MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { __(X1, X2) -> n____(X1, X2) , __(X, nil()) -> X , __(__(X, Y), Z) -> __(X, __(Y, Z)) , __(nil(), X) -> X , nil() -> n__nil() , U11(tt(), V) -> U12(isPalListKind(activate(V)), activate(V)) , U12(tt(), V) -> U13(isNeList(activate(V))) , isPalListKind(n__nil()) -> tt() , isPalListKind(n____(V1, V2)) -> U91(isPalListKind(activate(V1)), activate(V2)) , isPalListKind(n__a()) -> tt() , isPalListKind(n__e()) -> tt() , isPalListKind(n__i()) -> tt() , isPalListKind(n__o()) -> tt() , isPalListKind(n__u()) -> tt() , activate(X) -> X , activate(n__nil()) -> nil() , activate(n____(X1, X2)) -> __(activate(X1), activate(X2)) , activate(n__a()) -> a() , activate(n__e()) -> e() , activate(n__i()) -> i() , activate(n__o()) -> o() , activate(n__u()) -> u() , U13(tt()) -> tt() , isNeList(V) -> U31(isPalListKind(activate(V)), activate(V)) , isNeList(n____(V1, V2)) -> U41(isPalListKind(activate(V1)), activate(V1), activate(V2)) , isNeList(n____(V1, V2)) -> U51(isPalListKind(activate(V1)), activate(V1), activate(V2)) , U21(tt(), V1, V2) -> U22(isPalListKind(activate(V1)), activate(V1), activate(V2)) , U22(tt(), V1, V2) -> U23(isPalListKind(activate(V2)), activate(V1), activate(V2)) , U23(tt(), V1, V2) -> U24(isPalListKind(activate(V2)), activate(V1), activate(V2)) , U24(tt(), V1, V2) -> U25(isList(activate(V1)), activate(V2)) , U25(tt(), V2) -> U26(isList(activate(V2))) , isList(V) -> U11(isPalListKind(activate(V)), activate(V)) , isList(n__nil()) -> tt() , isList(n____(V1, V2)) -> U21(isPalListKind(activate(V1)), activate(V1), activate(V2)) , U26(tt()) -> tt() , U31(tt(), V) -> U32(isPalListKind(activate(V)), activate(V)) , U32(tt(), V) -> U33(isQid(activate(V))) , U33(tt()) -> tt() , isQid(n__a()) -> tt() , isQid(n__e()) -> tt() , isQid(n__i()) -> tt() , isQid(n__o()) -> tt() , isQid(n__u()) -> tt() , U41(tt(), V1, V2) -> U42(isPalListKind(activate(V1)), activate(V1), activate(V2)) , U42(tt(), V1, V2) -> U43(isPalListKind(activate(V2)), activate(V1), activate(V2)) , U43(tt(), V1, V2) -> U44(isPalListKind(activate(V2)), activate(V1), activate(V2)) , U44(tt(), V1, V2) -> U45(isList(activate(V1)), activate(V2)) , U45(tt(), V2) -> U46(isNeList(activate(V2))) , U46(tt()) -> tt() , U51(tt(), V1, V2) -> U52(isPalListKind(activate(V1)), activate(V1), activate(V2)) , U52(tt(), V1, V2) -> U53(isPalListKind(activate(V2)), activate(V1), activate(V2)) , U53(tt(), V1, V2) -> U54(isPalListKind(activate(V2)), activate(V1), activate(V2)) , U54(tt(), V1, V2) -> U55(isNeList(activate(V1)), activate(V2)) , U55(tt(), V2) -> U56(isList(activate(V2))) , U56(tt()) -> tt() , U61(tt(), V) -> U62(isPalListKind(activate(V)), activate(V)) , U62(tt(), V) -> U63(isQid(activate(V))) , U63(tt()) -> tt() , U71(tt(), I, P) -> U72(isPalListKind(activate(I)), activate(P)) , U72(tt(), P) -> U73(isPal(activate(P)), activate(P)) , U73(tt(), P) -> U74(isPalListKind(activate(P))) , isPal(V) -> U81(isPalListKind(activate(V)), activate(V)) , isPal(n__nil()) -> tt() , U74(tt()) -> tt() , U81(tt(), V) -> U82(isPalListKind(activate(V)), activate(V)) , U82(tt(), V) -> U83(isNePal(activate(V))) , U83(tt()) -> tt() , isNePal(V) -> U61(isPalListKind(activate(V)), activate(V)) , isNePal(n____(I, n____(P, I))) -> U71(isQid(activate(I)), activate(I), activate(P)) , U91(tt(), V2) -> U92(isPalListKind(activate(V2))) , U92(tt()) -> tt() , a() -> n__a() , e() -> n__e() , i() -> n__i() , o() -> n__o() , u() -> n__u() } Obligation: innermost runtime complexity Answer: MAYBE Arguments of following rules are not normal-forms: { __(X, nil()) -> X , __(__(X, Y), Z) -> __(X, __(Y, Z)) , __(nil(), X) -> X } All above mentioned rules can be savely removed. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { __(X1, X2) -> n____(X1, X2) , nil() -> n__nil() , U11(tt(), V) -> U12(isPalListKind(activate(V)), activate(V)) , U12(tt(), V) -> U13(isNeList(activate(V))) , isPalListKind(n__nil()) -> tt() , isPalListKind(n____(V1, V2)) -> U91(isPalListKind(activate(V1)), activate(V2)) , isPalListKind(n__a()) -> tt() , isPalListKind(n__e()) -> tt() , isPalListKind(n__i()) -> tt() , isPalListKind(n__o()) -> tt() , isPalListKind(n__u()) -> tt() , activate(X) -> X , activate(n__nil()) -> nil() , activate(n____(X1, X2)) -> __(activate(X1), activate(X2)) , activate(n__a()) -> a() , activate(n__e()) -> e() , activate(n__i()) -> i() , activate(n__o()) -> o() , activate(n__u()) -> u() , U13(tt()) -> tt() , isNeList(V) -> U31(isPalListKind(activate(V)), activate(V)) , isNeList(n____(V1, V2)) -> U41(isPalListKind(activate(V1)), activate(V1), activate(V2)) , isNeList(n____(V1, V2)) -> U51(isPalListKind(activate(V1)), activate(V1), activate(V2)) , U21(tt(), V1, V2) -> U22(isPalListKind(activate(V1)), activate(V1), activate(V2)) , U22(tt(), V1, V2) -> U23(isPalListKind(activate(V2)), activate(V1), activate(V2)) , U23(tt(), V1, V2) -> U24(isPalListKind(activate(V2)), activate(V1), activate(V2)) , U24(tt(), V1, V2) -> U25(isList(activate(V1)), activate(V2)) , U25(tt(), V2) -> U26(isList(activate(V2))) , isList(V) -> U11(isPalListKind(activate(V)), activate(V)) , isList(n__nil()) -> tt() , isList(n____(V1, V2)) -> U21(isPalListKind(activate(V1)), activate(V1), activate(V2)) , U26(tt()) -> tt() , U31(tt(), V) -> U32(isPalListKind(activate(V)), activate(V)) , U32(tt(), V) -> U33(isQid(activate(V))) , U33(tt()) -> tt() , isQid(n__a()) -> tt() , isQid(n__e()) -> tt() , isQid(n__i()) -> tt() , isQid(n__o()) -> tt() , isQid(n__u()) -> tt() , U41(tt(), V1, V2) -> U42(isPalListKind(activate(V1)), activate(V1), activate(V2)) , U42(tt(), V1, V2) -> U43(isPalListKind(activate(V2)), activate(V1), activate(V2)) , U43(tt(), V1, V2) -> U44(isPalListKind(activate(V2)), activate(V1), activate(V2)) , U44(tt(), V1, V2) -> U45(isList(activate(V1)), activate(V2)) , U45(tt(), V2) -> U46(isNeList(activate(V2))) , U46(tt()) -> tt() , U51(tt(), V1, V2) -> U52(isPalListKind(activate(V1)), activate(V1), activate(V2)) , U52(tt(), V1, V2) -> U53(isPalListKind(activate(V2)), activate(V1), activate(V2)) , U53(tt(), V1, V2) -> U54(isPalListKind(activate(V2)), activate(V1), activate(V2)) , U54(tt(), V1, V2) -> U55(isNeList(activate(V1)), activate(V2)) , U55(tt(), V2) -> U56(isList(activate(V2))) , U56(tt()) -> tt() , U61(tt(), V) -> U62(isPalListKind(activate(V)), activate(V)) , U62(tt(), V) -> U63(isQid(activate(V))) , U63(tt()) -> tt() , U71(tt(), I, P) -> U72(isPalListKind(activate(I)), activate(P)) , U72(tt(), P) -> U73(isPal(activate(P)), activate(P)) , U73(tt(), P) -> U74(isPalListKind(activate(P))) , isPal(V) -> U81(isPalListKind(activate(V)), activate(V)) , isPal(n__nil()) -> tt() , U74(tt()) -> tt() , U81(tt(), V) -> U82(isPalListKind(activate(V)), activate(V)) , U82(tt(), V) -> U83(isNePal(activate(V))) , U83(tt()) -> tt() , isNePal(V) -> U61(isPalListKind(activate(V)), activate(V)) , isNePal(n____(I, n____(P, I))) -> U71(isQid(activate(I)), activate(I), activate(P)) , U91(tt(), V2) -> U92(isPalListKind(activate(V2))) , U92(tt()) -> tt() , a() -> n__a() , e() -> n__e() , i() -> n__i() , o() -> n__o() , u() -> n__u() } 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..