MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { active(zeros()) -> mark(cons(0(), zeros())) , active(cons(X1, X2)) -> cons(active(X1), X2) , active(U11(X1, X2)) -> U11(active(X1), X2) , active(U11(tt(), V1)) -> mark(U12(isNatList(V1))) , active(U12(X)) -> U12(active(X)) , active(U12(tt())) -> mark(tt()) , active(isNatList(cons(V1, V2))) -> mark(U51(and(isNatKind(V1), isNatIListKind(V2)), V1, V2)) , active(isNatList(nil())) -> mark(tt()) , active(isNatList(take(V1, V2))) -> mark(U61(and(isNatKind(V1), isNatIListKind(V2)), V1, V2)) , active(U21(X1, X2)) -> U21(active(X1), X2) , active(U21(tt(), V1)) -> mark(U22(isNat(V1))) , active(U22(X)) -> U22(active(X)) , active(U22(tt())) -> mark(tt()) , active(isNat(0())) -> mark(tt()) , active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)) , active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1), V1)) , active(U31(X1, X2)) -> U31(active(X1), X2) , active(U31(tt(), V)) -> mark(U32(isNatList(V))) , active(U32(X)) -> U32(active(X)) , active(U32(tt())) -> mark(tt()) , active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) , active(U41(tt(), V1, V2)) -> mark(U42(isNat(V1), V2)) , active(U42(X1, X2)) -> U42(active(X1), X2) , active(U42(tt(), V2)) -> mark(U43(isNatIList(V2))) , active(U43(X)) -> U43(active(X)) , active(U43(tt())) -> mark(tt()) , active(isNatIList(V)) -> mark(U31(isNatIListKind(V), V)) , active(isNatIList(zeros())) -> mark(tt()) , active(isNatIList(cons(V1, V2))) -> mark(U41(and(isNatKind(V1), isNatIListKind(V2)), V1, V2)) , active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) , active(U51(tt(), V1, V2)) -> mark(U52(isNat(V1), V2)) , active(U52(X1, X2)) -> U52(active(X1), X2) , active(U52(tt(), V2)) -> mark(U53(isNatList(V2))) , active(U53(X)) -> U53(active(X)) , active(U53(tt())) -> mark(tt()) , active(U61(X1, X2, X3)) -> U61(active(X1), X2, X3) , active(U61(tt(), V1, V2)) -> mark(U62(isNat(V1), V2)) , active(U62(X1, X2)) -> U62(active(X1), X2) , active(U62(tt(), V2)) -> mark(U63(isNatIList(V2))) , active(U63(X)) -> U63(active(X)) , active(U63(tt())) -> mark(tt()) , active(U71(X1, X2)) -> U71(active(X1), X2) , active(U71(tt(), L)) -> mark(s(length(L))) , active(s(X)) -> s(active(X)) , active(length(X)) -> length(active(X)) , active(length(cons(N, L))) -> mark(U71(and(and(isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L)) , active(length(nil())) -> mark(0()) , active(U81(X)) -> U81(active(X)) , active(U81(tt())) -> mark(nil()) , active(U91(X1, X2, X3, X4)) -> U91(active(X1), X2, X3, X4) , active(U91(tt(), IL, M, N)) -> mark(cons(N, take(M, IL))) , active(take(X1, X2)) -> take(X1, active(X2)) , active(take(X1, X2)) -> take(active(X1), X2) , active(take(0(), IL)) -> mark(U81(and(isNatIList(IL), isNatIListKind(IL)))) , active(take(s(M), cons(N, IL))) -> mark(U91(and(and(isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), IL, M, N)) , active(and(X1, X2)) -> and(active(X1), X2) , active(and(tt(), X)) -> mark(X) , active(isNatIListKind(zeros())) -> mark(tt()) , active(isNatIListKind(cons(V1, V2))) -> mark(and(isNatKind(V1), isNatIListKind(V2))) , active(isNatIListKind(nil())) -> mark(tt()) , active(isNatIListKind(take(V1, V2))) -> mark(and(isNatKind(V1), isNatIListKind(V2))) , active(isNatKind(0())) -> mark(tt()) , active(isNatKind(s(V1))) -> mark(isNatKind(V1)) , active(isNatKind(length(V1))) -> mark(isNatIListKind(V1)) , cons(mark(X1), X2) -> mark(cons(X1, X2)) , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) , U11(mark(X1), X2) -> mark(U11(X1, X2)) , U11(ok(X1), ok(X2)) -> ok(U11(X1, X2)) , U12(mark(X)) -> mark(U12(X)) , U12(ok(X)) -> ok(U12(X)) , isNatList(ok(X)) -> ok(isNatList(X)) , U21(mark(X1), X2) -> mark(U21(X1, X2)) , U21(ok(X1), ok(X2)) -> ok(U21(X1, X2)) , U22(mark(X)) -> mark(U22(X)) , U22(ok(X)) -> ok(U22(X)) , isNat(ok(X)) -> ok(isNat(X)) , U31(mark(X1), X2) -> mark(U31(X1, X2)) , U31(ok(X1), ok(X2)) -> ok(U31(X1, X2)) , U32(mark(X)) -> mark(U32(X)) , U32(ok(X)) -> ok(U32(X)) , U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) , U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) , U42(mark(X1), X2) -> mark(U42(X1, X2)) , U42(ok(X1), ok(X2)) -> ok(U42(X1, X2)) , U43(mark(X)) -> mark(U43(X)) , U43(ok(X)) -> ok(U43(X)) , isNatIList(ok(X)) -> ok(isNatIList(X)) , U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) , U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) , U52(mark(X1), X2) -> mark(U52(X1, X2)) , U52(ok(X1), ok(X2)) -> ok(U52(X1, X2)) , U53(mark(X)) -> mark(U53(X)) , U53(ok(X)) -> ok(U53(X)) , U61(mark(X1), X2, X3) -> mark(U61(X1, X2, X3)) , U61(ok(X1), ok(X2), ok(X3)) -> ok(U61(X1, X2, X3)) , U62(mark(X1), X2) -> mark(U62(X1, X2)) , U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) , U63(mark(X)) -> mark(U63(X)) , U63(ok(X)) -> ok(U63(X)) , U71(mark(X1), X2) -> mark(U71(X1, X2)) , U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) , s(mark(X)) -> mark(s(X)) , s(ok(X)) -> ok(s(X)) , length(mark(X)) -> mark(length(X)) , length(ok(X)) -> ok(length(X)) , U81(mark(X)) -> mark(U81(X)) , U81(ok(X)) -> ok(U81(X)) , U91(mark(X1), X2, X3, X4) -> mark(U91(X1, X2, X3, X4)) , U91(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U91(X1, X2, X3, X4)) , take(X1, mark(X2)) -> mark(take(X1, X2)) , take(mark(X1), X2) -> mark(take(X1, X2)) , take(ok(X1), ok(X2)) -> ok(take(X1, X2)) , and(mark(X1), X2) -> mark(and(X1, X2)) , and(ok(X1), ok(X2)) -> ok(and(X1, X2)) , isNatIListKind(ok(X)) -> ok(isNatIListKind(X)) , isNatKind(ok(X)) -> ok(isNatKind(X)) , proper(zeros()) -> ok(zeros()) , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) , proper(0()) -> ok(0()) , proper(U11(X1, X2)) -> U11(proper(X1), proper(X2)) , proper(tt()) -> ok(tt()) , proper(U12(X)) -> U12(proper(X)) , proper(isNatList(X)) -> isNatList(proper(X)) , proper(U21(X1, X2)) -> U21(proper(X1), proper(X2)) , proper(U22(X)) -> U22(proper(X)) , proper(isNat(X)) -> isNat(proper(X)) , proper(U31(X1, X2)) -> U31(proper(X1), proper(X2)) , proper(U32(X)) -> U32(proper(X)) , proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) , proper(U42(X1, X2)) -> U42(proper(X1), proper(X2)) , proper(U43(X)) -> U43(proper(X)) , proper(isNatIList(X)) -> isNatIList(proper(X)) , proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) , proper(U52(X1, X2)) -> U52(proper(X1), proper(X2)) , proper(U53(X)) -> U53(proper(X)) , proper(U61(X1, X2, X3)) -> U61(proper(X1), proper(X2), proper(X3)) , proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) , proper(U63(X)) -> U63(proper(X)) , proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) , proper(s(X)) -> s(proper(X)) , proper(length(X)) -> length(proper(X)) , proper(U81(X)) -> U81(proper(X)) , proper(nil()) -> ok(nil()) , proper(U91(X1, X2, X3, X4)) -> U91(proper(X1), proper(X2), proper(X3), proper(X4)) , proper(take(X1, X2)) -> take(proper(X1), proper(X2)) , proper(and(X1, X2)) -> and(proper(X1), proper(X2)) , proper(isNatIListKind(X)) -> isNatIListKind(proper(X)) , proper(isNatKind(X)) -> isNatKind(proper(X)) , top(mark(X)) -> top(proper(X)) , top(ok(X)) -> top(active(X)) } Obligation: innermost runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem (timeout of 60 seconds)' failed due to the following reason: Computation stopped due to timeout after 60.0 seconds. 2) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem (timeout of 30 seconds) (timeout of 60 seconds)' failed due to the following reason: Computation stopped due to timeout after 30.0 seconds. 2) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'bsearch-popstar (timeout of 60 seconds)' failed due to the following reason: The input cannot be shown compatible 2) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due to the following reason: The input cannot be shown compatible 3) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. Arrrr..