MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { zeros() -> cons(0(), n__zeros()) , zeros() -> n__zeros() , cons(X1, X2) -> n__cons(X1, X2) , 0() -> n__0() , U11(tt(), V1) -> U12(isNatList(activate(V1))) , U12(tt()) -> tt() , isNatList(n__cons(V1, V2)) -> U51(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), activate(V1), activate(V2)) , isNatList(n__nil()) -> tt() , activate(X) -> X , activate(n__zeros()) -> zeros() , activate(n__0()) -> 0() , activate(n__length(X)) -> length(activate(X)) , activate(n__s(X)) -> s(activate(X)) , activate(n__cons(X1, X2)) -> cons(activate(X1), X2) , activate(n__isNatIListKind(X)) -> isNatIListKind(X) , activate(n__nil()) -> nil() , activate(n__and(X1, X2)) -> and(activate(X1), X2) , activate(n__isNat(X)) -> isNat(X) , activate(n__isNatKind(X)) -> isNatKind(X) , U21(tt(), V1) -> U22(isNat(activate(V1))) , U22(tt()) -> tt() , isNat(X) -> n__isNat(X) , isNat(n__0()) -> tt() , isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1)) , isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) , U31(tt(), V) -> U32(isNatList(activate(V))) , U32(tt()) -> tt() , U41(tt(), V1, V2) -> U42(isNat(activate(V1)), activate(V2)) , U42(tt(), V2) -> U43(isNatIList(activate(V2))) , U43(tt()) -> tt() , isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)) , isNatIList(n__zeros()) -> tt() , isNatIList(n__cons(V1, V2)) -> U41(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), activate(V1), activate(V2)) , U51(tt(), V1, V2) -> U52(isNat(activate(V1)), activate(V2)) , U52(tt(), V2) -> U53(isNatList(activate(V2))) , U53(tt()) -> tt() , U61(tt(), L) -> s(length(activate(L))) , s(X) -> n__s(X) , length(X) -> n__length(X) , length(cons(N, L)) -> U61(and(and(isNatList(activate(L)), n__isNatIListKind(activate(L))), n__and(n__isNat(N), n__isNatKind(N))), activate(L)) , length(nil()) -> 0() , and(X1, X2) -> n__and(X1, X2) , and(tt(), X) -> activate(X) , isNatIListKind(X) -> n__isNatIListKind(X) , isNatIListKind(n__zeros()) -> tt() , isNatIListKind(n__cons(V1, V2)) -> and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))) , isNatIListKind(n__nil()) -> tt() , isNatKind(X) -> n__isNatKind(X) , isNatKind(n__0()) -> tt() , isNatKind(n__length(V1)) -> isNatIListKind(activate(V1)) , isNatKind(n__s(V1)) -> isNatKind(activate(V1)) , nil() -> n__nil() } Obligation: innermost runtime complexity Answer: MAYBE Arguments of following rules are not normal-forms: { length(cons(N, L)) -> U61(and(and(isNatList(activate(L)), n__isNatIListKind(activate(L))), n__and(n__isNat(N), n__isNatKind(N))), activate(L)) , length(nil()) -> 0() } All above mentioned rules can be savely removed. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { zeros() -> cons(0(), n__zeros()) , zeros() -> n__zeros() , cons(X1, X2) -> n__cons(X1, X2) , 0() -> n__0() , U11(tt(), V1) -> U12(isNatList(activate(V1))) , U12(tt()) -> tt() , isNatList(n__cons(V1, V2)) -> U51(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), activate(V1), activate(V2)) , isNatList(n__nil()) -> tt() , activate(X) -> X , activate(n__zeros()) -> zeros() , activate(n__0()) -> 0() , activate(n__length(X)) -> length(activate(X)) , activate(n__s(X)) -> s(activate(X)) , activate(n__cons(X1, X2)) -> cons(activate(X1), X2) , activate(n__isNatIListKind(X)) -> isNatIListKind(X) , activate(n__nil()) -> nil() , activate(n__and(X1, X2)) -> and(activate(X1), X2) , activate(n__isNat(X)) -> isNat(X) , activate(n__isNatKind(X)) -> isNatKind(X) , U21(tt(), V1) -> U22(isNat(activate(V1))) , U22(tt()) -> tt() , isNat(X) -> n__isNat(X) , isNat(n__0()) -> tt() , isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1)) , isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) , U31(tt(), V) -> U32(isNatList(activate(V))) , U32(tt()) -> tt() , U41(tt(), V1, V2) -> U42(isNat(activate(V1)), activate(V2)) , U42(tt(), V2) -> U43(isNatIList(activate(V2))) , U43(tt()) -> tt() , isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)) , isNatIList(n__zeros()) -> tt() , isNatIList(n__cons(V1, V2)) -> U41(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), activate(V1), activate(V2)) , U51(tt(), V1, V2) -> U52(isNat(activate(V1)), activate(V2)) , U52(tt(), V2) -> U53(isNatList(activate(V2))) , U53(tt()) -> tt() , U61(tt(), L) -> s(length(activate(L))) , s(X) -> n__s(X) , length(X) -> n__length(X) , and(X1, X2) -> n__and(X1, X2) , and(tt(), X) -> activate(X) , isNatIListKind(X) -> n__isNatIListKind(X) , isNatIListKind(n__zeros()) -> tt() , isNatIListKind(n__cons(V1, V2)) -> and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))) , isNatIListKind(n__nil()) -> tt() , isNatKind(X) -> n__isNatKind(X) , isNatKind(n__0()) -> tt() , isNatKind(n__length(V1)) -> isNatIListKind(activate(V1)) , isNatKind(n__s(V1)) -> isNatKind(activate(V1)) , nil() -> n__nil() } 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) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due to the following reason: The input cannot be shown compatible 2) 'bsearch-popstar (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..