | → | mark#(X1) | mark#(U32(X1, X2)) | → | a__U32#(mark(X1), X2) | |
| mark#(U71(X1, X2)) | → | a__U71#(mark(X1), X2) | mark#(U63(X1, X2, X3, X4)) | → | mark#(X1) | |
| mark#(U61(X1, X2, X3, X4)) | → | mark#(X1) | mark#(U71(X1, X2)) | → | mark#(X1) | |
| a__splitAt#(s(N), cons(X, XS)) | → | a__U61#(tt, N, X, XS) | mark#(snd(X)) | → | a__snd#(mark(X)) | |
| a__U63#(tt, N, X, XS) | → | a__U64#(a__splitAt(mark(N), mark(XS)), X) | mark#(U42(X1, X2, X3)) | → | a__U42#(mark(X1), X2, X3) | |
| a__U42#(tt, N, XS) | → | a__afterNth#(mark(N), mark(XS)) | mark#(U11(X1, X2, X3)) | → | a__U11#(mark(X1), X2, X3) | |
| a__natsFrom#(N) | → | mark#(N) | a__U11#(tt, N, XS) | → | a__U12#(tt, N, XS) | |
| a__U82#(tt, N, XS) | → | a__fst#(a__splitAt(mark(N), mark(XS))) | a__sel#(N, XS) | → | a__U41#(tt, N, XS) | |
| mark#(U21(X1, X2)) | → | mark#(X1) | mark#(U31(X1, X2)) | → | a__U31#(mark(X1), X2) | |
| mark#(U51(X1, X2)) | → | mark#(X1) | mark#(U82(X1, X2, X3)) | → | a__U82#(mark(X1), X2, X3) | |
| mark#(sel(X1, X2)) | → | mark#(X2) | mark#(U62(X1, X2, X3, X4)) | → | mark#(X1) | |
| mark#(tail(X)) | → | a__tail#(mark(X)) | mark#(U12(X1, X2, X3)) | → | mark#(X1) | |
| a__U63#(tt, N, X, XS) | → | mark#(XS) | a__fst#(pair(X, Y)) | → | a__U21#(tt, X) | |
| mark#(U52(X1, X2)) | → | mark#(X1) | mark#(U63(X1, X2, X3, X4)) | → | a__U63#(mark(X1), X2, X3, X4) | |
| a__U82#(tt, N, XS) | → | mark#(N) | mark#(splitAt(X1, X2)) | → | mark#(X2) | |
| a__U42#(tt, N, XS) | → | mark#(XS) | a__U42#(tt, N, XS) | → | a__head#(a__afterNth(mark(N), mark(XS))) | |
| mark#(U21(X1, X2)) | → | a__U21#(mark(X1), X2) | mark#(sel(X1, X2)) | → | a__sel#(mark(X1), mark(X2)) | |
| mark#(take(X1, X2)) | → | mark#(X2) | a__U42#(tt, N, XS) | → | mark#(N) | |
| mark#(U81(X1, X2, X3)) | → | a__U81#(mark(X1), X2, X3) | a__U61#(tt, N, X, XS) | → | a__U62#(tt, N, X, XS) | |
| mark#(natsFrom(X)) | → | a__natsFrom#(mark(X)) |
| a__U11(tt, N, XS) | → | a__U12(tt, N, XS) | a__U12(tt, N, XS) | → | a__snd(a__splitAt(mark(N), mark(XS))) | |
| a__U21(tt, X) | → | a__U22(tt, X) | a__U22(tt, X) | → | mark(X) | |
| a__U31(tt, N) | → | a__U32(tt, N) | a__U32(tt, N) | → | mark(N) | |
| a__U41(tt, N, XS) | → | a__U42(tt, N, XS) | a__U42(tt, N, XS) | → | a__head(a__afterNth(mark(N), mark(XS))) | |
| a__U51(tt, Y) | → | a__U52(tt, Y) | a__U52(tt, Y) | → | mark(Y) | |
| a__U61(tt, N, X, XS) | → | a__U62(tt, N, X, XS) | a__U62(tt, N, X, XS) | → | a__U63(tt, N, X, XS) | |
| a__U63(tt, N, X, XS) | → | a__U64(a__splitAt(mark(N), mark(XS)), X) | a__U64(pair(YS, ZS), X) | → | pair(cons(mark(X), YS), mark(ZS)) | |
| a__U71(tt, XS) | → | a__U72(tt, XS) | a__U72(tt, XS) | → | mark(XS) | |
| a__U81(tt, N, XS) | → | a__U82(tt, N, XS) | a__U82(tt, N, XS) | → | a__fst(a__splitAt(mark(N), mark(XS))) | |
| a__afterNth(N, XS) | → | a__U11(tt, N, XS) | a__fst(pair(X, Y)) | → | a__U21(tt, X) | |
| a__head(cons(N, XS)) | → | a__U31(tt, N) | a__natsFrom(N) | → | cons(mark(N), natsFrom(s(N))) | |
| a__sel(N, XS) | → | a__U41(tt, N, XS) | a__snd(pair(X, Y)) | → | a__U51(tt, Y) | |
| a__splitAt(0, XS) | → | pair(nil, mark(XS)) | a__splitAt(s(N), cons(X, XS)) | → | a__U61(tt, N, X, XS) | |
| a__tail(cons(N, XS)) | → | a__U71(tt, XS) | a__take(N, XS) | → | a__U81(tt, N, XS) | |
| mark(U11(X1, X2, X3)) | → | a__U11(mark(X1), X2, X3) | mark(U12(X1, X2, X3)) | → | a__U12(mark(X1), X2, X3) | |
| mark(snd(X)) | → | a__snd(mark(X)) | mark(splitAt(X1, X2)) | → | a__splitAt(mark(X1), mark(X2)) | |
| mark(U21(X1, X2)) | → | a__U21(mark(X1), X2) | mark(U22(X1, X2)) | → | a__U22(mark(X1), X2) | |
| mark(U31(X1, X2)) | → | a__U31(mark(X1), X2) | mark(U32(X1, X2)) | → | a__U32(mark(X1), X2) | |
| mark(U41(X1, X2, X3)) | → | a__U41(mark(X1), X2, X3) | mark(U42(X1, X2, X3)) | → | a__U42(mark(X1), X2, X3) | |
| mark(head(X)) | → | a__head(mark(X)) | mark(afterNth(X1, X2)) | → | a__afterNth(mark(X1), mark(X2)) | |
| mark(U51(X1, X2)) | → | a__U51(mark(X1), X2) | mark(U52(X1, X2)) | → | a__U52(mark(X1), X2) | |
| mark(U61(X1, X2, X3, X4)) | → | a__U61(mark(X1), X2, X3, X4) | mark(U62(X1, X2, X3, X4)) | → | a__U62(mark(X1), X2, X3, X4) | |
| mark(U63(X1, X2, X3, X4)) | → | a__U63(mark(X1), X2, X3, X4) | mark(U64(X1, X2)) | → | a__U64(mark(X1), X2) | |
| mark(U71(X1, X2)) | → | a__U71(mark(X1), X2) | mark(U72(X1, X2)) | → | a__U72(mark(X1), X2) | |
| mark(U81(X1, X2, X3)) | → | a__U81(mark(X1), X2, X3) | mark(U82(X1, X2, X3)) | → | a__U82(mark(X1), X2, X3) | |
| mark(fst(X)) | → | a__fst(mark(X)) | mark(natsFrom(X)) | → | a__natsFrom(mark(X)) | |
| mark(sel(X1, X2)) | → | a__sel(mark(X1), mark(X2)) | mark(tail(X)) | → | a__tail(mark(X)) | |
| mark(take(X1, X2)) | → | a__take(mark(X1), mark(X2)) | mark(tt) | → | tt | |
| mark(pair(X1, X2)) | → | pair(mark(X1), mark(X2)) | mark(cons(X1, X2)) | → | cons(mark(X1), X2) | |
| mark(s(X)) | → | s(mark(X)) | mark(0) | → | 0 | |
| mark(nil) | → | nil | a__U11(X1, X2, X3) | → | U11(X1, X2, X3) | |
| a__U12(X1, X2, X3) | → | U12(X1, X2, X3) | a__snd(X) | → | snd(X) | |
| a__splitAt(X1, X2) | → | splitAt(X1, X2) | a__U21(X1, X2) | → | U21(X1, X2) | |
| a__U22(X1, X2) | → | U22(X1, X2) | a__U31(X1, X2) | → | U31(X1, X2) | |
| a__U32(X1, X2) | → | U32(X1, X2) | a__U41(X1, X2, X3) | → | U41(X1, X2, X3) | |
| a__U42(X1, X2, X3) | → | U42(X1, X2, X3) | a__head(X) | → | head(X) | |
| a__afterNth(X1, X2) | → | afterNth(X1, X2) | a__U51(X1, X2) | → | U51(X1, X2) | |
| a__U52(X1, X2) | → | U52(X1, X2) | a__U61(X1, X2, X3, X4) | → | U61(X1, X2, X3, X4) | |
| a__U62(X1, X2, X3, X4) | → | U62(X1, X2, X3, X4) | a__U63(X1, X2, X3, X4) | → | U63(X1, X2, X3, X4) | |
| a__U64(X1, X2) | → | U64(X1, X2) | a__U71(X1, X2) | → | U71(X1, X2) | |
| a__U72(X1, X2) | → | U72(X1, X2) | a__U81(X1, X2, X3) | → | U81(X1, X2, X3) | |
| a__U82(X1, X2, X3) | → | U82(X1, X2, X3) | a__fst(X) | → | fst(X) | |
| a__natsFrom(X) | → | natsFrom(X) | a__sel(X1, X2) | → | sel(X1, X2) | |
| a__tail(X) | → | tail(X) | a__take(X1, X2) | → | take(X1, X2) |
Termination of terms over the following signature is verified: natsFrom, a__natsFrom, fst, U64, U63, U62, U61, a__U41, a__U72, a__U71, a__U42, head, U21, U22, mark, tail, U71, U72, 0, a__U32, a__U82, a__U31, a__sel, a__U81, U31, U32, a__U51, a__U52, a__take, pair, U42, U41, a__fst, a__U22, a__head, a__snd, a__U21, cons, snd, a__U64, a__afterNth, a__U62, a__U63, splitAt, a__tail, s, U51, tt, a__splitAt, take, U82, U81, U52, U11, a__U12, U12, a__U11, afterNth, a__U61, sel, nil