MAYBE 731.31/297.10 MAYBE 731.31/297.10 731.31/297.10 We are left with following problem, upon which TcT provides the 731.31/297.10 certificate MAYBE. 731.31/297.10 731.31/297.10 Strict Trs: 731.31/297.10 { active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 731.31/297.10 , active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)) 731.31/297.10 , active(U12(X1, X2)) -> U12(active(X1), X2) 731.31/297.10 , active(U12(tt(), V2)) -> mark(U13(isNat(V2))) 731.31/297.10 , active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)) 731.31/297.10 , active(isNat(plus(V1, V2))) -> 731.31/297.10 mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)) 731.31/297.10 , active(isNat(0())) -> mark(tt()) 731.31/297.10 , active(U13(X)) -> U13(active(X)) 731.31/297.10 , active(U13(tt())) -> mark(tt()) 731.31/297.10 , active(U21(X1, X2)) -> U21(active(X1), X2) 731.31/297.10 , active(U21(tt(), V1)) -> mark(U22(isNat(V1))) 731.31/297.10 , active(U22(X)) -> U22(active(X)) 731.31/297.10 , active(U22(tt())) -> mark(tt()) 731.31/297.10 , active(U31(X1, X2)) -> U31(active(X1), X2) 731.31/297.10 , active(U31(tt(), N)) -> mark(N) 731.31/297.10 , active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 731.31/297.10 , active(U41(tt(), M, N)) -> mark(s(plus(N, M))) 731.31/297.10 , active(s(X)) -> s(active(X)) 731.31/297.10 , active(plus(X1, X2)) -> plus(X1, active(X2)) 731.31/297.10 , active(plus(X1, X2)) -> plus(active(X1), X2) 731.31/297.10 , active(plus(N, s(M))) -> 731.31/297.10 mark(U41(and(and(isNat(M), isNatKind(M)), 731.31/297.10 and(isNat(N), isNatKind(N))), 731.31/297.10 M, 731.31/297.10 N)) 731.31/297.10 , active(plus(N, 0())) -> mark(U31(and(isNat(N), isNatKind(N)), N)) 731.31/297.10 , active(and(X1, X2)) -> and(active(X1), X2) 731.31/297.10 , active(and(tt(), X)) -> mark(X) 731.31/297.10 , active(isNatKind(s(V1))) -> mark(isNatKind(V1)) 731.31/297.10 , active(isNatKind(plus(V1, V2))) -> 731.31/297.10 mark(and(isNatKind(V1), isNatKind(V2))) 731.31/297.10 , active(isNatKind(0())) -> mark(tt()) 731.31/297.10 , U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 731.31/297.10 , U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 731.31/297.10 , U12(mark(X1), X2) -> mark(U12(X1, X2)) 731.31/297.10 , U12(ok(X1), ok(X2)) -> ok(U12(X1, X2)) 731.31/297.10 , isNat(ok(X)) -> ok(isNat(X)) 731.31/297.10 , U13(mark(X)) -> mark(U13(X)) 731.31/297.10 , U13(ok(X)) -> ok(U13(X)) 731.31/297.10 , U21(mark(X1), X2) -> mark(U21(X1, X2)) 731.31/297.10 , U21(ok(X1), ok(X2)) -> ok(U21(X1, X2)) 731.31/297.10 , U22(mark(X)) -> mark(U22(X)) 731.31/297.10 , U22(ok(X)) -> ok(U22(X)) 731.31/297.10 , U31(mark(X1), X2) -> mark(U31(X1, X2)) 731.31/297.10 , U31(ok(X1), ok(X2)) -> ok(U31(X1, X2)) 731.31/297.10 , U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 731.31/297.10 , U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 731.31/297.10 , s(mark(X)) -> mark(s(X)) 731.31/297.10 , s(ok(X)) -> ok(s(X)) 731.31/297.10 , plus(X1, mark(X2)) -> mark(plus(X1, X2)) 731.31/297.10 , plus(mark(X1), X2) -> mark(plus(X1, X2)) 731.31/297.10 , plus(ok(X1), ok(X2)) -> ok(plus(X1, X2)) 731.31/297.10 , and(mark(X1), X2) -> mark(and(X1, X2)) 731.31/297.10 , and(ok(X1), ok(X2)) -> ok(and(X1, X2)) 731.31/297.10 , isNatKind(ok(X)) -> ok(isNatKind(X)) 731.31/297.10 , proper(U11(X1, X2, X3)) -> 731.31/297.10 U11(proper(X1), proper(X2), proper(X3)) 731.31/297.10 , proper(tt()) -> ok(tt()) 731.31/297.10 , proper(U12(X1, X2)) -> U12(proper(X1), proper(X2)) 731.31/297.10 , proper(isNat(X)) -> isNat(proper(X)) 731.31/297.10 , proper(U13(X)) -> U13(proper(X)) 731.31/297.10 , proper(U21(X1, X2)) -> U21(proper(X1), proper(X2)) 731.31/297.10 , proper(U22(X)) -> U22(proper(X)) 731.31/297.10 , proper(U31(X1, X2)) -> U31(proper(X1), proper(X2)) 731.31/297.10 , proper(U41(X1, X2, X3)) -> 731.31/297.10 U41(proper(X1), proper(X2), proper(X3)) 731.31/297.10 , proper(s(X)) -> s(proper(X)) 731.31/297.10 , proper(plus(X1, X2)) -> plus(proper(X1), proper(X2)) 731.31/297.10 , proper(and(X1, X2)) -> and(proper(X1), proper(X2)) 731.31/297.10 , proper(0()) -> ok(0()) 731.31/297.10 , proper(isNatKind(X)) -> isNatKind(proper(X)) 731.31/297.10 , top(mark(X)) -> top(proper(X)) 731.31/297.10 , top(ok(X)) -> top(active(X)) } 731.31/297.10 Obligation: 731.31/297.10 innermost runtime complexity 731.31/297.10 Answer: 731.31/297.10 MAYBE 731.31/297.10 731.31/297.10 None of the processors succeeded. 731.31/297.10 731.31/297.10 Details of failed attempt(s): 731.31/297.10 ----------------------------- 731.31/297.10 1) 'empty' failed due to the following reason: 731.31/297.10 731.31/297.10 Empty strict component of the problem is NOT empty. 731.31/297.10 731.31/297.10 2) 'Best' failed due to the following reason: 731.31/297.10 731.31/297.10 None of the processors succeeded. 731.31/297.10 731.31/297.10 Details of failed attempt(s): 731.31/297.10 ----------------------------- 731.31/297.10 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 731.31/297.10 following reason: 731.31/297.10 731.31/297.10 Computation stopped due to timeout after 297.0 seconds. 731.31/297.10 731.31/297.10 2) 'Best' failed due to the following reason: 731.31/297.10 731.31/297.10 None of the processors succeeded. 731.31/297.10 731.31/297.10 Details of failed attempt(s): 731.31/297.10 ----------------------------- 731.31/297.10 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 731.31/297.10 seconds)' failed due to the following reason: 731.31/297.10 731.31/297.10 Computation stopped due to timeout after 148.0 seconds. 731.31/297.10 731.31/297.10 2) 'Best' failed due to the following reason: 731.31/297.10 731.31/297.10 None of the processors succeeded. 731.31/297.10 731.31/297.10 Details of failed attempt(s): 731.31/297.10 ----------------------------- 731.31/297.10 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 731.31/297.10 to the following reason: 731.31/297.10 731.31/297.10 The input cannot be shown compatible 731.31/297.10 731.31/297.10 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 731.31/297.10 following reason: 731.31/297.10 731.31/297.10 The input cannot be shown compatible 731.31/297.10 731.31/297.10 731.31/297.10 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 731.31/297.10 failed due to the following reason: 731.31/297.10 731.31/297.10 None of the processors succeeded. 731.31/297.10 731.31/297.10 Details of failed attempt(s): 731.31/297.10 ----------------------------- 731.31/297.10 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 731.31/297.10 failed due to the following reason: 731.31/297.10 731.31/297.10 match-boundness of the problem could not be verified. 731.31/297.10 731.31/297.10 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 731.31/297.10 failed due to the following reason: 731.31/297.10 731.31/297.10 match-boundness of the problem could not be verified. 731.31/297.10 731.31/297.10 731.31/297.10 731.31/297.10 731.31/297.10 731.31/297.10 Arrrr.. 731.31/297.19 EOF