MAYBE 748.17/297.17 MAYBE 748.17/297.17 748.17/297.17 We are left with following problem, upon which TcT provides the 748.17/297.17 certificate MAYBE. 748.17/297.17 748.17/297.17 Strict Trs: 748.17/297.17 { active(zeros()) -> mark(cons(0(), zeros())) 748.17/297.17 , active(cons(X1, X2)) -> cons(active(X1), X2) 748.17/297.17 , active(U11(X1, X2)) -> U11(active(X1), X2) 748.17/297.17 , active(U11(tt(), V1)) -> mark(U12(isNatList(V1))) 748.17/297.17 , active(U12(X)) -> U12(active(X)) 748.17/297.17 , active(U12(tt())) -> mark(tt()) 748.17/297.17 , active(isNatList(cons(V1, V2))) -> 748.17/297.17 mark(U51(and(isNatKind(V1), isNatIListKind(V2)), V1, V2)) 748.17/297.17 , active(isNatList(nil())) -> mark(tt()) 748.17/297.17 , active(U21(X1, X2)) -> U21(active(X1), X2) 748.17/297.17 , active(U21(tt(), V1)) -> mark(U22(isNat(V1))) 748.17/297.17 , active(U22(X)) -> U22(active(X)) 748.17/297.17 , active(U22(tt())) -> mark(tt()) 748.17/297.17 , active(isNat(0())) -> mark(tt()) 748.17/297.17 , active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)) 748.17/297.17 , active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1), V1)) 748.17/297.17 , active(U31(X1, X2)) -> U31(active(X1), X2) 748.17/297.17 , active(U31(tt(), V)) -> mark(U32(isNatList(V))) 748.17/297.17 , active(U32(X)) -> U32(active(X)) 748.17/297.17 , active(U32(tt())) -> mark(tt()) 748.17/297.17 , active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 748.17/297.17 , active(U41(tt(), V1, V2)) -> mark(U42(isNat(V1), V2)) 748.17/297.17 , active(U42(X1, X2)) -> U42(active(X1), X2) 748.17/297.17 , active(U42(tt(), V2)) -> mark(U43(isNatIList(V2))) 748.17/297.17 , active(U43(X)) -> U43(active(X)) 748.17/297.17 , active(U43(tt())) -> mark(tt()) 748.17/297.17 , active(isNatIList(V)) -> mark(U31(isNatIListKind(V), V)) 748.17/297.17 , active(isNatIList(zeros())) -> mark(tt()) 748.17/297.17 , active(isNatIList(cons(V1, V2))) -> 748.17/297.17 mark(U41(and(isNatKind(V1), isNatIListKind(V2)), V1, V2)) 748.17/297.17 , active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 748.17/297.17 , active(U51(tt(), V1, V2)) -> mark(U52(isNat(V1), V2)) 748.17/297.17 , active(U52(X1, X2)) -> U52(active(X1), X2) 748.17/297.17 , active(U52(tt(), V2)) -> mark(U53(isNatList(V2))) 748.17/297.17 , active(U53(X)) -> U53(active(X)) 748.17/297.17 , active(U53(tt())) -> mark(tt()) 748.17/297.17 , active(U61(X1, X2)) -> U61(active(X1), X2) 748.17/297.17 , active(U61(tt(), L)) -> mark(s(length(L))) 748.17/297.17 , active(s(X)) -> s(active(X)) 748.17/297.17 , active(length(X)) -> length(active(X)) 748.17/297.17 , active(length(cons(N, L))) -> 748.17/297.17 mark(U61(and(and(isNatList(L), isNatIListKind(L)), 748.17/297.17 and(isNat(N), isNatKind(N))), 748.17/297.17 L)) 748.17/297.17 , active(length(nil())) -> mark(0()) 748.17/297.17 , active(and(X1, X2)) -> and(active(X1), X2) 748.17/297.17 , active(and(tt(), X)) -> mark(X) 748.17/297.17 , active(isNatIListKind(zeros())) -> mark(tt()) 748.17/297.17 , active(isNatIListKind(cons(V1, V2))) -> 748.17/297.17 mark(and(isNatKind(V1), isNatIListKind(V2))) 748.17/297.17 , active(isNatIListKind(nil())) -> mark(tt()) 748.17/297.17 , active(isNatKind(0())) -> mark(tt()) 748.17/297.17 , active(isNatKind(s(V1))) -> mark(isNatKind(V1)) 748.17/297.17 , active(isNatKind(length(V1))) -> mark(isNatIListKind(V1)) 748.17/297.17 , cons(mark(X1), X2) -> mark(cons(X1, X2)) 748.17/297.17 , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 748.17/297.17 , U11(mark(X1), X2) -> mark(U11(X1, X2)) 748.17/297.17 , U11(ok(X1), ok(X2)) -> ok(U11(X1, X2)) 748.17/297.17 , U12(mark(X)) -> mark(U12(X)) 748.17/297.17 , U12(ok(X)) -> ok(U12(X)) 748.17/297.17 , isNatList(ok(X)) -> ok(isNatList(X)) 748.17/297.17 , U21(mark(X1), X2) -> mark(U21(X1, X2)) 748.17/297.17 , U21(ok(X1), ok(X2)) -> ok(U21(X1, X2)) 748.17/297.17 , U22(mark(X)) -> mark(U22(X)) 748.17/297.17 , U22(ok(X)) -> ok(U22(X)) 748.17/297.17 , isNat(ok(X)) -> ok(isNat(X)) 748.17/297.17 , U31(mark(X1), X2) -> mark(U31(X1, X2)) 748.17/297.17 , U31(ok(X1), ok(X2)) -> ok(U31(X1, X2)) 748.17/297.17 , U32(mark(X)) -> mark(U32(X)) 748.17/297.17 , U32(ok(X)) -> ok(U32(X)) 748.17/297.17 , U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 748.17/297.17 , U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 748.17/297.17 , U42(mark(X1), X2) -> mark(U42(X1, X2)) 748.17/297.17 , U42(ok(X1), ok(X2)) -> ok(U42(X1, X2)) 748.17/297.17 , U43(mark(X)) -> mark(U43(X)) 748.17/297.17 , U43(ok(X)) -> ok(U43(X)) 748.17/297.17 , isNatIList(ok(X)) -> ok(isNatIList(X)) 748.17/297.17 , U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 748.17/297.17 , U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 748.17/297.17 , U52(mark(X1), X2) -> mark(U52(X1, X2)) 748.17/297.17 , U52(ok(X1), ok(X2)) -> ok(U52(X1, X2)) 748.17/297.17 , U53(mark(X)) -> mark(U53(X)) 748.17/297.17 , U53(ok(X)) -> ok(U53(X)) 748.17/297.17 , U61(mark(X1), X2) -> mark(U61(X1, X2)) 748.17/297.17 , U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 748.17/297.17 , s(mark(X)) -> mark(s(X)) 748.17/297.17 , s(ok(X)) -> ok(s(X)) 748.17/297.17 , length(mark(X)) -> mark(length(X)) 748.17/297.17 , length(ok(X)) -> ok(length(X)) 748.17/297.17 , and(mark(X1), X2) -> mark(and(X1, X2)) 748.17/297.17 , and(ok(X1), ok(X2)) -> ok(and(X1, X2)) 748.17/297.17 , isNatIListKind(ok(X)) -> ok(isNatIListKind(X)) 748.17/297.17 , isNatKind(ok(X)) -> ok(isNatKind(X)) 748.17/297.17 , proper(zeros()) -> ok(zeros()) 748.17/297.17 , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 748.17/297.17 , proper(0()) -> ok(0()) 748.17/297.17 , proper(U11(X1, X2)) -> U11(proper(X1), proper(X2)) 748.17/297.17 , proper(tt()) -> ok(tt()) 748.17/297.17 , proper(U12(X)) -> U12(proper(X)) 748.17/297.17 , proper(isNatList(X)) -> isNatList(proper(X)) 748.17/297.17 , proper(U21(X1, X2)) -> U21(proper(X1), proper(X2)) 748.17/297.17 , proper(U22(X)) -> U22(proper(X)) 748.17/297.17 , proper(isNat(X)) -> isNat(proper(X)) 748.17/297.17 , proper(U31(X1, X2)) -> U31(proper(X1), proper(X2)) 748.17/297.17 , proper(U32(X)) -> U32(proper(X)) 748.17/297.17 , proper(U41(X1, X2, X3)) -> 748.17/297.17 U41(proper(X1), proper(X2), proper(X3)) 748.17/297.17 , proper(U42(X1, X2)) -> U42(proper(X1), proper(X2)) 748.17/297.17 , proper(U43(X)) -> U43(proper(X)) 748.17/297.17 , proper(isNatIList(X)) -> isNatIList(proper(X)) 748.17/297.17 , proper(U51(X1, X2, X3)) -> 748.17/297.17 U51(proper(X1), proper(X2), proper(X3)) 748.17/297.17 , proper(U52(X1, X2)) -> U52(proper(X1), proper(X2)) 748.17/297.17 , proper(U53(X)) -> U53(proper(X)) 748.17/297.17 , proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 748.17/297.17 , proper(s(X)) -> s(proper(X)) 748.17/297.17 , proper(length(X)) -> length(proper(X)) 748.17/297.17 , proper(and(X1, X2)) -> and(proper(X1), proper(X2)) 748.17/297.17 , proper(isNatIListKind(X)) -> isNatIListKind(proper(X)) 748.17/297.17 , proper(isNatKind(X)) -> isNatKind(proper(X)) 748.17/297.17 , proper(nil()) -> ok(nil()) 748.17/297.17 , top(mark(X)) -> top(proper(X)) 748.17/297.17 , top(ok(X)) -> top(active(X)) } 748.17/297.17 Obligation: 748.17/297.17 innermost runtime complexity 748.17/297.17 Answer: 748.17/297.17 MAYBE 748.17/297.17 748.17/297.17 None of the processors succeeded. 748.17/297.17 748.17/297.17 Details of failed attempt(s): 748.17/297.17 ----------------------------- 748.17/297.17 1) 'empty' failed due to the following reason: 748.17/297.17 748.17/297.17 Empty strict component of the problem is NOT empty. 748.17/297.17 748.17/297.17 2) 'Best' failed due to the following reason: 748.17/297.17 748.17/297.17 None of the processors succeeded. 748.17/297.17 748.17/297.17 Details of failed attempt(s): 748.17/297.17 ----------------------------- 748.17/297.17 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 748.17/297.17 following reason: 748.17/297.17 748.17/297.17 Computation stopped due to timeout after 297.0 seconds. 748.17/297.17 748.17/297.17 2) 'Best' failed due to the following reason: 748.17/297.17 748.17/297.17 None of the processors succeeded. 748.17/297.17 748.17/297.17 Details of failed attempt(s): 748.17/297.17 ----------------------------- 748.17/297.17 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 748.17/297.17 seconds)' failed due to the following reason: 748.17/297.17 748.17/297.17 Computation stopped due to timeout after 148.0 seconds. 748.17/297.17 748.17/297.17 2) 'Best' failed due to the following reason: 748.17/297.17 748.17/297.17 None of the processors succeeded. 748.17/297.17 748.17/297.17 Details of failed attempt(s): 748.17/297.17 ----------------------------- 748.17/297.17 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 748.17/297.17 following reason: 748.17/297.17 748.17/297.17 The input cannot be shown compatible 748.17/297.17 748.17/297.17 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 748.17/297.17 to the following reason: 748.17/297.17 748.17/297.17 The input cannot be shown compatible 748.17/297.17 748.17/297.17 748.17/297.17 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 748.17/297.17 failed due to the following reason: 748.17/297.17 748.17/297.17 None of the processors succeeded. 748.17/297.17 748.17/297.17 Details of failed attempt(s): 748.17/297.17 ----------------------------- 748.17/297.17 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 748.17/297.17 failed due to the following reason: 748.17/297.17 748.17/297.17 match-boundness of the problem could not be verified. 748.17/297.17 748.17/297.17 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 748.17/297.17 failed due to the following reason: 748.17/297.17 748.17/297.17 match-boundness of the problem could not be verified. 748.17/297.17 748.17/297.17 748.17/297.17 748.17/297.17 748.17/297.17 748.17/297.17 Arrrr.. 748.59/297.58 EOF