The TRS could not be proven terminating. The proof attempt took 60019 ms.
Problem 1 remains open; application of the following processors failed [DependencyGraph (timeout)].
| 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) |
| 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)) |
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