TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60019 ms.

The following DP Processors were used


Problem 1 remains open; application of the following processors failed [DependencyGraph (timeout)].

The following open problems remain:



Open Dependency Pair Problem 1

Dependency Pairs

proper#(cons(X1, X2))proper#(X1)active#(U51(X1, X2))active#(X1)
proper#(U11(X1, X2, X3))proper#(X3)proper#(tail(X))proper#(X)
active#(U64(X1, X2))active#(X1)tail#(ok(X))tail#(X)
U51#(mark(X1), X2)U51#(X1, X2)U72#(mark(X1), X2)U72#(X1, X2)
proper#(U11(X1, X2, X3))proper#(X2)active#(splitAt(0, XS))pair#(nil, XS)
top#(mark(X))proper#(X)proper#(U62(X1, X2, X3, X4))U62#(proper(X1), proper(X2), proper(X3), proper(X4))
active#(U63(X1, X2, X3, X4))U63#(active(X1), X2, X3, X4)proper#(U72(X1, X2))proper#(X2)
proper#(U71(X1, X2))U71#(proper(X1), proper(X2))active#(U81(X1, X2, X3))active#(X1)
splitAt#(X1, mark(X2))splitAt#(X1, X2)active#(afterNth(X1, X2))afterNth#(active(X1), X2)
active#(U12(X1, X2, X3))active#(X1)proper#(U42(X1, X2, X3))U42#(proper(X1), proper(X2), proper(X3))
sel#(ok(X1), ok(X2))sel#(X1, X2)proper#(splitAt(X1, X2))proper#(X2)
active#(U72(X1, X2))active#(X1)proper#(U82(X1, X2, X3))proper#(X1)
active#(U82(tt, N, XS))fst#(splitAt(N, XS))active#(U64(pair(YS, ZS), X))pair#(cons(X, YS), ZS)
proper#(U12(X1, X2, X3))proper#(X1)proper#(U63(X1, X2, X3, X4))proper#(X3)
proper#(U52(X1, X2))proper#(X1)proper#(head(X))proper#(X)
proper#(U62(X1, X2, X3, X4))proper#(X2)natsFrom#(mark(X))natsFrom#(X)
active#(U41(X1, X2, X3))U41#(active(X1), X2, X3)active#(U52(X1, X2))active#(X1)
active#(U12(X1, X2, X3))U12#(active(X1), X2, X3)active#(snd(X))snd#(active(X))
active#(sel(X1, X2))active#(X1)U63#(mark(X1), X2, X3, X4)U63#(X1, X2, X3, X4)
U52#(ok(X1), ok(X2))U52#(X1, X2)proper#(U41(X1, X2, X3))proper#(X1)
active#(U22(X1, X2))active#(X1)active#(U31(X1, X2))active#(X1)
proper#(U51(X1, X2))proper#(X2)take#(ok(X1), ok(X2))take#(X1, X2)
active#(head(cons(N, XS)))U31#(tt, N)active#(take(N, XS))U81#(tt, N, XS)
proper#(U22(X1, X2))U22#(proper(X1), proper(X2))U41#(ok(X1), ok(X2), ok(X3))U41#(X1, X2, X3)
active#(U21(X1, X2))U21#(active(X1), X2)active#(sel(X1, X2))sel#(X1, active(X2))
active#(sel(X1, X2))sel#(active(X1), X2)snd#(mark(X))snd#(X)
active#(afterNth(X1, X2))active#(X2)proper#(pair(X1, X2))pair#(proper(X1), proper(X2))
U63#(ok(X1), ok(X2), ok(X3), ok(X4))U63#(X1, X2, X3, X4)proper#(tail(X))tail#(proper(X))
U22#(ok(X1), ok(X2))U22#(X1, X2)active#(U62(tt, N, X, XS))U63#(tt, N, X, XS)
active#(U63(X1, X2, X3, X4))active#(X1)proper#(U31(X1, X2))U31#(proper(X1), proper(X2))
proper#(U21(X1, X2))proper#(X1)U31#(ok(X1), ok(X2))U31#(X1, X2)
U52#(mark(X1), X2)U52#(X1, X2)proper#(U81(X1, X2, X3))U81#(proper(X1), proper(X2), proper(X3))
active#(U22(X1, X2))U22#(active(X1), X2)afterNth#(X1, mark(X2))afterNth#(X1, X2)
cons#(ok(X1), ok(X2))cons#(X1, X2)active#(U42(X1, X2, X3))active#(X1)
proper#(U72(X1, X2))U72#(proper(X1), proper(X2))active#(U64(pair(YS, ZS), X))cons#(X, YS)
U71#(ok(X1), ok(X2))U71#(X1, X2)proper#(U71(X1, X2))proper#(X2)
proper#(U51(X1, X2))U51#(proper(X1), proper(X2))active#(sel(X1, X2))active#(X2)
active#(U51(X1, X2))U51#(active(X1), X2)afterNth#(mark(X1), X2)afterNth#(X1, X2)
proper#(U81(X1, X2, X3))proper#(X2)proper#(U32(X1, X2))proper#(X1)
proper#(U41(X1, X2, X3))U41#(proper(X1), proper(X2), proper(X3))proper#(afterNth(X1, X2))proper#(X1)
proper#(fst(X))fst#(proper(X))proper#(pair(X1, X2))proper#(X2)
active#(pair(X1, X2))pair#(active(X1), X2)U11#(mark(X1), X2, X3)U11#(X1, X2, X3)
tail#(mark(X))tail#(X)take#(X1, mark(X2))take#(X1, X2)
proper#(U12(X1, X2, X3))proper#(X3)proper#(pair(X1, X2))proper#(X1)
proper#(s(X))proper#(X)U32#(ok(X1), ok(X2))U32#(X1, X2)
active#(U62(X1, X2, X3, X4))U62#(active(X1), X2, X3, X4)proper#(U64(X1, X2))proper#(X1)
proper#(natsFrom(X))natsFrom#(proper(X))proper#(take(X1, X2))take#(proper(X1), proper(X2))
proper#(U62(X1, X2, X3, X4))proper#(X3)proper#(U32(X1, X2))U32#(proper(X1), proper(X2))
active#(snd(X))active#(X)active#(cons(X1, X2))active#(X1)
sel#(mark(X1), X2)sel#(X1, X2)U61#(ok(X1), ok(X2), ok(X3), ok(X4))U61#(X1, X2, X3, X4)
proper#(U81(X1, X2, X3))proper#(X3)active#(U82(X1, X2, X3))active#(X1)
take#(mark(X1), X2)take#(X1, X2)proper#(U31(X1, X2))proper#(X2)
active#(pair(X1, X2))pair#(X1, active(X2))active#(U31(tt, N))U32#(tt, N)
active#(natsFrom(X))active#(X)active#(U11(X1, X2, X3))U11#(active(X1), X2, X3)
proper#(U51(X1, X2))proper#(X1)proper#(sel(X1, X2))sel#(proper(X1), proper(X2))
active#(afterNth(N, XS))U11#(tt, N, XS)splitAt#(ok(X1), ok(X2))splitAt#(X1, X2)
active#(fst(pair(X, Y)))U21#(tt, X)proper#(take(X1, X2))proper#(X1)
fst#(mark(X))fst#(X)proper#(U64(X1, X2))U64#(proper(X1), proper(X2))
proper#(U81(X1, X2, X3))proper#(X1)proper#(U42(X1, X2, X3))proper#(X2)
active#(U71(X1, X2))active#(X1)active#(natsFrom(X))natsFrom#(active(X))
active#(U61(tt, N, X, XS))U62#(tt, N, X, XS)active#(fst(X))fst#(active(X))
proper#(take(X1, X2))proper#(X2)active#(take(X1, X2))active#(X1)
proper#(U61(X1, X2, X3, X4))U61#(proper(X1), proper(X2), proper(X3), proper(X4))active#(U61(X1, X2, X3, X4))active#(X1)
active#(splitAt(s(N), cons(X, XS)))U61#(tt, N, X, XS)proper#(U11(X1, X2, X3))U11#(proper(X1), proper(X2), proper(X3))
U72#(ok(X1), ok(X2))U72#(X1, X2)s#(mark(X))s#(X)
active#(U63(tt, N, X, XS))U64#(splitAt(N, XS), X)active#(s(X))active#(X)
active#(tail(X))active#(X)proper#(afterNth(X1, X2))afterNth#(proper(X1), proper(X2))
U21#(ok(X1), ok(X2))U21#(X1, X2)active#(U82(X1, X2, X3))U82#(active(X1), X2, X3)
proper#(splitAt(X1, X2))proper#(X1)U42#(ok(X1), ok(X2), ok(X3))U42#(X1, X2, X3)
U64#(ok(X1), ok(X2))U64#(X1, X2)active#(U42(X1, X2, X3))U42#(active(X1), X2, X3)
proper#(U41(X1, X2, X3))proper#(X2)splitAt#(mark(X1), X2)splitAt#(X1, X2)
proper#(snd(X))snd#(proper(X))proper#(U32(X1, X2))proper#(X2)
active#(take(X1, X2))take#(active(X1), X2)active#(splitAt(X1, X2))splitAt#(active(X1), X2)
proper#(U62(X1, X2, X3, X4))proper#(X4)active#(tail(cons(N, XS)))U71#(tt, XS)
active#(splitAt(X1, X2))splitAt#(X1, active(X2))active#(sel(N, XS))U41#(tt, N, XS)
U12#(mark(X1), X2, X3)U12#(X1, X2, X3)active#(U51(tt, Y))U52#(tt, Y)
active#(take(X1, X2))active#(X2)U62#(mark(X1), X2, X3, X4)U62#(X1, X2, X3, X4)
proper#(U63(X1, X2, X3, X4))proper#(X2)pair#(X1, mark(X2))pair#(X1, X2)
sel#(X1, mark(X2))sel#(X1, X2)active#(U41(X1, X2, X3))active#(X1)
head#(ok(X))head#(X)proper#(U42(X1, X2, X3))proper#(X3)
active#(snd(pair(X, Y)))U51#(tt, Y)U11#(ok(X1), ok(X2), ok(X3))U11#(X1, X2, X3)
pair#(mark(X1), X2)pair#(X1, X2)U22#(mark(X1), X2)U22#(X1, X2)
active#(U41(tt, N, XS))U42#(tt, N, XS)cons#(mark(X1), X2)cons#(X1, X2)
U61#(mark(X1), X2, X3, X4)U61#(X1, X2, X3, X4)active#(U52(X1, X2))U52#(active(X1), X2)
active#(afterNth(X1, X2))afterNth#(X1, active(X2))active#(U61(X1, X2, X3, X4))U61#(active(X1), X2, X3, X4)
active#(U12(tt, N, XS))snd#(splitAt(N, XS))active#(U42(tt, N, XS))head#(afterNth(N, XS))
top#(ok(X))active#(X)U82#(mark(X1), X2, X3)U82#(X1, X2, X3)
U64#(mark(X1), X2)U64#(X1, X2)active#(pair(X1, X2))active#(X1)
natsFrom#(ok(X))natsFrom#(X)U71#(mark(X1), X2)U71#(X1, X2)
proper#(sel(X1, X2))proper#(X2)proper#(U61(X1, X2, X3, X4))proper#(X4)
U51#(ok(X1), ok(X2))U51#(X1, X2)pair#(ok(X1), ok(X2))pair#(X1, X2)
head#(mark(X))head#(X)proper#(U12(X1, X2, X3))proper#(X2)
proper#(U12(X1, X2, X3))U12#(proper(X1), proper(X2), proper(X3))active#(head(X))head#(active(X))
proper#(U72(X1, X2))proper#(X1)active#(s(X))s#(active(X))
proper#(U42(X1, X2, X3))proper#(X1)s#(ok(X))s#(X)
U81#(ok(X1), ok(X2), ok(X3))U81#(X1, X2, X3)proper#(U11(X1, X2, X3))proper#(X1)
proper#(sel(X1, X2))proper#(X1)active#(U32(X1, X2))U32#(active(X1), X2)
active#(U32(X1, X2))active#(X1)active#(U72(X1, X2))U72#(active(X1), X2)
active#(U81(tt, N, XS))U82#(tt, N, XS)active#(take(X1, X2))take#(X1, active(X2))
proper#(s(X))s#(proper(X))active#(splitAt(X1, X2))active#(X1)
proper#(U63(X1, X2, X3, X4))proper#(X4)active#(natsFrom(N))natsFrom#(s(N))
top#(ok(X))top#(active(X))active#(U62(X1, X2, X3, X4))active#(X1)
proper#(natsFrom(X))proper#(X)proper#(U31(X1, X2))proper#(X1)
active#(U12(tt, N, XS))splitAt#(N, XS)proper#(U52(X1, X2))U52#(proper(X1), proper(X2))
active#(cons(X1, X2))cons#(active(X1), X2)proper#(U64(X1, X2))proper#(X2)
active#(tail(X))tail#(active(X))U82#(ok(X1), ok(X2), ok(X3))U82#(X1, X2, X3)
active#(pair(X1, X2))active#(X2)snd#(ok(X))snd#(X)
active#(head(X))active#(X)U81#(mark(X1), X2, X3)U81#(X1, X2, X3)
top#(mark(X))top#(proper(X))U42#(mark(X1), X2, X3)U42#(X1, X2, X3)
proper#(cons(X1, X2))proper#(X2)active#(U42(tt, N, XS))afterNth#(N, XS)
proper#(U22(X1, X2))proper#(X2)proper#(U61(X1, X2, X3, X4))proper#(X2)
proper#(afterNth(X1, X2))proper#(X2)active#(U11(X1, X2, X3))active#(X1)
proper#(snd(X))proper#(X)proper#(U63(X1, X2, X3, X4))proper#(X1)
proper#(head(X))head#(proper(X))U62#(ok(X1), ok(X2), ok(X3), ok(X4))U62#(X1, X2, X3, X4)
U12#(ok(X1), ok(X2), ok(X3))U12#(X1, X2, X3)proper#(U82(X1, X2, X3))U82#(proper(X1), proper(X2), proper(X3))
proper#(splitAt(X1, X2))splitAt#(proper(X1), proper(X2))active#(U71(tt, XS))U72#(tt, XS)
active#(U81(X1, X2, X3))U81#(active(X1), X2, X3)proper#(U82(X1, X2, X3))proper#(X3)
active#(U11(tt, N, XS))U12#(tt, N, XS)active#(U71(X1, X2))U71#(active(X1), X2)
active#(natsFrom(N))s#(N)proper#(U41(X1, X2, X3))proper#(X3)
proper#(fst(X))proper#(X)afterNth#(ok(X1), ok(X2))afterNth#(X1, X2)
proper#(U21(X1, X2))proper#(X2)proper#(U61(X1, X2, X3, X4))proper#(X3)
proper#(U22(X1, X2))proper#(X1)active#(U64(X1, X2))U64#(active(X1), X2)
active#(afterNth(X1, X2))active#(X1)active#(splitAt(X1, X2))active#(X2)
active#(U31(X1, X2))U31#(active(X1), X2)proper#(U71(X1, X2))proper#(X1)
U41#(mark(X1), X2, X3)U41#(X1, X2, X3)proper#(U21(X1, X2))U21#(proper(X1), proper(X2))
proper#(U63(X1, X2, X3, X4))U63#(proper(X1), proper(X2), proper(X3), proper(X4))active#(fst(X))active#(X)
active#(U63(tt, N, X, XS))splitAt#(N, XS)U31#(mark(X1), X2)U31#(X1, X2)
fst#(ok(X))fst#(X)proper#(U52(X1, X2))proper#(X2)
active#(U21(X1, X2))active#(X1)proper#(cons(X1, X2))cons#(proper(X1), proper(X2))
proper#(U82(X1, X2, X3))proper#(X2)U21#(mark(X1), X2)U21#(X1, X2)
U32#(mark(X1), X2)U32#(X1, X2)proper#(U62(X1, X2, X3, X4))proper#(X1)
active#(U82(tt, N, XS))splitAt#(N, XS)active#(natsFrom(N))cons#(N, natsFrom(s(N)))
active#(U21(tt, X))U22#(tt, X)proper#(U61(X1, X2, X3, X4))proper#(X1)

Rewrite Rules

active(U11(tt, N, XS))mark(U12(tt, N, XS))active(U12(tt, N, XS))mark(snd(splitAt(N, XS)))
active(U21(tt, X))mark(U22(tt, X))active(U22(tt, X))mark(X)
active(U31(tt, N))mark(U32(tt, N))active(U32(tt, N))mark(N)
active(U41(tt, N, XS))mark(U42(tt, N, XS))active(U42(tt, N, XS))mark(head(afterNth(N, XS)))
active(U51(tt, Y))mark(U52(tt, Y))active(U52(tt, Y))mark(Y)
active(U61(tt, N, X, XS))mark(U62(tt, N, X, XS))active(U62(tt, N, X, XS))mark(U63(tt, N, X, XS))
active(U63(tt, N, X, XS))mark(U64(splitAt(N, XS), X))active(U64(pair(YS, ZS), X))mark(pair(cons(X, YS), ZS))
active(U71(tt, XS))mark(U72(tt, XS))active(U72(tt, XS))mark(XS)
active(U81(tt, N, XS))mark(U82(tt, N, XS))active(U82(tt, N, XS))mark(fst(splitAt(N, XS)))
active(afterNth(N, XS))mark(U11(tt, N, XS))active(fst(pair(X, Y)))mark(U21(tt, X))
active(head(cons(N, XS)))mark(U31(tt, N))active(natsFrom(N))mark(cons(N, natsFrom(s(N))))
active(sel(N, XS))mark(U41(tt, N, XS))active(snd(pair(X, Y)))mark(U51(tt, Y))
active(splitAt(0, XS))mark(pair(nil, XS))active(splitAt(s(N), cons(X, XS)))mark(U61(tt, N, X, XS))
active(tail(cons(N, XS)))mark(U71(tt, XS))active(take(N, XS))mark(U81(tt, N, XS))
active(U11(X1, X2, X3))U11(active(X1), X2, X3)active(U12(X1, X2, X3))U12(active(X1), X2, X3)
active(snd(X))snd(active(X))active(splitAt(X1, X2))splitAt(active(X1), X2)
active(splitAt(X1, X2))splitAt(X1, active(X2))active(U21(X1, X2))U21(active(X1), X2)
active(U22(X1, X2))U22(active(X1), X2)active(U31(X1, X2))U31(active(X1), X2)
active(U32(X1, X2))U32(active(X1), X2)active(U41(X1, X2, X3))U41(active(X1), X2, X3)
active(U42(X1, X2, X3))U42(active(X1), X2, X3)active(head(X))head(active(X))
active(afterNth(X1, X2))afterNth(active(X1), X2)active(afterNth(X1, X2))afterNth(X1, active(X2))
active(U51(X1, X2))U51(active(X1), X2)active(U52(X1, X2))U52(active(X1), X2)
active(U61(X1, X2, X3, X4))U61(active(X1), X2, X3, X4)active(U62(X1, X2, X3, X4))U62(active(X1), X2, X3, X4)
active(U63(X1, X2, X3, X4))U63(active(X1), X2, X3, X4)active(U64(X1, X2))U64(active(X1), X2)
active(pair(X1, X2))pair(active(X1), X2)active(pair(X1, X2))pair(X1, active(X2))
active(cons(X1, X2))cons(active(X1), X2)active(U71(X1, X2))U71(active(X1), X2)
active(U72(X1, X2))U72(active(X1), X2)active(U81(X1, X2, X3))U81(active(X1), X2, X3)
active(U82(X1, X2, X3))U82(active(X1), X2, X3)active(fst(X))fst(active(X))
active(natsFrom(X))natsFrom(active(X))active(s(X))s(active(X))
active(sel(X1, X2))sel(active(X1), X2)active(sel(X1, X2))sel(X1, active(X2))
active(tail(X))tail(active(X))active(take(X1, X2))take(active(X1), X2)
active(take(X1, X2))take(X1, active(X2))U11(mark(X1), X2, X3)mark(U11(X1, X2, X3))
U12(mark(X1), X2, X3)mark(U12(X1, X2, X3))snd(mark(X))mark(snd(X))
splitAt(mark(X1), X2)mark(splitAt(X1, X2))splitAt(X1, mark(X2))mark(splitAt(X1, X2))
U21(mark(X1), X2)mark(U21(X1, X2))U22(mark(X1), X2)mark(U22(X1, X2))
U31(mark(X1), X2)mark(U31(X1, X2))U32(mark(X1), X2)mark(U32(X1, X2))
U41(mark(X1), X2, X3)mark(U41(X1, X2, X3))U42(mark(X1), X2, X3)mark(U42(X1, X2, X3))
head(mark(X))mark(head(X))afterNth(mark(X1), X2)mark(afterNth(X1, X2))
afterNth(X1, mark(X2))mark(afterNth(X1, X2))U51(mark(X1), X2)mark(U51(X1, X2))
U52(mark(X1), X2)mark(U52(X1, X2))U61(mark(X1), X2, X3, X4)mark(U61(X1, X2, X3, X4))
U62(mark(X1), X2, X3, X4)mark(U62(X1, X2, X3, X4))U63(mark(X1), X2, X3, X4)mark(U63(X1, X2, X3, X4))
U64(mark(X1), X2)mark(U64(X1, X2))pair(mark(X1), X2)mark(pair(X1, X2))
pair(X1, mark(X2))mark(pair(X1, X2))cons(mark(X1), X2)mark(cons(X1, X2))
U71(mark(X1), X2)mark(U71(X1, X2))U72(mark(X1), X2)mark(U72(X1, X2))
U81(mark(X1), X2, X3)mark(U81(X1, X2, X3))U82(mark(X1), X2, X3)mark(U82(X1, X2, X3))
fst(mark(X))mark(fst(X))natsFrom(mark(X))mark(natsFrom(X))
s(mark(X))mark(s(X))sel(mark(X1), X2)mark(sel(X1, X2))
sel(X1, mark(X2))mark(sel(X1, X2))tail(mark(X))mark(tail(X))
take(mark(X1), X2)mark(take(X1, X2))take(X1, mark(X2))mark(take(X1, X2))
proper(U11(X1, X2, X3))U11(proper(X1), proper(X2), proper(X3))proper(tt)ok(tt)
proper(U12(X1, X2, X3))U12(proper(X1), proper(X2), proper(X3))proper(snd(X))snd(proper(X))
proper(splitAt(X1, X2))splitAt(proper(X1), proper(X2))proper(U21(X1, X2))U21(proper(X1), proper(X2))
proper(U22(X1, X2))U22(proper(X1), proper(X2))proper(U31(X1, X2))U31(proper(X1), proper(X2))
proper(U32(X1, X2))U32(proper(X1), proper(X2))proper(U41(X1, X2, X3))U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3))U42(proper(X1), proper(X2), proper(X3))proper(head(X))head(proper(X))
proper(afterNth(X1, X2))afterNth(proper(X1), proper(X2))proper(U51(X1, X2))U51(proper(X1), proper(X2))
proper(U52(X1, X2))U52(proper(X1), proper(X2))proper(U61(X1, X2, X3, X4))U61(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U62(X1, X2, X3, X4))U62(proper(X1), proper(X2), proper(X3), proper(X4))proper(U63(X1, X2, X3, X4))U63(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U64(X1, X2))U64(proper(X1), proper(X2))proper(pair(X1, X2))pair(proper(X1), proper(X2))
proper(cons(X1, X2))cons(proper(X1), proper(X2))proper(U71(X1, X2))U71(proper(X1), proper(X2))
proper(U72(X1, X2))U72(proper(X1), proper(X2))proper(U81(X1, X2, X3))U81(proper(X1), proper(X2), proper(X3))
proper(U82(X1, X2, X3))U82(proper(X1), proper(X2), proper(X3))proper(fst(X))fst(proper(X))
proper(natsFrom(X))natsFrom(proper(X))proper(s(X))s(proper(X))
proper(sel(X1, X2))sel(proper(X1), proper(X2))proper(0)ok(0)
proper(nil)ok(nil)proper(tail(X))tail(proper(X))
proper(take(X1, X2))take(proper(X1), proper(X2))U11(ok(X1), ok(X2), ok(X3))ok(U11(X1, X2, X3))
U12(ok(X1), ok(X2), ok(X3))ok(U12(X1, X2, X3))snd(ok(X))ok(snd(X))
splitAt(ok(X1), ok(X2))ok(splitAt(X1, X2))U21(ok(X1), ok(X2))ok(U21(X1, X2))
U22(ok(X1), ok(X2))ok(U22(X1, X2))U31(ok(X1), ok(X2))ok(U31(X1, X2))
U32(ok(X1), ok(X2))ok(U32(X1, X2))U41(ok(X1), ok(X2), ok(X3))ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3))ok(U42(X1, X2, X3))head(ok(X))ok(head(X))
afterNth(ok(X1), ok(X2))ok(afterNth(X1, X2))U51(ok(X1), ok(X2))ok(U51(X1, X2))
U52(ok(X1), ok(X2))ok(U52(X1, X2))U61(ok(X1), ok(X2), ok(X3), ok(X4))ok(U61(X1, X2, X3, X4))
U62(ok(X1), ok(X2), ok(X3), ok(X4))ok(U62(X1, X2, X3, X4))U63(ok(X1), ok(X2), ok(X3), ok(X4))ok(U63(X1, X2, X3, X4))
U64(ok(X1), ok(X2))ok(U64(X1, X2))pair(ok(X1), ok(X2))ok(pair(X1, X2))
cons(ok(X1), ok(X2))ok(cons(X1, X2))U71(ok(X1), ok(X2))ok(U71(X1, X2))
U72(ok(X1), ok(X2))ok(U72(X1, X2))U81(ok(X1), ok(X2), ok(X3))ok(U81(X1, X2, X3))
U82(ok(X1), ok(X2), ok(X3))ok(U82(X1, X2, X3))fst(ok(X))ok(fst(X))
natsFrom(ok(X))ok(natsFrom(X))s(ok(X))ok(s(X))
sel(ok(X1), ok(X2))ok(sel(X1, X2))tail(ok(X))ok(tail(X))
take(ok(X1), ok(X2))ok(take(X1, X2))top(mark(X))top(proper(X))
top(ok(X))top(active(X))

Original Signature

Termination of terms over the following signature is verified: pair, natsFrom, fst, U64, U63, U62, U61, U42, U41, ok, proper, head, U21, top, U22, snd, cons, mark, tail, splitAt, U71, U72, 0, s, U51, tt, take, U82, U81, U52, U11, active, U12, U31, afterNth, U32, sel, nil