TIMEOUT
The TRS could not be proven terminating. The proof attempt took 60027 ms.
Problem 1 remains open; application of the following processors failed [DependencyGraph (timeout)].
active#(take(s(M), cons(N, IL))) | → | U91#(isNatIList(IL), IL, M, N) | active#(U72(tt, L)) | → | length#(L) | |
mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) | active#(U72(tt, L)) | → | s#(length(L)) | |
mark#(take(X1, X2)) | → | active#(take(mark(X1), mark(X2))) | active#(U51(tt, V2)) | → | U52#(isNatList(V2)) | |
active#(U51(tt, V2)) | → | isNatList#(V2) | U91#(active(X1), X2, X3, X4) | → | U91#(X1, X2, X3, X4) | |
U51#(mark(X1), X2) | → | U51#(X1, X2) | U72#(mark(X1), X2) | → | U72#(X1, X2) | |
isNat#(active(X)) | → | isNat#(X) | mark#(s(X)) | → | mark#(X) | |
U71#(X1, mark(X2), X3) | → | U71#(X1, X2, X3) | length#(mark(X)) | → | length#(X) | |
mark#(U81(X)) | → | active#(U81(mark(X))) | U81#(mark(X)) | → | U81#(X) | |
mark#(U52(X)) | → | mark#(X) | active#(U31(tt)) | → | mark#(tt) | |
mark#(U42(X)) | → | active#(U42(mark(X))) | U92#(X1, mark(X2), X3, X4) | → | U92#(X1, X2, X3, X4) | |
mark#(U92(X1, X2, X3, X4)) | → | mark#(X1) | U93#(X1, X2, X3, active(X4)) | → | U93#(X1, X2, X3, X4) | |
active#(U42(tt)) | → | mark#(tt) | active#(U91(tt, IL, M, N)) | → | U92#(isNat(M), IL, M, N) | |
mark#(U62(X)) | → | active#(U62(mark(X))) | mark#(U11(X)) | → | mark#(X) | |
mark#(U21(X)) | → | mark#(X) | active#(isNat(length(V1))) | → | U11#(isNatList(V1)) | |
active#(U93(tt, IL, M, N)) | → | take#(M, IL) | active#(U93(tt, IL, M, N)) | → | mark#(cons(N, take(M, IL))) | |
U71#(active(X1), X2, X3) | → | U71#(X1, X2, X3) | active#(isNatList(cons(V1, V2))) | → | mark#(U51(isNat(V1), V2)) | |
mark#(U41(X1, X2)) | → | mark#(X1) | mark#(U11(X)) | → | active#(U11(mark(X))) | |
cons#(X1, mark(X2)) | → | cons#(X1, X2) | U41#(X1, active(X2)) | → | U41#(X1, X2) | |
active#(isNat(s(V1))) | → | isNat#(V1) | active#(isNatIList(cons(V1, V2))) | → | mark#(U41(isNat(V1), V2)) | |
U62#(active(X)) | → | U62#(X) | active#(U61(tt, V2)) | → | isNatIList#(V2) | |
cons#(active(X1), X2) | → | cons#(X1, X2) | active#(isNatList(cons(V1, V2))) | → | U51#(isNat(V1), V2) | |
U91#(mark(X1), X2, X3, X4) | → | U91#(X1, X2, X3, X4) | mark#(U71(X1, X2, X3)) | → | U71#(mark(X1), X2, X3) | |
U93#(X1, X2, X3, mark(X4)) | → | U93#(X1, X2, X3, X4) | U51#(X1, mark(X2)) | → | U51#(X1, X2) | |
mark#(isNatList(X)) | → | isNatList#(X) | isNatList#(mark(X)) | → | isNatList#(X) | |
active#(isNatIList(V)) | → | U31#(isNatList(V)) | mark#(U72(X1, X2)) | → | active#(U72(mark(X1), X2)) | |
mark#(take(X1, X2)) | → | mark#(X1) | mark#(U21(X)) | → | active#(U21(mark(X))) | |
active#(U21(tt)) | → | mark#(tt) | active#(length(cons(N, L))) | → | mark#(U71(isNatList(L), L, N)) | |
active#(U41(tt, V2)) | → | mark#(U42(isNatIList(V2))) | active#(take(s(M), cons(N, IL))) | → | isNatIList#(IL) | |
active#(isNatIList(cons(V1, V2))) | → | U41#(isNat(V1), V2) | active#(U91(tt, IL, M, N)) | → | mark#(U92(isNat(M), IL, M, N)) | |
active#(U81(tt)) | → | mark#(nil) | U61#(active(X1), X2) | → | U61#(X1, X2) | |
mark#(s(X)) | → | s#(mark(X)) | U52#(active(X)) | → | U52#(X) | |
U61#(mark(X1), X2) | → | U61#(X1, X2) | active#(isNatIList(V)) | → | mark#(U31(isNatList(V))) | |
isNatList#(active(X)) | → | isNatList#(X) | active#(U62(tt)) | → | mark#(tt) | |
U41#(X1, mark(X2)) | → | U41#(X1, X2) | active#(isNat(0)) | → | mark#(tt) | |
active#(take(0, IL)) | → | mark#(U81(isNatIList(IL))) | take#(X1, mark(X2)) | → | take#(X1, X2) | |
mark#(U61(X1, X2)) | → | active#(U61(mark(X1), X2)) | mark#(isNatIList(X)) | → | isNatIList#(X) | |
isNatIList#(mark(X)) | → | isNatIList#(X) | mark#(U92(X1, X2, X3, X4)) | → | U92#(mark(X1), X2, X3, X4) | |
mark#(U93(X1, X2, X3, X4)) | → | mark#(X1) | cons#(X1, active(X2)) | → | cons#(X1, X2) | |
U92#(X1, X2, mark(X3), X4) | → | U92#(X1, X2, X3, X4) | U93#(X1, X2, active(X3), X4) | → | U93#(X1, X2, X3, X4) | |
active#(U52(tt)) | → | mark#(tt) | mark#(U61(X1, X2)) | → | mark#(X1) | |
take#(mark(X1), X2) | → | take#(X1, X2) | mark#(U11(X)) | → | U11#(mark(X)) | |
U71#(X1, X2, active(X3)) | → | U71#(X1, X2, X3) | mark#(U42(X)) | → | mark#(X) | |
mark#(isNat(X)) | → | isNat#(X) | U61#(X1, mark(X2)) | → | U61#(X1, X2) | |
isNat#(mark(X)) | → | isNat#(X) | active#(U11(tt)) | → | mark#(tt) | |
active#(length(cons(N, L))) | → | isNatList#(L) | active#(isNatList(nil)) | → | mark#(tt) | |
mark#(nil) | → | active#(nil) | take#(X1, active(X2)) | → | take#(X1, X2) | |
active#(isNatIList(zeros)) | → | mark#(tt) | U41#(mark(X1), X2) | → | U41#(X1, X2) | |
mark#(cons(X1, X2)) | → | cons#(mark(X1), X2) | mark#(U91(X1, X2, X3, X4)) | → | active#(U91(mark(X1), X2, X3, X4)) | |
mark#(length(X)) | → | length#(mark(X)) | U31#(active(X)) | → | U31#(X) | |
U93#(X1, X2, mark(X3), X4) | → | U93#(X1, X2, X3, X4) | U72#(active(X1), X2) | → | U72#(X1, X2) | |
active#(isNatIList(V)) | → | isNatList#(V) | mark#(take(X1, X2)) | → | take#(mark(X1), mark(X2)) | |
s#(mark(X)) | → | s#(X) | U52#(mark(X)) | → | U52#(X) | |
active#(U51(tt, V2)) | → | mark#(U52(isNatList(V2))) | U93#(X1, active(X2), X3, X4) | → | U93#(X1, X2, X3, X4) | |
mark#(length(X)) | → | active#(length(mark(X))) | U91#(X1, X2, X3, active(X4)) | → | U91#(X1, X2, X3, X4) | |
active#(take(0, IL)) | → | isNatIList#(IL) | U92#(X1, X2, X3, mark(X4)) | → | U92#(X1, X2, X3, X4) | |
active#(U92(tt, IL, M, N)) | → | U93#(isNat(N), IL, M, N) | active#(U92(tt, IL, M, N)) | → | mark#(U93(isNat(N), IL, M, N)) | |
active#(U41(tt, V2)) | → | isNatIList#(V2) | active#(length(nil)) | → | mark#(0) | |
U81#(active(X)) | → | U81#(X) | U93#(X1, mark(X2), X3, X4) | → | U93#(X1, X2, X3, X4) | |
active#(isNat(length(V1))) | → | isNatList#(V1) | active#(take(s(M), cons(N, IL))) | → | mark#(U91(isNatIList(IL), IL, M, N)) | |
U72#(X1, active(X2)) | → | U72#(X1, X2) | mark#(U42(X)) | → | U42#(mark(X)) | |
mark#(U72(X1, X2)) | → | mark#(X1) | active#(U71(tt, L, N)) | → | mark#(U72(isNat(N), L)) | |
mark#(cons(X1, X2)) | → | mark#(X1) | U71#(mark(X1), X2, X3) | → | U71#(X1, X2, X3) | |
mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) | active#(isNatList(take(V1, V2))) | → | mark#(U61(isNat(V1), V2)) | |
U41#(active(X1), X2) | → | U41#(X1, X2) | active#(isNatIList(cons(V1, V2))) | → | isNat#(V1) | |
mark#(U62(X)) | → | mark#(X) | mark#(U31(X)) | → | mark#(X) | |
U92#(active(X1), X2, X3, X4) | → | U92#(X1, X2, X3, X4) | U51#(X1, active(X2)) | → | U51#(X1, X2) | |
mark#(tt) | → | active#(tt) | cons#(mark(X1), X2) | → | cons#(X1, X2) | |
active#(U61(tt, V2)) | → | mark#(U62(isNatIList(V2))) | mark#(U61(X1, X2)) | → | U61#(mark(X1), X2) | |
mark#(U93(X1, X2, X3, X4)) | → | active#(U93(mark(X1), X2, X3, X4)) | mark#(U52(X)) | → | active#(U52(mark(X))) | |
active#(U41(tt, V2)) | → | U42#(isNatIList(V2)) | U62#(mark(X)) | → | U62#(X) | |
U61#(X1, active(X2)) | → | U61#(X1, X2) | active#(U61(tt, V2)) | → | U62#(isNatIList(V2)) | |
mark#(length(X)) | → | mark#(X) | mark#(zeros) | → | active#(zeros) | |
U11#(mark(X)) | → | U11#(X) | U92#(X1, X2, active(X3), X4) | → | U92#(X1, X2, X3, X4) | |
mark#(0) | → | active#(0) | mark#(s(X)) | → | active#(s(mark(X))) | |
active#(isNat(s(V1))) | → | U21#(isNat(V1)) | U91#(X1, mark(X2), X3, X4) | → | U91#(X1, X2, X3, X4) | |
U71#(X1, X2, mark(X3)) | → | U71#(X1, X2, X3) | active#(U91(tt, IL, M, N)) | → | isNat#(M) | |
mark#(U62(X)) | → | U62#(mark(X)) | mark#(U31(X)) | → | U31#(mark(X)) | |
active#(zeros) | → | cons#(0, zeros) | mark#(U72(X1, X2)) | → | U72#(mark(X1), X2) | |
U72#(X1, mark(X2)) | → | U72#(X1, X2) | U92#(mark(X1), X2, X3, X4) | → | U92#(X1, X2, X3, X4) | |
mark#(U21(X)) | → | U21#(mark(X)) | mark#(cons(X1, X2)) | → | active#(cons(mark(X1), X2)) | |
mark#(U71(X1, X2, X3)) | → | active#(U71(mark(X1), X2, X3)) | U11#(active(X)) | → | U11#(X) | |
active#(isNat(length(V1))) | → | mark#(U11(isNatList(V1))) | U93#(active(X1), X2, X3, X4) | → | U93#(X1, X2, X3, X4) | |
U42#(active(X)) | → | U42#(X) | mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | |
mark#(U52(X)) | → | U52#(mark(X)) | U42#(mark(X)) | → | U42#(X) | |
U91#(X1, X2, active(X3), X4) | → | U91#(X1, X2, X3, X4) | mark#(U81(X)) | → | mark#(X) | |
length#(active(X)) | → | length#(X) | U71#(X1, active(X2), X3) | → | U71#(X1, X2, X3) | |
active#(length(cons(N, L))) | → | U71#(isNatList(L), L, N) | mark#(isNatIList(X)) | → | active#(isNatIList(X)) | |
mark#(U71(X1, X2, X3)) | → | mark#(X1) | isNatIList#(active(X)) | → | isNatIList#(X) | |
mark#(U92(X1, X2, X3, X4)) | → | active#(U92(mark(X1), X2, X3, X4)) | U92#(X1, X2, X3, active(X4)) | → | U92#(X1, X2, X3, X4) | |
active#(isNatList(take(V1, V2))) | → | U61#(isNat(V1), V2) | mark#(U41(X1, X2)) | → | U41#(mark(X1), X2) | |
active#(isNatList(cons(V1, V2))) | → | isNat#(V1) | mark#(U93(X1, X2, X3, X4)) | → | U93#(mark(X1), X2, X3, X4) | |
U31#(mark(X)) | → | U31#(X) | mark#(isNat(X)) | → | active#(isNat(X)) | |
U93#(mark(X1), X2, X3, X4) | → | U93#(X1, X2, X3, X4) | U51#(active(X1), X2) | → | U51#(X1, X2) | |
mark#(U81(X)) | → | U81#(mark(X)) | mark#(U51(X1, X2)) | → | mark#(X1) | |
active#(U72(tt, L)) | → | mark#(s(length(L))) | active#(U92(tt, IL, M, N)) | → | isNat#(N) | |
active#(isNatList(take(V1, V2))) | → | isNat#(V1) | active#(U71(tt, L, N)) | → | isNat#(N) | |
mark#(U91(X1, X2, X3, X4)) | → | U91#(mark(X1), X2, X3, X4) | U92#(X1, active(X2), X3, X4) | → | U92#(X1, X2, X3, X4) | |
U21#(mark(X)) | → | U21#(X) | U21#(active(X)) | → | U21#(X) | |
mark#(U31(X)) | → | active#(U31(mark(X))) | active#(isNat(s(V1))) | → | mark#(U21(isNat(V1))) | |
active#(take(0, IL)) | → | U81#(isNatIList(IL)) | mark#(U91(X1, X2, X3, X4)) | → | mark#(X1) | |
active#(U93(tt, IL, M, N)) | → | cons#(N, take(M, IL)) | mark#(take(X1, X2)) | → | mark#(X2) | |
active#(zeros) | → | mark#(cons(0, zeros)) | s#(active(X)) | → | s#(X) | |
U91#(X1, X2, mark(X3), X4) | → | U91#(X1, X2, X3, X4) | U91#(X1, active(X2), X3, X4) | → | U91#(X1, X2, X3, X4) | |
mark#(isNatList(X)) | → | active#(isNatList(X)) | active#(U71(tt, L, N)) | → | U72#(isNat(N), L) | |
take#(active(X1), X2) | → | take#(X1, X2) | U91#(X1, X2, X3, mark(X4)) | → | U91#(X1, X2, X3, X4) |
active(zeros) | → | mark(cons(0, zeros)) | active(U11(tt)) | → | mark(tt) | |
active(U21(tt)) | → | mark(tt) | active(U31(tt)) | → | mark(tt) | |
active(U41(tt, V2)) | → | mark(U42(isNatIList(V2))) | active(U42(tt)) | → | mark(tt) | |
active(U51(tt, V2)) | → | mark(U52(isNatList(V2))) | active(U52(tt)) | → | mark(tt) | |
active(U61(tt, V2)) | → | mark(U62(isNatIList(V2))) | active(U62(tt)) | → | mark(tt) | |
active(U71(tt, L, N)) | → | mark(U72(isNat(N), L)) | active(U72(tt, L)) | → | mark(s(length(L))) | |
active(U81(tt)) | → | mark(nil) | active(U91(tt, IL, M, N)) | → | mark(U92(isNat(M), IL, M, N)) | |
active(U92(tt, IL, M, N)) | → | mark(U93(isNat(N), IL, M, N)) | active(U93(tt, IL, M, N)) | → | mark(cons(N, take(M, IL))) | |
active(isNat(0)) | → | mark(tt) | active(isNat(length(V1))) | → | mark(U11(isNatList(V1))) | |
active(isNat(s(V1))) | → | mark(U21(isNat(V1))) | active(isNatIList(V)) | → | mark(U31(isNatList(V))) | |
active(isNatIList(zeros)) | → | mark(tt) | active(isNatIList(cons(V1, V2))) | → | mark(U41(isNat(V1), V2)) | |
active(isNatList(nil)) | → | mark(tt) | active(isNatList(cons(V1, V2))) | → | mark(U51(isNat(V1), V2)) | |
active(isNatList(take(V1, V2))) | → | mark(U61(isNat(V1), V2)) | active(length(nil)) | → | mark(0) | |
active(length(cons(N, L))) | → | mark(U71(isNatList(L), L, N)) | active(take(0, IL)) | → | mark(U81(isNatIList(IL))) | |
active(take(s(M), cons(N, IL))) | → | mark(U91(isNatIList(IL), IL, M, N)) | mark(zeros) | → | active(zeros) | |
mark(cons(X1, X2)) | → | active(cons(mark(X1), X2)) | mark(0) | → | active(0) | |
mark(U11(X)) | → | active(U11(mark(X))) | mark(tt) | → | active(tt) | |
mark(U21(X)) | → | active(U21(mark(X))) | mark(U31(X)) | → | active(U31(mark(X))) | |
mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | mark(U42(X)) | → | active(U42(mark(X))) | |
mark(isNatIList(X)) | → | active(isNatIList(X)) | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) | |
mark(U52(X)) | → | active(U52(mark(X))) | mark(isNatList(X)) | → | active(isNatList(X)) | |
mark(U61(X1, X2)) | → | active(U61(mark(X1), X2)) | mark(U62(X)) | → | active(U62(mark(X))) | |
mark(U71(X1, X2, X3)) | → | active(U71(mark(X1), X2, X3)) | mark(U72(X1, X2)) | → | active(U72(mark(X1), X2)) | |
mark(isNat(X)) | → | active(isNat(X)) | mark(s(X)) | → | active(s(mark(X))) | |
mark(length(X)) | → | active(length(mark(X))) | mark(U81(X)) | → | active(U81(mark(X))) | |
mark(nil) | → | active(nil) | mark(U91(X1, X2, X3, X4)) | → | active(U91(mark(X1), X2, X3, X4)) | |
mark(U92(X1, X2, X3, X4)) | → | active(U92(mark(X1), X2, X3, X4)) | mark(U93(X1, X2, X3, X4)) | → | active(U93(mark(X1), X2, X3, X4)) | |
mark(take(X1, X2)) | → | active(take(mark(X1), mark(X2))) | cons(mark(X1), X2) | → | cons(X1, X2) | |
cons(X1, mark(X2)) | → | cons(X1, X2) | cons(active(X1), X2) | → | cons(X1, X2) | |
cons(X1, active(X2)) | → | cons(X1, X2) | U11(mark(X)) | → | U11(X) | |
U11(active(X)) | → | U11(X) | U21(mark(X)) | → | U21(X) | |
U21(active(X)) | → | U21(X) | U31(mark(X)) | → | U31(X) | |
U31(active(X)) | → | U31(X) | U41(mark(X1), X2) | → | U41(X1, X2) | |
U41(X1, mark(X2)) | → | U41(X1, X2) | U41(active(X1), X2) | → | U41(X1, X2) | |
U41(X1, active(X2)) | → | U41(X1, X2) | U42(mark(X)) | → | U42(X) | |
U42(active(X)) | → | U42(X) | isNatIList(mark(X)) | → | isNatIList(X) | |
isNatIList(active(X)) | → | isNatIList(X) | U51(mark(X1), X2) | → | U51(X1, X2) | |
U51(X1, mark(X2)) | → | U51(X1, X2) | U51(active(X1), X2) | → | U51(X1, X2) | |
U51(X1, active(X2)) | → | U51(X1, X2) | U52(mark(X)) | → | U52(X) | |
U52(active(X)) | → | U52(X) | isNatList(mark(X)) | → | isNatList(X) | |
isNatList(active(X)) | → | isNatList(X) | U61(mark(X1), X2) | → | U61(X1, X2) | |
U61(X1, mark(X2)) | → | U61(X1, X2) | U61(active(X1), X2) | → | U61(X1, X2) | |
U61(X1, active(X2)) | → | U61(X1, X2) | U62(mark(X)) | → | U62(X) | |
U62(active(X)) | → | U62(X) | U71(mark(X1), X2, X3) | → | U71(X1, X2, X3) | |
U71(X1, mark(X2), X3) | → | U71(X1, X2, X3) | U71(X1, X2, mark(X3)) | → | U71(X1, X2, X3) | |
U71(active(X1), X2, X3) | → | U71(X1, X2, X3) | U71(X1, active(X2), X3) | → | U71(X1, X2, X3) | |
U71(X1, X2, active(X3)) | → | U71(X1, X2, X3) | U72(mark(X1), X2) | → | U72(X1, X2) | |
U72(X1, mark(X2)) | → | U72(X1, X2) | U72(active(X1), X2) | → | U72(X1, X2) | |
U72(X1, active(X2)) | → | U72(X1, X2) | isNat(mark(X)) | → | isNat(X) | |
isNat(active(X)) | → | isNat(X) | s(mark(X)) | → | s(X) | |
s(active(X)) | → | s(X) | length(mark(X)) | → | length(X) | |
length(active(X)) | → | length(X) | U81(mark(X)) | → | U81(X) | |
U81(active(X)) | → | U81(X) | U91(mark(X1), X2, X3, X4) | → | U91(X1, X2, X3, X4) | |
U91(X1, mark(X2), X3, X4) | → | U91(X1, X2, X3, X4) | U91(X1, X2, mark(X3), X4) | → | U91(X1, X2, X3, X4) | |
U91(X1, X2, X3, mark(X4)) | → | U91(X1, X2, X3, X4) | U91(active(X1), X2, X3, X4) | → | U91(X1, X2, X3, X4) | |
U91(X1, active(X2), X3, X4) | → | U91(X1, X2, X3, X4) | U91(X1, X2, active(X3), X4) | → | U91(X1, X2, X3, X4) | |
U91(X1, X2, X3, active(X4)) | → | U91(X1, X2, X3, X4) | U92(mark(X1), X2, X3, X4) | → | U92(X1, X2, X3, X4) | |
U92(X1, mark(X2), X3, X4) | → | U92(X1, X2, X3, X4) | U92(X1, X2, mark(X3), X4) | → | U92(X1, X2, X3, X4) | |
U92(X1, X2, X3, mark(X4)) | → | U92(X1, X2, X3, X4) | U92(active(X1), X2, X3, X4) | → | U92(X1, X2, X3, X4) | |
U92(X1, active(X2), X3, X4) | → | U92(X1, X2, X3, X4) | U92(X1, X2, active(X3), X4) | → | U92(X1, X2, X3, X4) | |
U92(X1, X2, X3, active(X4)) | → | U92(X1, X2, X3, X4) | U93(mark(X1), X2, X3, X4) | → | U93(X1, X2, X3, X4) | |
U93(X1, mark(X2), X3, X4) | → | U93(X1, X2, X3, X4) | U93(X1, X2, mark(X3), X4) | → | U93(X1, X2, X3, X4) | |
U93(X1, X2, X3, mark(X4)) | → | U93(X1, X2, X3, X4) | U93(active(X1), X2, X3, X4) | → | U93(X1, X2, X3, X4) | |
U93(X1, active(X2), X3, X4) | → | U93(X1, X2, X3, X4) | U93(X1, X2, active(X3), X4) | → | U93(X1, X2, X3, X4) | |
U93(X1, X2, X3, active(X4)) | → | U93(X1, X2, X3, X4) | take(mark(X1), X2) | → | take(X1, X2) | |
take(X1, mark(X2)) | → | take(X1, X2) | take(active(X1), X2) | → | take(X1, X2) | |
take(X1, active(X2)) | → | take(X1, X2) |
Termination of terms over the following signature is verified: isNat, U62, U61, U93, U42, U41, U92, U91, length, U21, cons, isNatIList, mark, U71, U72, 0, isNatList, U51, s, tt, zeros, take, U52, U81, U11, active, U31, nil