MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) , active(U11(tt(), V1, V2)) -> mark(U12(isNatKind(V1), V1, V2)) , active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) , active(U12(tt(), V1, V2)) -> mark(U13(isNatKind(V2), V1, V2)) , active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) , active(isNatKind(plus(V1, V2))) -> mark(U31(isNatKind(V1), V2)) , active(isNatKind(0())) -> mark(tt()) , active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) , active(U13(tt(), V1, V2)) -> mark(U14(isNatKind(V2), V1, V2)) , active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) , active(U14(tt(), V1, V2)) -> mark(U15(isNat(V1), V2)) , active(U15(X1, X2)) -> U15(active(X1), X2) , active(U15(tt(), V2)) -> mark(U16(isNat(V2))) , active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)) , active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2)) , active(isNat(0())) -> mark(tt()) , active(U16(X)) -> U16(active(X)) , active(U16(tt())) -> mark(tt()) , active(U21(X1, X2)) -> U21(active(X1), X2) , active(U21(tt(), V1)) -> mark(U22(isNatKind(V1), V1)) , active(U22(X1, X2)) -> U22(active(X1), X2) , active(U22(tt(), V1)) -> mark(U23(isNat(V1))) , active(U23(X)) -> U23(active(X)) , active(U23(tt())) -> mark(tt()) , active(U31(X1, X2)) -> U31(active(X1), X2) , active(U31(tt(), V2)) -> mark(U32(isNatKind(V2))) , active(U32(X)) -> U32(active(X)) , active(U32(tt())) -> mark(tt()) , active(U41(X)) -> U41(active(X)) , active(U41(tt())) -> mark(tt()) , active(U51(X1, X2)) -> U51(active(X1), X2) , active(U51(tt(), N)) -> mark(U52(isNatKind(N), N)) , active(U52(X1, X2)) -> U52(active(X1), X2) , active(U52(tt(), N)) -> mark(N) , active(U61(X1, X2, X3)) -> U61(active(X1), X2, X3) , active(U61(tt(), M, N)) -> mark(U62(isNatKind(M), M, N)) , active(U62(X1, X2, X3)) -> U62(active(X1), X2, X3) , active(U62(tt(), M, N)) -> mark(U63(isNat(N), M, N)) , active(U63(X1, X2, X3)) -> U63(active(X1), X2, X3) , active(U63(tt(), M, N)) -> mark(U64(isNatKind(N), M, N)) , active(U64(X1, X2, X3)) -> U64(active(X1), X2, X3) , active(U64(tt(), M, N)) -> mark(s(plus(N, M))) , active(s(X)) -> s(active(X)) , active(plus(X1, X2)) -> plus(X1, active(X2)) , active(plus(X1, X2)) -> plus(active(X1), X2) , active(plus(N, s(M))) -> mark(U61(isNat(M), M, N)) , active(plus(N, 0())) -> mark(U51(isNat(N), N)) , U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) , U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) , U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) , U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) , isNatKind(ok(X)) -> ok(isNatKind(X)) , U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) , U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) , U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) , U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) , U15(mark(X1), X2) -> mark(U15(X1, X2)) , U15(ok(X1), ok(X2)) -> ok(U15(X1, X2)) , isNat(ok(X)) -> ok(isNat(X)) , U16(mark(X)) -> mark(U16(X)) , U16(ok(X)) -> ok(U16(X)) , U21(mark(X1), X2) -> mark(U21(X1, X2)) , U21(ok(X1), ok(X2)) -> ok(U21(X1, X2)) , U22(mark(X1), X2) -> mark(U22(X1, X2)) , U22(ok(X1), ok(X2)) -> ok(U22(X1, X2)) , 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)) , U41(mark(X)) -> mark(U41(X)) , U41(ok(X)) -> ok(U41(X)) , U51(mark(X1), X2) -> mark(U51(X1, X2)) , U51(ok(X1), ok(X2)) -> ok(U51(X1, X2)) , U52(mark(X1), X2) -> mark(U52(X1, X2)) , U52(ok(X1), ok(X2)) -> ok(U52(X1, X2)) , 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, X3) -> mark(U62(X1, X2, X3)) , U62(ok(X1), ok(X2), ok(X3)) -> ok(U62(X1, X2, X3)) , U63(mark(X1), X2, X3) -> mark(U63(X1, X2, X3)) , U63(ok(X1), ok(X2), ok(X3)) -> ok(U63(X1, X2, X3)) , U64(mark(X1), X2, X3) -> mark(U64(X1, X2, X3)) , U64(ok(X1), ok(X2), ok(X3)) -> ok(U64(X1, X2, X3)) , s(mark(X)) -> mark(s(X)) , s(ok(X)) -> ok(s(X)) , plus(X1, mark(X2)) -> mark(plus(X1, X2)) , plus(mark(X1), X2) -> mark(plus(X1, X2)) , plus(ok(X1), ok(X2)) -> ok(plus(X1, X2)) , proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) , proper(tt()) -> ok(tt()) , proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) , proper(isNatKind(X)) -> isNatKind(proper(X)) , proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) , proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) , proper(U15(X1, X2)) -> U15(proper(X1), proper(X2)) , proper(isNat(X)) -> isNat(proper(X)) , proper(U16(X)) -> U16(proper(X)) , proper(U21(X1, X2)) -> U21(proper(X1), proper(X2)) , proper(U22(X1, X2)) -> U22(proper(X1), proper(X2)) , proper(U23(X)) -> U23(proper(X)) , proper(U31(X1, X2)) -> U31(proper(X1), proper(X2)) , proper(U32(X)) -> U32(proper(X)) , proper(U41(X)) -> U41(proper(X)) , proper(U51(X1, X2)) -> U51(proper(X1), proper(X2)) , proper(U52(X1, X2)) -> U52(proper(X1), proper(X2)) , proper(U61(X1, X2, X3)) -> U61(proper(X1), proper(X2), proper(X3)) , proper(U62(X1, X2, X3)) -> U62(proper(X1), proper(X2), proper(X3)) , proper(U63(X1, X2, X3)) -> U63(proper(X1), proper(X2), proper(X3)) , proper(U64(X1, X2, X3)) -> U64(proper(X1), proper(X2), proper(X3)) , proper(s(X)) -> s(proper(X)) , proper(plus(X1, X2)) -> plus(proper(X1), proper(X2)) , proper(0()) -> ok(0()) , 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 perSymbol-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 2) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. Arrrr..