MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { active(__(X1, X2)) -> __(X1, active(X2)) , active(__(X1, X2)) -> __(active(X1), X2) , active(__(X, nil())) -> mark(X) , active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z))) , active(__(nil(), X)) -> mark(X) , active(U11(X1, X2)) -> U11(active(X1), X2) , active(U11(tt(), V)) -> mark(U12(isNeList(V))) , active(U12(X)) -> U12(active(X)) , active(U12(tt())) -> mark(tt()) , active(isNeList(V)) -> mark(U31(isPalListKind(V), V)) , active(isNeList(__(V1, V2))) -> mark(U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)) , active(isNeList(__(V1, V2))) -> mark(U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)) , active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) , active(U21(tt(), V1, V2)) -> mark(U22(isList(V1), V2)) , active(U22(X1, X2)) -> U22(active(X1), X2) , active(U22(tt(), V2)) -> mark(U23(isList(V2))) , active(isList(V)) -> mark(U11(isPalListKind(V), V)) , active(isList(__(V1, V2))) -> mark(U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)) , active(isList(nil())) -> mark(tt()) , active(U23(X)) -> U23(active(X)) , active(U23(tt())) -> mark(tt()) , active(U31(X1, X2)) -> U31(active(X1), X2) , active(U31(tt(), V)) -> mark(U32(isQid(V))) , active(U32(X)) -> U32(active(X)) , active(U32(tt())) -> mark(tt()) , active(isQid(a())) -> mark(tt()) , active(isQid(e())) -> mark(tt()) , active(isQid(i())) -> mark(tt()) , active(isQid(o())) -> mark(tt()) , active(isQid(u())) -> mark(tt()) , active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) , active(U41(tt(), V1, V2)) -> mark(U42(isList(V1), V2)) , active(U42(X1, X2)) -> U42(active(X1), X2) , active(U42(tt(), V2)) -> mark(U43(isNeList(V2))) , active(U43(X)) -> U43(active(X)) , active(U43(tt())) -> mark(tt()) , active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) , active(U51(tt(), V1, V2)) -> mark(U52(isNeList(V1), V2)) , active(U52(X1, X2)) -> U52(active(X1), X2) , active(U52(tt(), V2)) -> mark(U53(isList(V2))) , active(U53(X)) -> U53(active(X)) , active(U53(tt())) -> mark(tt()) , active(U61(X1, X2)) -> U61(active(X1), X2) , active(U61(tt(), V)) -> mark(U62(isQid(V))) , active(U62(X)) -> U62(active(X)) , active(U62(tt())) -> mark(tt()) , active(U71(X1, X2)) -> U71(active(X1), X2) , active(U71(tt(), V)) -> mark(U72(isNePal(V))) , active(U72(X)) -> U72(active(X)) , active(U72(tt())) -> mark(tt()) , active(isNePal(V)) -> mark(U61(isPalListKind(V), V)) , active(isNePal(__(I, __(P, I)))) -> mark(and(and(isQid(I), isPalListKind(I)), and(isPal(P), isPalListKind(P)))) , active(and(X1, X2)) -> and(active(X1), X2) , active(and(tt(), X)) -> mark(X) , active(isPalListKind(__(V1, V2))) -> mark(and(isPalListKind(V1), isPalListKind(V2))) , active(isPalListKind(nil())) -> mark(tt()) , active(isPalListKind(a())) -> mark(tt()) , active(isPalListKind(e())) -> mark(tt()) , active(isPalListKind(i())) -> mark(tt()) , active(isPalListKind(o())) -> mark(tt()) , active(isPalListKind(u())) -> mark(tt()) , active(isPal(V)) -> mark(U71(isPalListKind(V), V)) , active(isPal(nil())) -> mark(tt()) , __(X1, mark(X2)) -> mark(__(X1, X2)) , __(mark(X1), X2) -> mark(__(X1, X2)) , __(ok(X1), ok(X2)) -> ok(__(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)) , isNeList(ok(X)) -> ok(isNeList(X)) , U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) , U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) , U22(mark(X1), X2) -> mark(U22(X1, X2)) , U22(ok(X1), ok(X2)) -> ok(U22(X1, X2)) , isList(ok(X)) -> ok(isList(X)) , U23(mark(X)) -> mark(U23(X)) , U23(ok(X)) -> ok(U23(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)) , isQid(ok(X)) -> ok(isQid(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)) , 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) -> mark(U61(X1, X2)) , U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) , U62(mark(X)) -> mark(U62(X)) , U62(ok(X)) -> ok(U62(X)) , U71(mark(X1), X2) -> mark(U71(X1, X2)) , U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) , U72(mark(X)) -> mark(U72(X)) , U72(ok(X)) -> ok(U72(X)) , isNePal(ok(X)) -> ok(isNePal(X)) , and(mark(X1), X2) -> mark(and(X1, X2)) , and(ok(X1), ok(X2)) -> ok(and(X1, X2)) , isPalListKind(ok(X)) -> ok(isPalListKind(X)) , isPal(ok(X)) -> ok(isPal(X)) , proper(__(X1, X2)) -> __(proper(X1), proper(X2)) , proper(nil()) -> ok(nil()) , proper(U11(X1, X2)) -> U11(proper(X1), proper(X2)) , proper(tt()) -> ok(tt()) , proper(U12(X)) -> U12(proper(X)) , proper(isNeList(X)) -> isNeList(proper(X)) , proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) , proper(U22(X1, X2)) -> U22(proper(X1), proper(X2)) , proper(isList(X)) -> isList(proper(X)) , proper(U23(X)) -> U23(proper(X)) , proper(U31(X1, X2)) -> U31(proper(X1), proper(X2)) , proper(U32(X)) -> U32(proper(X)) , proper(isQid(X)) -> isQid(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(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)) -> U61(proper(X1), proper(X2)) , proper(U62(X)) -> U62(proper(X)) , proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) , proper(U72(X)) -> U72(proper(X)) , proper(isNePal(X)) -> isNePal(proper(X)) , proper(and(X1, X2)) -> and(proper(X1), proper(X2)) , proper(isPalListKind(X)) -> isPalListKind(proper(X)) , proper(isPal(X)) -> isPal(proper(X)) , proper(a()) -> ok(a()) , proper(e()) -> ok(e()) , proper(i()) -> ok(i()) , proper(o()) -> ok(o()) , proper(u()) -> ok(u()) , 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) '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..