The TRS could not be proven terminating. The proof attempt took 60023 ms.
Problem 1 remains open; application of the following processors failed [DependencyGraph (timeout)].
| U114#(ok(X1), ok(X2)) | → | U114#(X1, X2) | proper#(cons(X1, X2)) | → | proper#(X1) | |
| active#(U111(tt, L, N)) | → | U112#(isNatIListKind(L), L, N) | U94#(mark(X1), X2, X3) | → | U94#(X1, X2, X3) | |
| active#(U93(X1, X2, X3)) | → | active#(X1) | proper#(U131(X1, X2, X3, X4)) | → | proper#(X3) | |
| U51#(mark(X1), X2) | → | U51#(X1, X2) | active#(U106(X)) | → | active#(X) | |
| active#(isNatIListKind(cons(V1, V2))) | → | isNatKind#(V1) | proper#(U112(X1, X2, X3)) | → | proper#(X3) | |
| proper#(U132(X1, X2, X3, X4)) | → | proper#(X2) | active#(U111(X1, X2, X3)) | → | active#(X1) | |
| U81#(mark(X)) | → | U81#(X) | proper#(U104(X1, X2, X3)) | → | proper#(X2) | |
| proper#(U94(X1, X2, X3)) | → | proper#(X1) | active#(length(X)) | → | active#(X) | |
| active#(U101(tt, V1, V2)) | → | U102#(isNatKind(V1), V1, V2) | active#(U91(tt, V1, V2)) | → | isNatKind#(V1) | |
| active#(U121(X1, X2)) | → | active#(X1) | proper#(U23(X)) | → | U23#(proper(X)) | |
| U43#(ok(X1), ok(X2), ok(X3)) | → | U43#(X1, X2, X3) | proper#(U132(X1, X2, X3, X4)) | → | U132#(proper(X1), proper(X2), proper(X3), proper(X4)) | |
| active#(U32(tt, V)) | → | U33#(isNatList(V)) | U102#(mark(X1), X2, X3) | → | U102#(X1, X2, X3) | |
| proper#(U113(X1, X2, X3)) | → | proper#(X3) | proper#(isNatKind(X)) | → | isNatKind#(proper(X)) | |
| proper#(U104(X1, X2, X3)) | → | U104#(proper(X1), proper(X2), proper(X3)) | active#(U33(X)) | → | active#(X) | |
| active#(U43(tt, V1, V2)) | → | U44#(isNatIListKind(V2), V1, V2) | U45#(ok(X1), ok(X2)) | → | U45#(X1, X2) | |
| active#(U102(X1, X2, X3)) | → | U102#(active(X1), X2, X3) | active#(U93(tt, V1, V2)) | → | U94#(isNatIListKind(V2), V1, V2) | |
| active#(U132(tt, IL, M, N)) | → | isNat#(M) | proper#(U131(X1, X2, X3, X4)) | → | proper#(X4) | |
| active#(U45(tt, V2)) | → | U46#(isNatIList(V2)) | active#(U44(X1, X2, X3)) | → | active#(X1) | |
| active#(U52(X)) | → | active#(X) | active#(U22(X1, X2)) | → | active#(X1) | |
| proper#(U51(X1, X2)) | → | proper#(X2) | proper#(U91(X1, X2, X3)) | → | proper#(X3) | |
| proper#(U71(X)) | → | U71#(proper(X)) | U41#(ok(X1), ok(X2), ok(X3)) | → | U41#(X1, X2, X3) | |
| active#(isNatKind(length(V1))) | → | U71#(isNatIListKind(V1)) | active#(U21(X1, X2)) | → | U21#(active(X1), X2) | |
| active#(U12(tt, V1)) | → | isNatList#(V1) | proper#(U91(X1, X2, X3)) | → | U91#(proper(X1), proper(X2), proper(X3)) | |
| proper#(U121(X1, X2)) | → | proper#(X1) | U22#(ok(X1), ok(X2)) | → | U22#(X1, X2) | |
| U111#(mark(X1), X2, X3) | → | U111#(X1, X2, X3) | proper#(U134(X1, X2, X3, X4)) | → | proper#(X3) | |
| U91#(ok(X1), ok(X2), ok(X3)) | → | U91#(X1, X2, X3) | active#(U51(tt, V2)) | → | isNatIListKind#(V2) | |
| active#(U106(X)) | → | U106#(active(X)) | proper#(U21(X1, X2)) | → | proper#(X1) | |
| active#(U114(X1, X2)) | → | active#(X1) | active#(U31(tt, V)) | → | U32#(isNatIListKind(V), V) | |
| active#(U112(tt, L, N)) | → | U113#(isNat(N), L, N) | active#(isNatKind(s(V1))) | → | U81#(isNatKind(V1)) | |
| U12#(ok(X1), ok(X2)) | → | U12#(X1, X2) | active#(take(s(M), cons(N, IL))) | → | isNatIList#(IL) | |
| cons#(ok(X1), ok(X2)) | → | cons#(X1, X2) | proper#(U135(X1, X2, X3, X4)) | → | proper#(X1) | |
| active#(U42(X1, X2, X3)) | → | active#(X1) | active#(U101(tt, V1, V2)) | → | isNatKind#(V1) | |
| proper#(U96(X)) | → | U96#(proper(X)) | proper#(U51(X1, X2)) | → | U51#(proper(X1), proper(X2)) | |
| U122#(ok(X)) | → | U122#(X) | U61#(mark(X1), X2) | → | U61#(X1, X2) | |
| active#(U51(X1, X2)) | → | U51#(active(X1), X2) | active#(U101(X1, X2, X3)) | → | active#(X1) | |
| proper#(U121(X1, X2)) | → | U121#(proper(X1), proper(X2)) | proper#(U41(X1, X2, X3)) | → | U41#(proper(X1), proper(X2), proper(X3)) | |
| proper#(U103(X1, X2, X3)) | → | proper#(X3) | U61#(ok(X1), ok(X2)) | → | U61#(X1, X2) | |
| U71#(mark(X)) | → | U71#(X) | proper#(U106(X)) | → | proper#(X) | |
| active#(U11(tt, V1)) | → | isNatIListKind#(V1) | proper#(U111(X1, X2, X3)) | → | proper#(X2) | |
| U52#(ok(X)) | → | U52#(X) | take#(X1, mark(X2)) | → | take#(X1, X2) | |
| active#(U93(X1, X2, X3)) | → | U93#(active(X1), X2, X3) | active#(U134(X1, X2, X3, X4)) | → | U134#(active(X1), X2, X3, X4) | |
| proper#(U131(X1, X2, X3, X4)) | → | proper#(X1) | proper#(U136(X1, X2, X3, X4)) | → | U136#(proper(X1), proper(X2), proper(X3), proper(X4)) | |
| U32#(ok(X1), ok(X2)) | → | U32#(X1, X2) | active#(U13(X)) | → | U13#(active(X)) | |
| proper#(isNatList(X)) | → | isNatList#(proper(X)) | proper#(U135(X1, X2, X3, X4)) | → | proper#(X3) | |
| proper#(U45(X1, X2)) | → | proper#(X2) | active#(isNat(length(V1))) | → | U11#(isNatIListKind(V1), V1) | |
| active#(U33(X)) | → | U33#(active(X)) | proper#(take(X1, X2)) | → | take#(proper(X1), proper(X2)) | |
| active#(U96(X)) | → | U96#(active(X)) | U33#(ok(X)) | → | U33#(X) | |
| active#(cons(X1, X2)) | → | active#(X1) | active#(U43(tt, V1, V2)) | → | isNatIListKind#(V2) | |
| proper#(U105(X1, X2)) | → | proper#(X1) | U96#(ok(X)) | → | U96#(X) | |
| proper#(U31(X1, X2)) | → | proper#(X2) | proper#(U92(X1, X2, X3)) | → | U92#(proper(X1), proper(X2), proper(X3)) | |
| active#(U103(X1, X2, X3)) | → | U103#(active(X1), X2, X3) | active#(U91(tt, V1, V2)) | → | U92#(isNatKind(V1), V1, V2) | |
| proper#(U51(X1, X2)) | → | proper#(X1) | active#(U113(X1, X2, X3)) | → | U113#(active(X1), X2, X3) | |
| active#(U95(X1, X2)) | → | active#(X1) | U134#(mark(X1), X2, X3, X4) | → | U134#(X1, X2, X3, X4) | |
| U135#(ok(X1), ok(X2), ok(X3), ok(X4)) | → | U135#(X1, X2, X3, X4) | proper#(take(X1, X2)) | → | proper#(X1) | |
| active#(U114(tt, L)) | → | s#(length(L)) | proper#(U131(X1, X2, X3, X4)) | → | proper#(X2) | |
| proper#(U42(X1, X2, X3)) | → | proper#(X2) | proper#(U95(X1, X2)) | → | proper#(X2) | |
| U103#(ok(X1), ok(X2), ok(X3)) | → | U103#(X1, X2, X3) | U94#(ok(X1), ok(X2), ok(X3)) | → | U94#(X1, X2, X3) | |
| active#(U105(tt, V2)) | → | isNatIList#(V2) | active#(take(X1, X2)) | → | active#(X1) | |
| proper#(take(X1, X2)) | → | proper#(X2) | proper#(U33(X)) | → | U33#(proper(X)) | |
| s#(mark(X)) | → | s#(X) | active#(U31(tt, V)) | → | isNatIListKind#(V) | |
| proper#(U106(X)) | → | U106#(proper(X)) | active#(U45(X1, X2)) | → | U45#(active(X1), X2) | |
| active#(U136(tt, IL, M, N)) | → | cons#(N, take(M, IL)) | active#(s(X)) | → | active#(X) | |
| U105#(ok(X1), ok(X2)) | → | U105#(X1, X2) | proper#(U46(X)) | → | proper#(X) | |
| U52#(mark(X)) | → | U52#(X) | U92#(ok(X1), ok(X2), ok(X3)) | → | U92#(X1, X2, X3) | |
| active#(U105(tt, V2)) | → | U106#(isNatIList(V2)) | active#(isNatIList(V)) | → | U31#(isNatIListKind(V), V) | |
| U122#(mark(X)) | → | U122#(X) | U21#(ok(X1), ok(X2)) | → | U21#(X1, X2) | |
| U42#(ok(X1), ok(X2), ok(X3)) | → | U42#(X1, X2, X3) | proper#(U44(X1, X2, X3)) | → | proper#(X2) | |
| U106#(ok(X)) | → | U106#(X) | active#(U132(tt, IL, M, N)) | → | U133#(isNat(M), IL, M, N) | |
| proper#(U11(X1, X2)) | → | proper#(X1) | proper#(U91(X1, X2, X3)) | → | proper#(X2) | |
| active#(U42(X1, X2, X3)) | → | U42#(active(X1), X2, X3) | active#(U94(tt, V1, V2)) | → | U95#(isNat(V1), V2) | |
| proper#(U41(X1, X2, X3)) | → | proper#(X2) | proper#(U32(X1, X2)) | → | proper#(X2) | |
| active#(take(X1, X2)) | → | take#(active(X1), X2) | proper#(U133(X1, X2, X3, X4)) | → | proper#(X4) | |
| proper#(isNatKind(X)) | → | proper#(X) | proper#(U133(X1, X2, X3, X4)) | → | proper#(X2) | |
| proper#(U111(X1, X2, X3)) | → | proper#(X1) | active#(U22(tt, V1)) | → | isNat#(V1) | |
| active#(U92(tt, V1, V2)) | → | isNatIListKind#(V2) | active#(U94(X1, X2, X3)) | → | active#(X1) | |
| active#(U42(tt, V1, V2)) | → | U43#(isNatIListKind(V2), V1, V2) | active#(take(X1, X2)) | → | active#(X2) | |
| active#(U62(X)) | → | active#(X) | isNat#(ok(X)) | → | isNat#(X) | |
| active#(isNatList(cons(V1, V2))) | → | U91#(isNatKind(V1), V1, V2) | active#(U41(X1, X2, X3)) | → | active#(X1) | |
| active#(isNatKind(length(V1))) | → | isNatIListKind#(V1) | active#(U102(tt, V1, V2)) | → | isNatIListKind#(V2) | |
| active#(U94(tt, V1, V2)) | → | isNat#(V1) | proper#(U13(X)) | → | U13#(proper(X)) | |
| active#(U135(X1, X2, X3, X4)) | → | U135#(active(X1), X2, X3, X4) | active#(U104(tt, V1, V2)) | → | U105#(isNat(V1), V2) | |
| active#(U105(X1, X2)) | → | active#(X1) | proper#(U101(X1, X2, X3)) | → | proper#(X3) | |
| active#(U133(X1, X2, X3, X4)) | → | active#(X1) | proper#(U93(X1, X2, X3)) | → | proper#(X1) | |
| U131#(mark(X1), X2, X3, X4) | → | U131#(X1, X2, X3, X4) | U22#(mark(X1), X2) | → | U22#(X1, X2) | |
| proper#(U44(X1, X2, X3)) | → | proper#(X1) | active#(U43(X1, X2, X3)) | → | active#(X1) | |
| top#(ok(X)) | → | active#(X) | active#(U91(X1, X2, X3)) | → | U91#(active(X1), X2, X3) | |
| U136#(mark(X1), X2, X3, X4) | → | U136#(X1, X2, X3, X4) | proper#(U103(X1, X2, X3)) | → | proper#(X1) | |
| proper#(U134(X1, X2, X3, X4)) | → | U134#(proper(X1), proper(X2), proper(X3), proper(X4)) | proper#(U93(X1, X2, X3)) | → | proper#(X3) | |
| U45#(mark(X1), X2) | → | U45#(X1, X2) | U13#(mark(X)) | → | U13#(X) | |
| proper#(U102(X1, X2, X3)) | → | U102#(proper(X1), proper(X2), proper(X3)) | active#(isNat(length(V1))) | → | isNatIListKind#(V1) | |
| proper#(U81(X)) | → | U81#(proper(X)) | proper#(U114(X1, X2)) | → | U114#(proper(X1), proper(X2)) | |
| proper#(U42(X1, X2, X3)) | → | proper#(X1) | U121#(ok(X1), ok(X2)) | → | U121#(X1, X2) | |
| active#(U32(X1, X2)) | → | active#(X1) | active#(U121(tt, IL)) | → | isNatIListKind#(IL) | |
| proper#(s(X)) | → | s#(proper(X)) | active#(U46(X)) | → | U46#(active(X)) | |
| active#(U133(tt, IL, M, N)) | → | U134#(isNatKind(M), IL, M, N) | active#(U136(X1, X2, X3, X4)) | → | active#(X1) | |
| active#(U103(tt, V1, V2)) | → | isNatIListKind#(V2) | proper#(U133(X1, X2, X3, X4)) | → | U133#(proper(X1), proper(X2), proper(X3), proper(X4)) | |
| top#(ok(X)) | → | top#(active(X)) | U92#(mark(X1), X2, X3) | → | U92#(X1, X2, X3) | |
| U11#(ok(X1), ok(X2)) | → | U11#(X1, X2) | active#(U136(tt, IL, M, N)) | → | take#(M, IL) | |
| U102#(ok(X1), ok(X2), ok(X3)) | → | U102#(X1, X2, X3) | active#(U45(tt, V2)) | → | isNatIList#(V2) | |
| U93#(mark(X1), X2, X3) | → | U93#(X1, X2, X3) | U42#(mark(X1), X2, X3) | → | U42#(X1, X2, X3) | |
| active#(U45(X1, X2)) | → | active#(X1) | U62#(ok(X)) | → | U62#(X) | |
| proper#(U102(X1, X2, X3)) | → | proper#(X3) | active#(U92(X1, X2, X3)) | → | U92#(active(X1), X2, X3) | |
| proper#(U136(X1, X2, X3, X4)) | → | proper#(X4) | active#(U134(tt, IL, M, N)) | → | isNat#(N) | |
| proper#(U94(X1, X2, X3)) | → | proper#(X3) | active#(U103(tt, V1, V2)) | → | U104#(isNatIListKind(V2), V1, V2) | |
| proper#(U61(X1, X2)) | → | U61#(proper(X1), proper(X2)) | proper#(U102(X1, X2, X3)) | → | proper#(X1) | |
| active#(U113(tt, L, N)) | → | U114#(isNatKind(N), L) | active#(U132(X1, X2, X3, X4)) | → | U132#(active(X1), X2, X3, X4) | |
| proper#(U41(X1, X2, X3)) | → | proper#(X3) | proper#(U13(X)) | → | proper#(X) | |
| active#(U132(X1, X2, X3, X4)) | → | active#(X1) | proper#(U21(X1, X2)) | → | proper#(X2) | |
| proper#(U122(X)) | → | proper#(X) | active#(U31(X1, X2)) | → | U31#(active(X1), X2) | |
| U136#(ok(X1), ok(X2), ok(X3), ok(X4)) | → | U136#(X1, X2, X3, X4) | U112#(mark(X1), X2, X3) | → | U112#(X1, X2, X3) | |
| proper#(U102(X1, X2, X3)) | → | proper#(X2) | U41#(mark(X1), X2, X3) | → | U41#(X1, X2, X3) | |
| proper#(isNatIListKind(X)) | → | isNatIListKind#(proper(X)) | U23#(ok(X)) | → | U23#(X) | |
| active#(U112(X1, X2, X3)) | → | active#(X1) | active#(U44(tt, V1, V2)) | → | isNat#(V1) | |
| active#(isNatKind(s(V1))) | → | isNatKind#(V1) | proper#(U21(X1, X2)) | → | U21#(proper(X1), proper(X2)) | |
| active#(length(X)) | → | length#(active(X)) | proper#(U43(X1, X2, X3)) | → | U43#(proper(X1), proper(X2), proper(X3)) | |
| active#(U104(tt, V1, V2)) | → | isNat#(V1) | proper#(U81(X)) | → | proper#(X) | |
| U46#(mark(X)) | → | U46#(X) | active#(U131(X1, X2, X3, X4)) | → | U131#(active(X1), X2, X3, X4) | |
| proper#(U92(X1, X2, X3)) | → | proper#(X2) | proper#(U112(X1, X2, X3)) | → | proper#(X2) | |
| U95#(mark(X1), X2) | → | U95#(X1, X2) | proper#(U93(X1, X2, X3)) | → | proper#(X2) | |
| active#(U12(tt, V1)) | → | U13#(isNatList(V1)) | active#(take(0, IL)) | → | U121#(isNatIList(IL), IL) | |
| proper#(U134(X1, X2, X3, X4)) | → | proper#(X1) | U21#(mark(X1), X2) | → | U21#(X1, X2) | |
| active#(isNatList(cons(V1, V2))) | → | isNatKind#(V1) | U46#(ok(X)) | → | U46#(X) | |
| active#(U71(X)) | → | active#(X) | proper#(U52(X)) | → | proper#(X) | |
| proper#(U132(X1, X2, X3, X4)) | → | proper#(X1) | proper#(length(X)) | → | length#(proper(X)) | |
| active#(U51(X1, X2)) | → | active#(X1) | proper#(U132(X1, X2, X3, X4)) | → | proper#(X3) | |
| U11#(mark(X1), X2) | → | U11#(X1, X2) | proper#(U95(X1, X2)) | → | U95#(proper(X1), proper(X2)) | |
| active#(isNatIListKind(cons(V1, V2))) | → | U51#(isNatKind(V1), V2) | proper#(U92(X1, X2, X3)) | → | proper#(X1) | |
| active#(U134(X1, X2, X3, X4)) | → | active#(X1) | U91#(mark(X1), X2, X3) | → | U91#(X1, X2, X3) | |
| proper#(U62(X)) | → | proper#(X) | active#(U122(X)) | → | U122#(active(X)) | |
| active#(U135(tt, IL, M, N)) | → | isNatKind#(N) | active#(isNatIList(cons(V1, V2))) | → | U41#(isNatKind(V1), V1, V2) | |
| top#(mark(X)) | → | proper#(X) | length#(mark(X)) | → | length#(X) | |
| isNatKind#(ok(X)) | → | isNatKind#(X) | active#(U101(X1, X2, X3)) | → | U101#(active(X1), X2, X3) | |
| U43#(mark(X1), X2, X3) | → | U43#(X1, X2, X3) | active#(U41(tt, V1, V2)) | → | isNatKind#(V1) | |
| active#(U61(X1, X2)) | → | active#(X1) | proper#(U104(X1, X2, X3)) | → | proper#(X1) | |
| proper#(U43(X1, X2, X3)) | → | proper#(X3) | active#(U21(tt, V1)) | → | isNatKind#(V1) | |
| U132#(mark(X1), X2, X3, X4) | → | U132#(X1, X2, X3, X4) | U135#(mark(X1), X2, X3, X4) | → | U135#(X1, X2, X3, X4) | |
| proper#(U42(X1, X2, X3)) | → | U42#(proper(X1), proper(X2), proper(X3)) | proper#(U101(X1, X2, X3)) | → | proper#(X2) | |
| proper#(U134(X1, X2, X3, X4)) | → | proper#(X4) | proper#(U94(X1, X2, X3)) | → | proper#(X2) | |
| proper#(U43(X1, X2, X3)) | → | proper#(X1) | active#(U111(X1, X2, X3)) | → | U111#(active(X1), X2, X3) | |
| proper#(U112(X1, X2, X3)) | → | U112#(proper(X1), proper(X2), proper(X3)) | proper#(U44(X1, X2, X3)) | → | U44#(proper(X1), proper(X2), proper(X3)) | |
| U104#(ok(X1), ok(X2), ok(X3)) | → | U104#(X1, X2, X3) | active#(U41(X1, X2, X3)) | → | U41#(active(X1), X2, X3) | |
| active#(U44(tt, V1, V2)) | → | U45#(isNat(V1), V2) | active#(U131(tt, IL, M, N)) | → | U132#(isNatIListKind(IL), IL, M, N) | |
| active#(length(cons(N, L))) | → | U111#(isNatList(L), L, N) | proper#(U45(X1, X2)) | → | U45#(proper(X1), proper(X2)) | |
| active#(isNatIListKind(take(V1, V2))) | → | isNatKind#(V1) | active#(U92(tt, V1, V2)) | → | U93#(isNatIListKind(V2), V1, V2) | |
| proper#(U41(X1, X2, X3)) | → | proper#(X1) | U93#(ok(X1), ok(X2), ok(X3)) | → | U93#(X1, X2, X3) | |
| active#(U31(X1, X2)) | → | active#(X1) | proper#(isNatList(X)) | → | proper#(X) | |
| active#(U13(X)) | → | active#(X) | take#(ok(X1), ok(X2)) | → | take#(X1, X2) | |
| U101#(ok(X1), ok(X2), ok(X3)) | → | U101#(X1, X2, X3) | proper#(U22(X1, X2)) | → | U22#(proper(X1), proper(X2)) | |
| active#(U52(X)) | → | U52#(active(X)) | proper#(isNat(X)) | → | proper#(X) | |
| proper#(U94(X1, X2, X3)) | → | U94#(proper(X1), proper(X2), proper(X3)) | proper#(U101(X1, X2, X3)) | → | proper#(X1) | |
| proper#(U132(X1, X2, X3, X4)) | → | proper#(X4) | active#(isNatList(take(V1, V2))) | → | U101#(isNatKind(V1), V1, V2) | |
| U33#(mark(X)) | → | U33#(X) | active#(U11(X1, X2)) | → | U11#(active(X1), X2) | |
| proper#(U92(X1, X2, X3)) | → | proper#(X3) | proper#(U121(X1, X2)) | → | proper#(X2) | |
| active#(U131(X1, X2, X3, X4)) | → | active#(X1) | active#(isNat(s(V1))) | → | U21#(isNatKind(V1), V1) | |
| active#(U114(X1, X2)) | → | U114#(active(X1), X2) | active#(U131(tt, IL, M, N)) | → | isNatIListKind#(IL) | |
| proper#(U31(X1, X2)) | → | U31#(proper(X1), proper(X2)) | proper#(U103(X1, X2, X3)) | → | U103#(proper(X1), proper(X2), proper(X3)) | |
| U81#(ok(X)) | → | U81#(X) | active#(U41(tt, V1, V2)) | → | U42#(isNatKind(V1), V1, V2) | |
| U31#(ok(X1), ok(X2)) | → | U31#(X1, X2) | active#(U136(X1, X2, X3, X4)) | → | U136#(active(X1), X2, X3, X4) | |
| active#(U22(X1, X2)) | → | U22#(active(X1), X2) | active#(U133(tt, IL, M, N)) | → | isNatKind#(M) | |
| active#(isNatList(take(V1, V2))) | → | isNatKind#(V1) | active#(U95(tt, V2)) | → | isNatList#(V2) | |
| isNatIListKind#(ok(X)) | → | isNatIListKind#(X) | proper#(U12(X1, X2)) | → | proper#(X2) | |
| proper#(U11(X1, X2)) | → | U11#(proper(X1), proper(X2)) | active#(U21(tt, V1)) | → | U22#(isNatKind(V1), V1) | |
| active#(U133(X1, X2, X3, X4)) | → | U133#(active(X1), X2, X3, X4) | proper#(U61(X1, X2)) | → | proper#(X2) | |
| proper#(U96(X)) | → | proper#(X) | length#(ok(X)) | → | length#(X) | |
| U12#(mark(X1), X2) | → | U12#(X1, X2) | proper#(U113(X1, X2, X3)) | → | proper#(X2) | |
| proper#(U32(X1, X2)) | → | proper#(X1) | U105#(mark(X1), X2) | → | U105#(X1, X2) | |
| proper#(U104(X1, X2, X3)) | → | proper#(X3) | active#(U102(tt, V1, V2)) | → | U103#(isNatIListKind(V2), V1, V2) | |
| active#(U92(X1, X2, X3)) | → | active#(X1) | active#(U81(X)) | → | active#(X) | |
| active#(U22(tt, V1)) | → | U23#(isNat(V1)) | proper#(s(X)) | → | proper#(X) | |
| active#(U51(tt, V2)) | → | U52#(isNatIListKind(V2)) | active#(U95(X1, X2)) | → | U95#(active(X1), X2) | |
| proper#(U95(X1, X2)) | → | proper#(X1) | proper#(U32(X1, X2)) | → | U32#(proper(X1), proper(X2)) | |
| active#(U113(tt, L, N)) | → | isNatKind#(N) | take#(mark(X1), X2) | → | take#(X1, X2) | |
| U44#(ok(X1), ok(X2), ok(X3)) | → | U44#(X1, X2, X3) | U132#(ok(X1), ok(X2), ok(X3), ok(X4)) | → | U132#(X1, X2, X3, X4) | |
| active#(U61(tt, V2)) | → | isNatIListKind#(V2) | active#(U105(X1, X2)) | → | U105#(active(X1), X2) | |
| active#(length(cons(N, L))) | → | isNatList#(L) | proper#(U43(X1, X2, X3)) | → | proper#(X2) | |
| active#(U11(tt, V1)) | → | U12#(isNatIListKind(V1), V1) | active#(U44(X1, X2, X3)) | → | U44#(active(X1), X2, X3) | |
| proper#(U135(X1, X2, X3, X4)) | → | proper#(X4) | proper#(U135(X1, X2, X3, X4)) | → | U135#(proper(X1), proper(X2), proper(X3), proper(X4)) | |
| active#(U103(X1, X2, X3)) | → | active#(X1) | proper#(U12(X1, X2)) | → | proper#(X1) | |
| U121#(mark(X1), X2) | → | U121#(X1, X2) | U104#(mark(X1), X2, X3) | → | U104#(X1, X2, X3) | |
| proper#(U135(X1, X2, X3, X4)) | → | proper#(X2) | active#(U134(tt, IL, M, N)) | → | U135#(isNat(N), IL, M, N) | |
| active#(U111(tt, L, N)) | → | isNatIListKind#(L) | active#(U104(X1, X2, X3)) | → | U104#(active(X1), X2, X3) | |
| active#(U102(X1, X2, X3)) | → | active#(X1) | active#(take(0, IL)) | → | isNatIList#(IL) | |
| proper#(U33(X)) | → | proper#(X) | proper#(U71(X)) | → | proper#(X) | |
| active#(isNatIList(V)) | → | isNatIListKind#(V) | proper#(U133(X1, X2, X3, X4)) | → | proper#(X3) | |
| active#(U32(tt, V)) | → | isNatList#(V) | proper#(U52(X)) | → | U52#(proper(X)) | |
| proper#(U91(X1, X2, X3)) | → | proper#(X1) | active#(U104(X1, X2, X3)) | → | active#(X1) | |
| active#(U113(X1, X2, X3)) | → | active#(X1) | U134#(ok(X1), ok(X2), ok(X3), ok(X4)) | → | U134#(X1, X2, X3, X4) | |
| active#(U95(tt, V2)) | → | U96#(isNatList(V2)) | proper#(U11(X1, X2)) | → | proper#(X2) | |
| active#(U42(tt, V1, V2)) | → | isNatIListKind#(V2) | proper#(U122(X)) | → | U122#(proper(X)) | |
| proper#(U23(X)) | → | proper#(X) | U44#(mark(X1), X2, X3) | → | U44#(X1, X2, X3) | |
| proper#(U136(X1, X2, X3, X4)) | → | proper#(X3) | proper#(U112(X1, X2, X3)) | → | proper#(X1) | |
| proper#(U136(X1, X2, X3, X4)) | → | proper#(X2) | active#(U46(X)) | → | active#(X) | |
| proper#(U131(X1, X2, X3, X4)) | → | U131#(proper(X1), proper(X2), proper(X3), proper(X4)) | proper#(U46(X)) | → | U46#(proper(X)) | |
| isNatIList#(ok(X)) | → | isNatIList#(X) | proper#(U113(X1, X2, X3)) | → | proper#(X1) | |
| active#(U12(X1, X2)) | → | U12#(active(X1), X2) | active#(isNat(s(V1))) | → | isNatKind#(V1) | |
| proper#(U42(X1, X2, X3)) | → | proper#(X3) | proper#(U62(X)) | → | U62#(proper(X)) | |
| active#(U112(X1, X2, X3)) | → | U112#(active(X1), X2, X3) | U103#(mark(X1), X2, X3) | → | U103#(X1, X2, X3) | |
| active#(U135(X1, X2, X3, X4)) | → | active#(X1) | proper#(isNatIListKind(X)) | → | proper#(X) | |
| cons#(mark(X1), X2) | → | cons#(X1, X2) | proper#(U113(X1, X2, X3)) | → | U113#(proper(X1), proper(X2), proper(X3)) | |
| proper#(U103(X1, X2, X3)) | → | proper#(X2) | active#(U114(tt, L)) | → | length#(L) | |
| active#(U135(tt, IL, M, N)) | → | U136#(isNatKind(N), IL, M, N) | active#(take(s(M), cons(N, IL))) | → | U131#(isNatIList(IL), IL, M, N) | |
| proper#(U93(X1, X2, X3)) | → | U93#(proper(X1), proper(X2), proper(X3)) | proper#(U133(X1, X2, X3, X4)) | → | proper#(X1) | |
| U62#(mark(X)) | → | U62#(X) | proper#(isNat(X)) | → | isNat#(proper(X)) | |
| U114#(mark(X1), X2) | → | U114#(X1, X2) | active#(U61(tt, V2)) | → | U62#(isNatIListKind(V2)) | |
| U51#(ok(X1), ok(X2)) | → | U51#(X1, X2) | proper#(U45(X1, X2)) | → | proper#(X1) | |
| active#(U12(X1, X2)) | → | active#(X1) | U112#(ok(X1), ok(X2), ok(X3)) | → | U112#(X1, X2, X3) | |
| active#(s(X)) | → | s#(active(X)) | s#(ok(X)) | → | s#(X) | |
| proper#(length(X)) | → | proper#(X) | active#(U32(X1, X2)) | → | U32#(active(X1), X2) | |
| active#(take(X1, X2)) | → | take#(X1, active(X2)) | active#(U23(X)) | → | active#(X) | |
| active#(zeros) | → | cons#(0, zeros) | U96#(mark(X)) | → | U96#(X) | |
| active#(U96(X)) | → | active#(X) | U106#(mark(X)) | → | U106#(X) | |
| proper#(U105(X1, X2)) | → | proper#(X2) | proper#(U114(X1, X2)) | → | proper#(X2) | |
| active#(U121(tt, IL)) | → | U122#(isNatIListKind(IL)) | proper#(U31(X1, X2)) | → | proper#(X1) | |
| U71#(ok(X)) | → | U71#(X) | U23#(mark(X)) | → | U23#(X) | |
| active#(U81(X)) | → | U81#(active(X)) | proper#(isNatIList(X)) | → | isNatIList#(proper(X)) | |
| active#(cons(X1, X2)) | → | cons#(active(X1), X2) | active#(U61(X1, X2)) | → | U61#(active(X1), X2) | |
| active#(U91(X1, X2, X3)) | → | active#(X1) | active#(U11(X1, X2)) | → | active#(X1) | |
| active#(U23(X)) | → | U23#(active(X)) | active#(U62(X)) | → | U62#(active(X)) | |
| U133#(mark(X1), X2, X3, X4) | → | U133#(X1, X2, X3, X4) | top#(mark(X)) | → | top#(proper(X)) | |
| proper#(cons(X1, X2)) | → | proper#(X2) | proper#(isNatIList(X)) | → | proper#(X) | |
| U13#(ok(X)) | → | U13#(X) | proper#(U136(X1, X2, X3, X4)) | → | proper#(X1) | |
| U95#(ok(X1), ok(X2)) | → | U95#(X1, X2) | active#(U43(X1, X2, X3)) | → | U43#(active(X1), X2, X3) | |
| active#(U94(X1, X2, X3)) | → | U94#(active(X1), X2, X3) | proper#(U22(X1, X2)) | → | proper#(X2) | |
| isNatList#(ok(X)) | → | isNatList#(X) | active#(U122(X)) | → | active#(X) | |
| proper#(U111(X1, X2, X3)) | → | proper#(X3) | proper#(U101(X1, X2, X3)) | → | U101#(proper(X1), proper(X2), proper(X3)) | |
| active#(U71(X)) | → | U71#(active(X)) | U133#(ok(X1), ok(X2), ok(X3), ok(X4)) | → | U133#(X1, X2, X3, X4) | |
| proper#(U105(X1, X2)) | → | U105#(proper(X1), proper(X2)) | proper#(U134(X1, X2, X3, X4)) | → | proper#(X2) | |
| proper#(U12(X1, X2)) | → | U12#(proper(X1), proper(X2)) | U113#(ok(X1), ok(X2), ok(X3)) | → | U113#(X1, X2, X3) | |
| active#(U93(tt, V1, V2)) | → | isNatIListKind#(V2) | U111#(ok(X1), ok(X2), ok(X3)) | → | U111#(X1, X2, X3) | |
| U101#(mark(X1), X2, X3) | → | U101#(X1, X2, X3) | proper#(U22(X1, X2)) | → | proper#(X1) | |
| active#(U112(tt, L, N)) | → | isNat#(N) | proper#(U114(X1, X2)) | → | proper#(X1) | |
| active#(isNatIList(cons(V1, V2))) | → | isNatKind#(V1) | proper#(U111(X1, X2, X3)) | → | U111#(proper(X1), proper(X2), proper(X3)) | |
| U31#(mark(X1), X2) | → | U31#(X1, X2) | proper#(U61(X1, X2)) | → | proper#(X1) | |
| active#(U121(X1, X2)) | → | U121#(active(X1), X2) | proper#(U44(X1, X2, X3)) | → | proper#(X3) | |
| active#(U21(X1, X2)) | → | active#(X1) | proper#(cons(X1, X2)) | → | cons#(proper(X1), proper(X2)) | |
| U32#(mark(X1), X2) | → | U32#(X1, X2) | U113#(mark(X1), X2, X3) | → | U113#(X1, X2, X3) | |
| active#(isNatIListKind(take(V1, V2))) | → | U61#(isNatKind(V1), V2) | U131#(ok(X1), ok(X2), ok(X3), ok(X4)) | → | U131#(X1, X2, X3, X4) |
| active(zeros) | → | mark(cons(0, zeros)) | active(U101(tt, V1, V2)) | → | mark(U102(isNatKind(V1), V1, V2)) | |
| active(U102(tt, V1, V2)) | → | mark(U103(isNatIListKind(V2), V1, V2)) | active(U103(tt, V1, V2)) | → | mark(U104(isNatIListKind(V2), V1, V2)) | |
| active(U104(tt, V1, V2)) | → | mark(U105(isNat(V1), V2)) | active(U105(tt, V2)) | → | mark(U106(isNatIList(V2))) | |
| active(U106(tt)) | → | mark(tt) | active(U11(tt, V1)) | → | mark(U12(isNatIListKind(V1), V1)) | |
| active(U111(tt, L, N)) | → | mark(U112(isNatIListKind(L), L, N)) | active(U112(tt, L, N)) | → | mark(U113(isNat(N), L, N)) | |
| active(U113(tt, L, N)) | → | mark(U114(isNatKind(N), L)) | active(U114(tt, L)) | → | mark(s(length(L))) | |
| active(U12(tt, V1)) | → | mark(U13(isNatList(V1))) | active(U121(tt, IL)) | → | mark(U122(isNatIListKind(IL))) | |
| active(U122(tt)) | → | mark(nil) | active(U13(tt)) | → | mark(tt) | |
| active(U131(tt, IL, M, N)) | → | mark(U132(isNatIListKind(IL), IL, M, N)) | active(U132(tt, IL, M, N)) | → | mark(U133(isNat(M), IL, M, N)) | |
| active(U133(tt, IL, M, N)) | → | mark(U134(isNatKind(M), IL, M, N)) | active(U134(tt, IL, M, N)) | → | mark(U135(isNat(N), IL, M, N)) | |
| active(U135(tt, IL, M, N)) | → | mark(U136(isNatKind(N), IL, M, N)) | active(U136(tt, IL, M, N)) | → | mark(cons(N, take(M, IL))) | |
| active(U21(tt, V1)) | → | mark(U22(isNatKind(V1), V1)) | active(U22(tt, V1)) | → | mark(U23(isNat(V1))) | |
| active(U23(tt)) | → | mark(tt) | active(U31(tt, V)) | → | mark(U32(isNatIListKind(V), V)) | |
| active(U32(tt, V)) | → | mark(U33(isNatList(V))) | active(U33(tt)) | → | mark(tt) | |
| active(U41(tt, V1, V2)) | → | mark(U42(isNatKind(V1), V1, V2)) | active(U42(tt, V1, V2)) | → | mark(U43(isNatIListKind(V2), V1, V2)) | |
| active(U43(tt, V1, V2)) | → | mark(U44(isNatIListKind(V2), V1, V2)) | active(U44(tt, V1, V2)) | → | mark(U45(isNat(V1), V2)) | |
| active(U45(tt, V2)) | → | mark(U46(isNatIList(V2))) | active(U46(tt)) | → | mark(tt) | |
| active(U51(tt, V2)) | → | mark(U52(isNatIListKind(V2))) | active(U52(tt)) | → | mark(tt) | |
| active(U61(tt, V2)) | → | mark(U62(isNatIListKind(V2))) | active(U62(tt)) | → | mark(tt) | |
| active(U71(tt)) | → | mark(tt) | active(U81(tt)) | → | mark(tt) | |
| active(U91(tt, V1, V2)) | → | mark(U92(isNatKind(V1), V1, V2)) | active(U92(tt, V1, V2)) | → | mark(U93(isNatIListKind(V2), V1, V2)) | |
| active(U93(tt, V1, V2)) | → | mark(U94(isNatIListKind(V2), V1, V2)) | active(U94(tt, V1, V2)) | → | mark(U95(isNat(V1), V2)) | |
| active(U95(tt, V2)) | → | mark(U96(isNatList(V2))) | active(U96(tt)) | → | mark(tt) | |
| active(isNat(0)) | → | mark(tt) | active(isNat(length(V1))) | → | mark(U11(isNatIListKind(V1), V1)) | |
| active(isNat(s(V1))) | → | mark(U21(isNatKind(V1), V1)) | active(isNatIList(V)) | → | mark(U31(isNatIListKind(V), V)) | |
| active(isNatIList(zeros)) | → | mark(tt) | active(isNatIList(cons(V1, V2))) | → | mark(U41(isNatKind(V1), V1, V2)) | |
| active(isNatIListKind(nil)) | → | mark(tt) | active(isNatIListKind(zeros)) | → | mark(tt) | |
| active(isNatIListKind(cons(V1, V2))) | → | mark(U51(isNatKind(V1), V2)) | active(isNatIListKind(take(V1, V2))) | → | mark(U61(isNatKind(V1), V2)) | |
| active(isNatKind(0)) | → | mark(tt) | active(isNatKind(length(V1))) | → | mark(U71(isNatIListKind(V1))) | |
| active(isNatKind(s(V1))) | → | mark(U81(isNatKind(V1))) | active(isNatList(nil)) | → | mark(tt) | |
| active(isNatList(cons(V1, V2))) | → | mark(U91(isNatKind(V1), V1, V2)) | active(isNatList(take(V1, V2))) | → | mark(U101(isNatKind(V1), V1, V2)) | |
| active(length(nil)) | → | mark(0) | active(length(cons(N, L))) | → | mark(U111(isNatList(L), L, N)) | |
| active(take(0, IL)) | → | mark(U121(isNatIList(IL), IL)) | active(take(s(M), cons(N, IL))) | → | mark(U131(isNatIList(IL), IL, M, N)) | |
| active(cons(X1, X2)) | → | cons(active(X1), X2) | active(U101(X1, X2, X3)) | → | U101(active(X1), X2, X3) | |
| active(U102(X1, X2, X3)) | → | U102(active(X1), X2, X3) | active(U103(X1, X2, X3)) | → | U103(active(X1), X2, X3) | |
| active(U104(X1, X2, X3)) | → | U104(active(X1), X2, X3) | active(U105(X1, X2)) | → | U105(active(X1), X2) | |
| active(U106(X)) | → | U106(active(X)) | active(U11(X1, X2)) | → | U11(active(X1), X2) | |
| active(U12(X1, X2)) | → | U12(active(X1), X2) | active(U111(X1, X2, X3)) | → | U111(active(X1), X2, X3) | |
| active(U112(X1, X2, X3)) | → | U112(active(X1), X2, X3) | active(U113(X1, X2, X3)) | → | U113(active(X1), X2, X3) | |
| active(U114(X1, X2)) | → | U114(active(X1), X2) | active(s(X)) | → | s(active(X)) | |
| active(length(X)) | → | length(active(X)) | active(U13(X)) | → | U13(active(X)) | |
| active(U121(X1, X2)) | → | U121(active(X1), X2) | active(U122(X)) | → | U122(active(X)) | |
| active(U131(X1, X2, X3, X4)) | → | U131(active(X1), X2, X3, X4) | active(U132(X1, X2, X3, X4)) | → | U132(active(X1), X2, X3, X4) | |
| active(U133(X1, X2, X3, X4)) | → | U133(active(X1), X2, X3, X4) | active(U134(X1, X2, X3, X4)) | → | U134(active(X1), X2, X3, X4) | |
| active(U135(X1, X2, X3, X4)) | → | U135(active(X1), X2, X3, X4) | active(U136(X1, X2, X3, X4)) | → | U136(active(X1), X2, X3, X4) | |
| active(take(X1, X2)) | → | take(active(X1), X2) | active(take(X1, X2)) | → | take(X1, active(X2)) | |
| active(U21(X1, X2)) | → | U21(active(X1), X2) | active(U22(X1, X2)) | → | U22(active(X1), X2) | |
| active(U23(X)) | → | U23(active(X)) | active(U31(X1, X2)) | → | U31(active(X1), X2) | |
| active(U32(X1, X2)) | → | U32(active(X1), X2) | active(U33(X)) | → | U33(active(X)) | |
| active(U41(X1, X2, X3)) | → | U41(active(X1), X2, X3) | active(U42(X1, X2, X3)) | → | U42(active(X1), X2, X3) | |
| active(U43(X1, X2, X3)) | → | U43(active(X1), X2, X3) | active(U44(X1, X2, X3)) | → | U44(active(X1), X2, X3) | |
| active(U45(X1, X2)) | → | U45(active(X1), X2) | active(U46(X)) | → | U46(active(X)) | |
| active(U51(X1, X2)) | → | U51(active(X1), X2) | active(U52(X)) | → | U52(active(X)) | |
| active(U61(X1, X2)) | → | U61(active(X1), X2) | active(U62(X)) | → | U62(active(X)) | |
| active(U71(X)) | → | U71(active(X)) | active(U81(X)) | → | U81(active(X)) | |
| active(U91(X1, X2, X3)) | → | U91(active(X1), X2, X3) | active(U92(X1, X2, X3)) | → | U92(active(X1), X2, X3) | |
| active(U93(X1, X2, X3)) | → | U93(active(X1), X2, X3) | active(U94(X1, X2, X3)) | → | U94(active(X1), X2, X3) | |
| active(U95(X1, X2)) | → | U95(active(X1), X2) | active(U96(X)) | → | U96(active(X)) | |
| cons(mark(X1), X2) | → | mark(cons(X1, X2)) | U101(mark(X1), X2, X3) | → | mark(U101(X1, X2, X3)) | |
| U102(mark(X1), X2, X3) | → | mark(U102(X1, X2, X3)) | U103(mark(X1), X2, X3) | → | mark(U103(X1, X2, X3)) | |
| U104(mark(X1), X2, X3) | → | mark(U104(X1, X2, X3)) | U105(mark(X1), X2) | → | mark(U105(X1, X2)) | |
| U106(mark(X)) | → | mark(U106(X)) | U11(mark(X1), X2) | → | mark(U11(X1, X2)) | |
| U12(mark(X1), X2) | → | mark(U12(X1, X2)) | U111(mark(X1), X2, X3) | → | mark(U111(X1, X2, X3)) | |
| U112(mark(X1), X2, X3) | → | mark(U112(X1, X2, X3)) | U113(mark(X1), X2, X3) | → | mark(U113(X1, X2, X3)) | |
| U114(mark(X1), X2) | → | mark(U114(X1, X2)) | s(mark(X)) | → | mark(s(X)) | |
| length(mark(X)) | → | mark(length(X)) | U13(mark(X)) | → | mark(U13(X)) | |
| U121(mark(X1), X2) | → | mark(U121(X1, X2)) | U122(mark(X)) | → | mark(U122(X)) | |
| U131(mark(X1), X2, X3, X4) | → | mark(U131(X1, X2, X3, X4)) | U132(mark(X1), X2, X3, X4) | → | mark(U132(X1, X2, X3, X4)) | |
| U133(mark(X1), X2, X3, X4) | → | mark(U133(X1, X2, X3, X4)) | U134(mark(X1), X2, X3, X4) | → | mark(U134(X1, X2, X3, X4)) | |
| U135(mark(X1), X2, X3, X4) | → | mark(U135(X1, X2, X3, X4)) | U136(mark(X1), X2, X3, X4) | → | mark(U136(X1, X2, X3, X4)) | |
| take(mark(X1), X2) | → | mark(take(X1, X2)) | take(X1, mark(X2)) | → | mark(take(X1, X2)) | |
| U21(mark(X1), X2) | → | mark(U21(X1, X2)) | U22(mark(X1), X2) | → | mark(U22(X1, X2)) | |
| U23(mark(X)) | → | mark(U23(X)) | U31(mark(X1), X2) | → | mark(U31(X1, X2)) | |
| U32(mark(X1), X2) | → | mark(U32(X1, X2)) | U33(mark(X)) | → | mark(U33(X)) | |
| U41(mark(X1), X2, X3) | → | mark(U41(X1, X2, X3)) | U42(mark(X1), X2, X3) | → | mark(U42(X1, X2, X3)) | |
| U43(mark(X1), X2, X3) | → | mark(U43(X1, X2, X3)) | U44(mark(X1), X2, X3) | → | mark(U44(X1, X2, X3)) | |
| U45(mark(X1), X2) | → | mark(U45(X1, X2)) | U46(mark(X)) | → | mark(U46(X)) | |
| U51(mark(X1), X2) | → | mark(U51(X1, X2)) | U52(mark(X)) | → | mark(U52(X)) | |
| U61(mark(X1), X2) | → | mark(U61(X1, X2)) | U62(mark(X)) | → | mark(U62(X)) | |
| U71(mark(X)) | → | mark(U71(X)) | U81(mark(X)) | → | mark(U81(X)) | |
| U91(mark(X1), X2, X3) | → | mark(U91(X1, X2, X3)) | U92(mark(X1), X2, X3) | → | mark(U92(X1, X2, X3)) | |
| U93(mark(X1), X2, X3) | → | mark(U93(X1, X2, X3)) | U94(mark(X1), X2, X3) | → | mark(U94(X1, X2, X3)) | |
| U95(mark(X1), X2) | → | mark(U95(X1, X2)) | U96(mark(X)) | → | mark(U96(X)) | |
| proper(zeros) | → | ok(zeros) | proper(cons(X1, X2)) | → | cons(proper(X1), proper(X2)) | |
| proper(0) | → | ok(0) | proper(U101(X1, X2, X3)) | → | U101(proper(X1), proper(X2), proper(X3)) | |
| proper(tt) | → | ok(tt) | proper(U102(X1, X2, X3)) | → | U102(proper(X1), proper(X2), proper(X3)) | |
| proper(isNatKind(X)) | → | isNatKind(proper(X)) | proper(U103(X1, X2, X3)) | → | U103(proper(X1), proper(X2), proper(X3)) | |
| proper(isNatIListKind(X)) | → | isNatIListKind(proper(X)) | proper(U104(X1, X2, X3)) | → | U104(proper(X1), proper(X2), proper(X3)) | |
| proper(U105(X1, X2)) | → | U105(proper(X1), proper(X2)) | proper(isNat(X)) | → | isNat(proper(X)) | |
| proper(U106(X)) | → | U106(proper(X)) | proper(isNatIList(X)) | → | isNatIList(proper(X)) | |
| proper(U11(X1, X2)) | → | U11(proper(X1), proper(X2)) | proper(U12(X1, X2)) | → | U12(proper(X1), proper(X2)) | |
| proper(U111(X1, X2, X3)) | → | U111(proper(X1), proper(X2), proper(X3)) | proper(U112(X1, X2, X3)) | → | U112(proper(X1), proper(X2), proper(X3)) | |
| proper(U113(X1, X2, X3)) | → | U113(proper(X1), proper(X2), proper(X3)) | proper(U114(X1, X2)) | → | U114(proper(X1), proper(X2)) | |
| proper(s(X)) | → | s(proper(X)) | proper(length(X)) | → | length(proper(X)) | |
| proper(U13(X)) | → | U13(proper(X)) | proper(isNatList(X)) | → | isNatList(proper(X)) | |
| proper(U121(X1, X2)) | → | U121(proper(X1), proper(X2)) | proper(U122(X)) | → | U122(proper(X)) | |
| proper(nil) | → | ok(nil) | proper(U131(X1, X2, X3, X4)) | → | U131(proper(X1), proper(X2), proper(X3), proper(X4)) | |
| proper(U132(X1, X2, X3, X4)) | → | U132(proper(X1), proper(X2), proper(X3), proper(X4)) | proper(U133(X1, X2, X3, X4)) | → | U133(proper(X1), proper(X2), proper(X3), proper(X4)) | |
| proper(U134(X1, X2, X3, X4)) | → | U134(proper(X1), proper(X2), proper(X3), proper(X4)) | proper(U135(X1, X2, X3, X4)) | → | U135(proper(X1), proper(X2), proper(X3), proper(X4)) | |
| proper(U136(X1, X2, X3, X4)) | → | U136(proper(X1), proper(X2), proper(X3), proper(X4)) | proper(take(X1, X2)) | → | take(proper(X1), proper(X2)) | |
| proper(U21(X1, X2)) | → | U21(proper(X1), proper(X2)) | proper(U22(X1, X2)) | → | U22(proper(X1), proper(X2)) | |
| proper(U23(X)) | → | U23(proper(X)) | proper(U31(X1, X2)) | → | U31(proper(X1), proper(X2)) | |
| proper(U32(X1, X2)) | → | U32(proper(X1), proper(X2)) | proper(U33(X)) | → | U33(proper(X)) | |
| 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(U43(X1, X2, X3)) | → | U43(proper(X1), proper(X2), proper(X3)) | proper(U44(X1, X2, X3)) | → | U44(proper(X1), proper(X2), proper(X3)) | |
| proper(U45(X1, X2)) | → | U45(proper(X1), proper(X2)) | proper(U46(X)) | → | U46(proper(X)) | |
| proper(U51(X1, X2)) | → | U51(proper(X1), proper(X2)) | proper(U52(X)) | → | U52(proper(X)) | |
| proper(U61(X1, X2)) | → | U61(proper(X1), proper(X2)) | proper(U62(X)) | → | U62(proper(X)) | |
| proper(U71(X)) | → | U71(proper(X)) | proper(U81(X)) | → | U81(proper(X)) | |
| proper(U91(X1, X2, X3)) | → | U91(proper(X1), proper(X2), proper(X3)) | proper(U92(X1, X2, X3)) | → | U92(proper(X1), proper(X2), proper(X3)) | |
| proper(U93(X1, X2, X3)) | → | U93(proper(X1), proper(X2), proper(X3)) | proper(U94(X1, X2, X3)) | → | U94(proper(X1), proper(X2), proper(X3)) | |
| proper(U95(X1, X2)) | → | U95(proper(X1), proper(X2)) | proper(U96(X)) | → | U96(proper(X)) | |
| cons(ok(X1), ok(X2)) | → | ok(cons(X1, X2)) | U101(ok(X1), ok(X2), ok(X3)) | → | ok(U101(X1, X2, X3)) | |
| U102(ok(X1), ok(X2), ok(X3)) | → | ok(U102(X1, X2, X3)) | isNatKind(ok(X)) | → | ok(isNatKind(X)) | |
| U103(ok(X1), ok(X2), ok(X3)) | → | ok(U103(X1, X2, X3)) | isNatIListKind(ok(X)) | → | ok(isNatIListKind(X)) | |
| U104(ok(X1), ok(X2), ok(X3)) | → | ok(U104(X1, X2, X3)) | U105(ok(X1), ok(X2)) | → | ok(U105(X1, X2)) | |
| isNat(ok(X)) | → | ok(isNat(X)) | U106(ok(X)) | → | ok(U106(X)) | |
| isNatIList(ok(X)) | → | ok(isNatIList(X)) | U11(ok(X1), ok(X2)) | → | ok(U11(X1, X2)) | |
| U12(ok(X1), ok(X2)) | → | ok(U12(X1, X2)) | U111(ok(X1), ok(X2), ok(X3)) | → | ok(U111(X1, X2, X3)) | |
| U112(ok(X1), ok(X2), ok(X3)) | → | ok(U112(X1, X2, X3)) | U113(ok(X1), ok(X2), ok(X3)) | → | ok(U113(X1, X2, X3)) | |
| U114(ok(X1), ok(X2)) | → | ok(U114(X1, X2)) | s(ok(X)) | → | ok(s(X)) | |
| length(ok(X)) | → | ok(length(X)) | U13(ok(X)) | → | ok(U13(X)) | |
| isNatList(ok(X)) | → | ok(isNatList(X)) | U121(ok(X1), ok(X2)) | → | ok(U121(X1, X2)) | |
| U122(ok(X)) | → | ok(U122(X)) | U131(ok(X1), ok(X2), ok(X3), ok(X4)) | → | ok(U131(X1, X2, X3, X4)) | |
| U132(ok(X1), ok(X2), ok(X3), ok(X4)) | → | ok(U132(X1, X2, X3, X4)) | U133(ok(X1), ok(X2), ok(X3), ok(X4)) | → | ok(U133(X1, X2, X3, X4)) | |
| U134(ok(X1), ok(X2), ok(X3), ok(X4)) | → | ok(U134(X1, X2, X3, X4)) | U135(ok(X1), ok(X2), ok(X3), ok(X4)) | → | ok(U135(X1, X2, X3, X4)) | |
| U136(ok(X1), ok(X2), ok(X3), ok(X4)) | → | ok(U136(X1, X2, X3, X4)) | take(ok(X1), ok(X2)) | → | ok(take(X1, X2)) | |
| U21(ok(X1), ok(X2)) | → | ok(U21(X1, X2)) | U22(ok(X1), ok(X2)) | → | ok(U22(X1, X2)) | |
| U23(ok(X)) | → | ok(U23(X)) | U31(ok(X1), ok(X2)) | → | ok(U31(X1, X2)) | |
| U32(ok(X1), ok(X2)) | → | ok(U32(X1, X2)) | U33(ok(X)) | → | ok(U33(X)) | |
| U41(ok(X1), ok(X2), ok(X3)) | → | ok(U41(X1, X2, X3)) | U42(ok(X1), ok(X2), ok(X3)) | → | ok(U42(X1, X2, X3)) | |
| U43(ok(X1), ok(X2), ok(X3)) | → | ok(U43(X1, X2, X3)) | U44(ok(X1), ok(X2), ok(X3)) | → | ok(U44(X1, X2, X3)) | |
| U45(ok(X1), ok(X2)) | → | ok(U45(X1, X2)) | U46(ok(X)) | → | ok(U46(X)) | |
| U51(ok(X1), ok(X2)) | → | ok(U51(X1, X2)) | U52(ok(X)) | → | ok(U52(X)) | |
| U61(ok(X1), ok(X2)) | → | ok(U61(X1, X2)) | U62(ok(X)) | → | ok(U62(X)) | |
| U71(ok(X)) | → | ok(U71(X)) | U81(ok(X)) | → | ok(U81(X)) | |
| U91(ok(X1), ok(X2), ok(X3)) | → | ok(U91(X1, X2, X3)) | U92(ok(X1), ok(X2), ok(X3)) | → | ok(U92(X1, X2, X3)) | |
| U93(ok(X1), ok(X2), ok(X3)) | → | ok(U93(X1, X2, X3)) | U94(ok(X1), ok(X2), ok(X3)) | → | ok(U94(X1, X2, X3)) | |
| U95(ok(X1), ok(X2)) | → | ok(U95(X1, X2)) | U96(ok(X)) | → | ok(U96(X)) | |
| top(mark(X)) | → | top(proper(X)) | top(ok(X)) | → | top(active(X)) |
Termination of terms over the following signature is verified: U104, U105, U106, U112, U111, U62, U114, U61, U113, ok, proper, U23, U21, U22, isNatIList, isNatKind, mark, U71, 0, U122, U121, zeros, active, U31, U32, U33, isNatIListKind, U96, U94, U95, isNat, U46, U45, U132, U44, U131, U43, U93, U134, U42, U92, U133, U41, U91, U136, U135, length, top, cons, isNatList, s, U51, tt, take, U81, U52, U11, U12, U13, U102, U103, U101, nil