MAYBE 945.78/297.14 MAYBE 945.78/297.14 945.78/297.14 We are left with following problem, upon which TcT provides the 945.78/297.14 certificate MAYBE. 945.78/297.14 945.78/297.14 Strict Trs: 945.78/297.14 { active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 945.78/297.14 , active(U101(tt(), M, N)) -> mark(U102(isNatKind(M), M, N)) 945.78/297.14 , active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 945.78/297.14 , active(U102(tt(), M, N)) -> mark(U103(isNat(N), M, N)) 945.78/297.14 , active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2)) 945.78/297.14 , active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2)) 945.78/297.14 , active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) 945.78/297.14 , active(isNatKind(0())) -> mark(tt()) 945.78/297.14 , active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 945.78/297.14 , active(U103(tt(), M, N)) -> mark(U104(isNatKind(N), M, N)) 945.78/297.14 , active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2)) 945.78/297.14 , active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2)) 945.78/297.14 , active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)) 945.78/297.14 , active(isNat(0())) -> mark(tt()) 945.78/297.14 , active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 945.78/297.14 , active(U104(tt(), M, N)) -> mark(plus(x(N, M), N)) 945.78/297.14 , active(plus(X1, X2)) -> plus(X1, active(X2)) 945.78/297.14 , active(plus(X1, X2)) -> plus(active(X1), X2) 945.78/297.14 , active(plus(N, s(M))) -> mark(U81(isNat(M), M, N)) 945.78/297.14 , active(plus(N, 0())) -> mark(U71(isNat(N), N)) 945.78/297.14 , active(x(X1, X2)) -> x(X1, active(X2)) 945.78/297.14 , active(x(X1, X2)) -> x(active(X1), X2) 945.78/297.14 , active(x(N, s(M))) -> mark(U101(isNat(M), M, N)) 945.78/297.14 , active(x(N, 0())) -> mark(U91(isNat(N), N)) 945.78/297.14 , active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 945.78/297.14 , active(U11(tt(), V1, V2)) -> mark(U12(isNatKind(V1), V1, V2)) 945.78/297.14 , active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 945.78/297.14 , active(U12(tt(), V1, V2)) -> mark(U13(isNatKind(V2), V1, V2)) 945.78/297.14 , active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 945.78/297.14 , active(U13(tt(), V1, V2)) -> mark(U14(isNatKind(V2), V1, V2)) 945.78/297.14 , active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 945.78/297.14 , active(U14(tt(), V1, V2)) -> mark(U15(isNat(V1), V2)) 945.78/297.14 , active(U15(X1, X2)) -> U15(active(X1), X2) 945.78/297.14 , active(U15(tt(), V2)) -> mark(U16(isNat(V2))) 945.78/297.14 , active(U16(X)) -> U16(active(X)) 945.78/297.14 , active(U16(tt())) -> mark(tt()) 945.78/297.14 , active(U21(X1, X2)) -> U21(active(X1), X2) 945.78/297.14 , active(U21(tt(), V1)) -> mark(U22(isNatKind(V1), V1)) 945.78/297.14 , active(U22(X1, X2)) -> U22(active(X1), X2) 945.78/297.14 , active(U22(tt(), V1)) -> mark(U23(isNat(V1))) 945.78/297.14 , active(U23(X)) -> U23(active(X)) 945.78/297.14 , active(U23(tt())) -> mark(tt()) 945.78/297.14 , active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 945.78/297.14 , active(U31(tt(), V1, V2)) -> mark(U32(isNatKind(V1), V1, V2)) 945.78/297.14 , active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 945.78/297.14 , active(U32(tt(), V1, V2)) -> mark(U33(isNatKind(V2), V1, V2)) 945.78/297.14 , active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 945.78/297.14 , active(U33(tt(), V1, V2)) -> mark(U34(isNatKind(V2), V1, V2)) 945.78/297.14 , active(U34(X1, X2, X3)) -> U34(active(X1), X2, X3) 945.78/297.14 , active(U34(tt(), V1, V2)) -> mark(U35(isNat(V1), V2)) 945.78/297.14 , active(U35(X1, X2)) -> U35(active(X1), X2) 945.78/297.14 , active(U35(tt(), V2)) -> mark(U36(isNat(V2))) 945.78/297.14 , active(U36(X)) -> U36(active(X)) 945.78/297.14 , active(U36(tt())) -> mark(tt()) 945.78/297.14 , active(U41(X1, X2)) -> U41(active(X1), X2) 945.78/297.14 , active(U41(tt(), V2)) -> mark(U42(isNatKind(V2))) 945.78/297.14 , active(U42(X)) -> U42(active(X)) 945.78/297.14 , active(U42(tt())) -> mark(tt()) 945.78/297.14 , active(U51(X)) -> U51(active(X)) 945.78/297.14 , active(U51(tt())) -> mark(tt()) 945.78/297.14 , active(U61(X1, X2)) -> U61(active(X1), X2) 945.78/297.14 , active(U61(tt(), V2)) -> mark(U62(isNatKind(V2))) 945.78/297.14 , active(U62(X)) -> U62(active(X)) 945.78/297.14 , active(U62(tt())) -> mark(tt()) 945.78/297.14 , active(U71(X1, X2)) -> U71(active(X1), X2) 945.78/297.14 , active(U71(tt(), N)) -> mark(U72(isNatKind(N), N)) 945.78/297.14 , active(U72(X1, X2)) -> U72(active(X1), X2) 945.78/297.14 , active(U72(tt(), N)) -> mark(N) 945.78/297.14 , active(U81(X1, X2, X3)) -> U81(active(X1), X2, X3) 945.78/297.14 , active(U81(tt(), M, N)) -> mark(U82(isNatKind(M), M, N)) 945.78/297.14 , active(U82(X1, X2, X3)) -> U82(active(X1), X2, X3) 945.78/297.14 , active(U82(tt(), M, N)) -> mark(U83(isNat(N), M, N)) 945.78/297.14 , active(U83(X1, X2, X3)) -> U83(active(X1), X2, X3) 945.78/297.14 , active(U83(tt(), M, N)) -> mark(U84(isNatKind(N), M, N)) 945.78/297.14 , active(U84(X1, X2, X3)) -> U84(active(X1), X2, X3) 945.78/297.14 , active(U84(tt(), M, N)) -> mark(s(plus(N, M))) 945.78/297.14 , active(s(X)) -> s(active(X)) 945.78/297.14 , active(U91(X1, X2)) -> U91(active(X1), X2) 945.78/297.14 , active(U91(tt(), N)) -> mark(U92(isNatKind(N))) 945.78/297.14 , active(U92(X)) -> U92(active(X)) 945.78/297.14 , active(U92(tt())) -> mark(0()) 945.78/297.14 , U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 945.78/297.14 , U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 945.78/297.14 , U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 945.78/297.14 , U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 945.78/297.14 , isNatKind(ok(X)) -> ok(isNatKind(X)) 945.78/297.14 , U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 945.78/297.14 , U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 945.78/297.14 , isNat(ok(X)) -> ok(isNat(X)) 945.78/297.14 , U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 945.78/297.14 , U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 945.78/297.14 , plus(X1, mark(X2)) -> mark(plus(X1, X2)) 945.78/297.14 , plus(mark(X1), X2) -> mark(plus(X1, X2)) 945.78/297.14 , plus(ok(X1), ok(X2)) -> ok(plus(X1, X2)) 945.78/297.14 , x(X1, mark(X2)) -> mark(x(X1, X2)) 945.78/297.14 , x(mark(X1), X2) -> mark(x(X1, X2)) 945.78/297.14 , x(ok(X1), ok(X2)) -> ok(x(X1, X2)) 945.78/297.14 , U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 945.78/297.14 , U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 945.78/297.14 , U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 945.78/297.14 , U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 945.78/297.14 , U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 945.78/297.14 , U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 945.78/297.14 , U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 945.78/297.14 , U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 945.78/297.14 , U15(mark(X1), X2) -> mark(U15(X1, X2)) 945.78/297.14 , U15(ok(X1), ok(X2)) -> ok(U15(X1, X2)) 945.78/297.14 , U16(mark(X)) -> mark(U16(X)) 945.78/297.14 , U16(ok(X)) -> ok(U16(X)) 945.78/297.14 , U21(mark(X1), X2) -> mark(U21(X1, X2)) 945.78/297.14 , U21(ok(X1), ok(X2)) -> ok(U21(X1, X2)) 945.78/297.14 , U22(mark(X1), X2) -> mark(U22(X1, X2)) 945.78/297.14 , U22(ok(X1), ok(X2)) -> ok(U22(X1, X2)) 945.78/297.14 , U23(mark(X)) -> mark(U23(X)) 945.78/297.14 , U23(ok(X)) -> ok(U23(X)) 945.78/297.14 , U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 945.78/297.14 , U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 945.78/297.14 , U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 945.78/297.14 , U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 945.78/297.14 , U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 945.78/297.14 , U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 945.78/297.14 , U34(mark(X1), X2, X3) -> mark(U34(X1, X2, X3)) 945.78/297.14 , U34(ok(X1), ok(X2), ok(X3)) -> ok(U34(X1, X2, X3)) 945.78/297.14 , U35(mark(X1), X2) -> mark(U35(X1, X2)) 945.78/297.14 , U35(ok(X1), ok(X2)) -> ok(U35(X1, X2)) 945.78/297.14 , U36(mark(X)) -> mark(U36(X)) 945.78/297.14 , U36(ok(X)) -> ok(U36(X)) 945.78/297.14 , U41(mark(X1), X2) -> mark(U41(X1, X2)) 945.78/297.14 , U41(ok(X1), ok(X2)) -> ok(U41(X1, X2)) 945.78/297.14 , U42(mark(X)) -> mark(U42(X)) 945.78/297.14 , U42(ok(X)) -> ok(U42(X)) 945.78/297.14 , U51(mark(X)) -> mark(U51(X)) 945.78/297.14 , U51(ok(X)) -> ok(U51(X)) 945.78/297.14 , U61(mark(X1), X2) -> mark(U61(X1, X2)) 945.78/297.14 , U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 945.78/297.14 , U62(mark(X)) -> mark(U62(X)) 945.78/297.14 , U62(ok(X)) -> ok(U62(X)) 945.78/297.14 , U71(mark(X1), X2) -> mark(U71(X1, X2)) 945.78/297.14 , U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 945.78/297.14 , U72(mark(X1), X2) -> mark(U72(X1, X2)) 945.78/297.14 , U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 945.78/297.14 , U81(mark(X1), X2, X3) -> mark(U81(X1, X2, X3)) 945.78/297.14 , U81(ok(X1), ok(X2), ok(X3)) -> ok(U81(X1, X2, X3)) 945.78/297.14 , U82(mark(X1), X2, X3) -> mark(U82(X1, X2, X3)) 945.78/297.14 , U82(ok(X1), ok(X2), ok(X3)) -> ok(U82(X1, X2, X3)) 945.78/297.14 , U83(mark(X1), X2, X3) -> mark(U83(X1, X2, X3)) 945.78/297.14 , U83(ok(X1), ok(X2), ok(X3)) -> ok(U83(X1, X2, X3)) 945.78/297.14 , U84(mark(X1), X2, X3) -> mark(U84(X1, X2, X3)) 945.78/297.14 , U84(ok(X1), ok(X2), ok(X3)) -> ok(U84(X1, X2, X3)) 945.78/297.14 , s(mark(X)) -> mark(s(X)) 945.78/297.14 , s(ok(X)) -> ok(s(X)) 945.78/297.14 , U91(mark(X1), X2) -> mark(U91(X1, X2)) 945.78/297.14 , U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 945.78/297.14 , U92(mark(X)) -> mark(U92(X)) 945.78/297.14 , U92(ok(X)) -> ok(U92(X)) 945.78/297.14 , proper(U101(X1, X2, X3)) -> 945.78/297.14 U101(proper(X1), proper(X2), proper(X3)) 945.78/297.14 , proper(tt()) -> ok(tt()) 945.78/297.14 , proper(U102(X1, X2, X3)) -> 945.78/297.14 U102(proper(X1), proper(X2), proper(X3)) 945.78/297.14 , proper(isNatKind(X)) -> isNatKind(proper(X)) 945.78/297.14 , proper(U103(X1, X2, X3)) -> 945.78/297.14 U103(proper(X1), proper(X2), proper(X3)) 945.78/297.14 , proper(isNat(X)) -> isNat(proper(X)) 945.78/297.14 , proper(U104(X1, X2, X3)) -> 945.78/297.14 U104(proper(X1), proper(X2), proper(X3)) 945.78/297.14 , proper(plus(X1, X2)) -> plus(proper(X1), proper(X2)) 945.78/297.14 , proper(x(X1, X2)) -> x(proper(X1), proper(X2)) 945.78/297.14 , proper(U11(X1, X2, X3)) -> 945.78/297.15 U11(proper(X1), proper(X2), proper(X3)) 945.78/297.15 , proper(U12(X1, X2, X3)) -> 945.78/297.15 U12(proper(X1), proper(X2), proper(X3)) 945.78/297.15 , proper(U13(X1, X2, X3)) -> 945.78/297.15 U13(proper(X1), proper(X2), proper(X3)) 945.78/297.15 , proper(U14(X1, X2, X3)) -> 945.78/297.15 U14(proper(X1), proper(X2), proper(X3)) 945.78/297.15 , proper(U15(X1, X2)) -> U15(proper(X1), proper(X2)) 945.78/297.15 , proper(U16(X)) -> U16(proper(X)) 945.78/297.15 , proper(U21(X1, X2)) -> U21(proper(X1), proper(X2)) 945.78/297.15 , proper(U22(X1, X2)) -> U22(proper(X1), proper(X2)) 945.78/297.15 , proper(U23(X)) -> U23(proper(X)) 945.78/297.15 , proper(U31(X1, X2, X3)) -> 945.78/297.15 U31(proper(X1), proper(X2), proper(X3)) 945.78/297.15 , proper(U32(X1, X2, X3)) -> 945.78/297.15 U32(proper(X1), proper(X2), proper(X3)) 945.78/297.15 , proper(U33(X1, X2, X3)) -> 945.78/297.15 U33(proper(X1), proper(X2), proper(X3)) 945.78/297.15 , proper(U34(X1, X2, X3)) -> 945.78/297.15 U34(proper(X1), proper(X2), proper(X3)) 945.78/297.15 , proper(U35(X1, X2)) -> U35(proper(X1), proper(X2)) 945.78/297.15 , proper(U36(X)) -> U36(proper(X)) 945.78/297.15 , proper(U41(X1, X2)) -> U41(proper(X1), proper(X2)) 945.78/297.15 , proper(U42(X)) -> U42(proper(X)) 945.78/297.15 , proper(U51(X)) -> U51(proper(X)) 945.78/297.15 , proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 945.78/297.15 , proper(U62(X)) -> U62(proper(X)) 945.78/297.15 , proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 945.78/297.15 , proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 945.78/297.15 , proper(U81(X1, X2, X3)) -> 945.78/297.15 U81(proper(X1), proper(X2), proper(X3)) 945.78/297.15 , proper(U82(X1, X2, X3)) -> 945.78/297.15 U82(proper(X1), proper(X2), proper(X3)) 945.78/297.15 , proper(U83(X1, X2, X3)) -> 945.78/297.15 U83(proper(X1), proper(X2), proper(X3)) 945.78/297.15 , proper(U84(X1, X2, X3)) -> 945.78/297.15 U84(proper(X1), proper(X2), proper(X3)) 945.78/297.15 , proper(s(X)) -> s(proper(X)) 945.78/297.15 , proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 945.78/297.15 , proper(U92(X)) -> U92(proper(X)) 945.78/297.15 , proper(0()) -> ok(0()) 945.78/297.15 , top(mark(X)) -> top(proper(X)) 945.78/297.15 , top(ok(X)) -> top(active(X)) } 945.78/297.15 Obligation: 945.78/297.15 innermost runtime complexity 945.78/297.15 Answer: 945.78/297.15 MAYBE 945.78/297.15 945.78/297.15 None of the processors succeeded. 945.78/297.15 945.78/297.15 Details of failed attempt(s): 945.78/297.15 ----------------------------- 945.78/297.15 1) 'empty' failed due to the following reason: 945.78/297.15 945.78/297.15 Empty strict component of the problem is NOT empty. 945.78/297.15 945.78/297.15 2) 'Best' failed due to the following reason: 945.78/297.15 945.78/297.15 None of the processors succeeded. 945.78/297.15 945.78/297.15 Details of failed attempt(s): 945.78/297.15 ----------------------------- 945.78/297.15 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 945.78/297.15 following reason: 945.78/297.15 945.78/297.15 Computation stopped due to timeout after 297.0 seconds. 945.78/297.15 945.78/297.15 2) 'Best' failed due to the following reason: 945.78/297.15 945.78/297.15 None of the processors succeeded. 945.78/297.15 945.78/297.15 Details of failed attempt(s): 945.78/297.15 ----------------------------- 945.78/297.15 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 945.78/297.15 seconds)' failed due to the following reason: 945.78/297.15 945.78/297.15 Computation stopped due to timeout after 148.0 seconds. 945.78/297.15 945.78/297.15 2) 'Best' failed due to the following reason: 945.78/297.15 945.78/297.15 None of the processors succeeded. 945.78/297.15 945.78/297.15 Details of failed attempt(s): 945.78/297.15 ----------------------------- 945.78/297.15 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 945.78/297.15 following reason: 945.78/297.15 945.78/297.15 The input cannot be shown compatible 945.78/297.15 945.78/297.15 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 945.78/297.15 to the following reason: 945.78/297.15 945.78/297.15 The input cannot be shown compatible 945.78/297.15 945.78/297.15 945.78/297.15 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 945.78/297.15 failed due to the following reason: 945.78/297.15 945.78/297.15 None of the processors succeeded. 945.78/297.15 945.78/297.15 Details of failed attempt(s): 945.78/297.15 ----------------------------- 945.78/297.15 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 945.78/297.15 failed due to the following reason: 945.78/297.15 945.78/297.15 match-boundness of the problem could not be verified. 945.78/297.15 945.78/297.15 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 945.78/297.15 failed due to the following reason: 945.78/297.15 945.78/297.15 match-boundness of the problem could not be verified. 945.78/297.15 945.78/297.15 945.78/297.15 945.78/297.15 945.78/297.15 945.78/297.15 Arrrr.. 946.67/297.91 EOF