MAYBE 760.06/297.13 MAYBE 760.06/297.13 760.06/297.13 We are left with following problem, upon which TcT provides the 760.06/297.13 certificate MAYBE. 760.06/297.13 760.06/297.13 Strict Trs: 760.06/297.13 { zeros() -> cons(0(), n__zeros()) 760.06/297.13 , zeros() -> n__zeros() 760.06/297.13 , cons(X1, X2) -> n__cons(X1, X2) 760.06/297.13 , 0() -> n__0() 760.06/297.13 , U11(tt(), V1) -> U12(isNatList(activate(V1))) 760.06/297.13 , U12(tt()) -> tt() 760.06/297.13 , isNatList(n__cons(V1, V2)) -> 760.06/297.13 U51(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), 760.06/297.13 activate(V1), 760.06/297.13 activate(V2)) 760.06/297.13 , isNatList(n__nil()) -> tt() 760.06/297.13 , activate(X) -> X 760.06/297.13 , activate(n__zeros()) -> zeros() 760.06/297.13 , activate(n__0()) -> 0() 760.06/297.13 , activate(n__length(X)) -> length(activate(X)) 760.06/297.13 , activate(n__s(X)) -> s(activate(X)) 760.06/297.13 , activate(n__cons(X1, X2)) -> cons(activate(X1), X2) 760.06/297.13 , activate(n__isNatIListKind(X)) -> isNatIListKind(X) 760.06/297.13 , activate(n__nil()) -> nil() 760.06/297.13 , activate(n__and(X1, X2)) -> and(activate(X1), X2) 760.06/297.13 , activate(n__isNat(X)) -> isNat(X) 760.06/297.13 , activate(n__isNatKind(X)) -> isNatKind(X) 760.06/297.13 , U21(tt(), V1) -> U22(isNat(activate(V1))) 760.06/297.13 , U22(tt()) -> tt() 760.06/297.13 , isNat(X) -> n__isNat(X) 760.06/297.13 , isNat(n__0()) -> tt() 760.06/297.13 , isNat(n__length(V1)) -> 760.06/297.13 U11(isNatIListKind(activate(V1)), activate(V1)) 760.06/297.13 , isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) 760.06/297.13 , U31(tt(), V) -> U32(isNatList(activate(V))) 760.06/297.13 , U32(tt()) -> tt() 760.06/297.13 , U41(tt(), V1, V2) -> U42(isNat(activate(V1)), activate(V2)) 760.06/297.13 , U42(tt(), V2) -> U43(isNatIList(activate(V2))) 760.06/297.13 , U43(tt()) -> tt() 760.06/297.13 , isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)) 760.06/297.13 , isNatIList(n__zeros()) -> tt() 760.06/297.13 , isNatIList(n__cons(V1, V2)) -> 760.06/297.13 U41(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), 760.06/297.13 activate(V1), 760.06/297.13 activate(V2)) 760.06/297.13 , U51(tt(), V1, V2) -> U52(isNat(activate(V1)), activate(V2)) 760.06/297.13 , U52(tt(), V2) -> U53(isNatList(activate(V2))) 760.06/297.13 , U53(tt()) -> tt() 760.06/297.13 , U61(tt(), L) -> s(length(activate(L))) 760.06/297.13 , s(X) -> n__s(X) 760.06/297.13 , length(X) -> n__length(X) 760.06/297.13 , length(cons(N, L)) -> 760.06/297.13 U61(and(and(isNatList(activate(L)), 760.06/297.13 n__isNatIListKind(activate(L))), 760.06/297.13 n__and(n__isNat(N), n__isNatKind(N))), 760.06/297.13 activate(L)) 760.06/297.13 , length(nil()) -> 0() 760.06/297.13 , and(X1, X2) -> n__and(X1, X2) 760.06/297.13 , and(tt(), X) -> activate(X) 760.06/297.13 , isNatIListKind(X) -> n__isNatIListKind(X) 760.06/297.13 , isNatIListKind(n__zeros()) -> tt() 760.06/297.13 , isNatIListKind(n__cons(V1, V2)) -> 760.06/297.13 and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))) 760.06/297.13 , isNatIListKind(n__nil()) -> tt() 760.06/297.13 , isNatKind(X) -> n__isNatKind(X) 760.06/297.13 , isNatKind(n__0()) -> tt() 760.06/297.13 , isNatKind(n__length(V1)) -> isNatIListKind(activate(V1)) 760.06/297.13 , isNatKind(n__s(V1)) -> isNatKind(activate(V1)) 760.06/297.13 , nil() -> n__nil() } 760.06/297.13 Obligation: 760.06/297.13 innermost runtime complexity 760.06/297.13 Answer: 760.06/297.13 MAYBE 760.06/297.13 760.06/297.13 Arguments of following rules are not normal-forms: 760.06/297.13 760.06/297.13 { length(cons(N, L)) -> 760.06/297.13 U61(and(and(isNatList(activate(L)), 760.06/297.13 n__isNatIListKind(activate(L))), 760.06/297.13 n__and(n__isNat(N), n__isNatKind(N))), 760.06/297.13 activate(L)) 760.06/297.13 , length(nil()) -> 0() } 760.06/297.13 760.06/297.13 All above mentioned rules can be savely removed. 760.06/297.13 760.06/297.13 We are left with following problem, upon which TcT provides the 760.06/297.13 certificate MAYBE. 760.06/297.13 760.06/297.13 Strict Trs: 760.06/297.13 { zeros() -> cons(0(), n__zeros()) 760.06/297.14 , zeros() -> n__zeros() 760.06/297.14 , cons(X1, X2) -> n__cons(X1, X2) 760.06/297.14 , 0() -> n__0() 760.06/297.14 , U11(tt(), V1) -> U12(isNatList(activate(V1))) 760.06/297.14 , U12(tt()) -> tt() 760.06/297.14 , isNatList(n__cons(V1, V2)) -> 760.06/297.14 U51(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), 760.06/297.14 activate(V1), 760.06/297.14 activate(V2)) 760.06/297.14 , isNatList(n__nil()) -> tt() 760.06/297.14 , activate(X) -> X 760.06/297.14 , activate(n__zeros()) -> zeros() 760.06/297.14 , activate(n__0()) -> 0() 760.06/297.14 , activate(n__length(X)) -> length(activate(X)) 760.06/297.14 , activate(n__s(X)) -> s(activate(X)) 760.06/297.14 , activate(n__cons(X1, X2)) -> cons(activate(X1), X2) 760.06/297.14 , activate(n__isNatIListKind(X)) -> isNatIListKind(X) 760.06/297.14 , activate(n__nil()) -> nil() 760.06/297.14 , activate(n__and(X1, X2)) -> and(activate(X1), X2) 760.06/297.14 , activate(n__isNat(X)) -> isNat(X) 760.06/297.14 , activate(n__isNatKind(X)) -> isNatKind(X) 760.06/297.14 , U21(tt(), V1) -> U22(isNat(activate(V1))) 760.06/297.14 , U22(tt()) -> tt() 760.06/297.14 , isNat(X) -> n__isNat(X) 760.06/297.14 , isNat(n__0()) -> tt() 760.06/297.14 , isNat(n__length(V1)) -> 760.06/297.14 U11(isNatIListKind(activate(V1)), activate(V1)) 760.06/297.14 , isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) 760.06/297.14 , U31(tt(), V) -> U32(isNatList(activate(V))) 760.06/297.14 , U32(tt()) -> tt() 760.06/297.14 , U41(tt(), V1, V2) -> U42(isNat(activate(V1)), activate(V2)) 760.06/297.14 , U42(tt(), V2) -> U43(isNatIList(activate(V2))) 760.06/297.14 , U43(tt()) -> tt() 760.06/297.14 , isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)) 760.06/297.14 , isNatIList(n__zeros()) -> tt() 760.06/297.14 , isNatIList(n__cons(V1, V2)) -> 760.06/297.14 U41(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), 760.06/297.14 activate(V1), 760.06/297.14 activate(V2)) 760.06/297.14 , U51(tt(), V1, V2) -> U52(isNat(activate(V1)), activate(V2)) 760.06/297.14 , U52(tt(), V2) -> U53(isNatList(activate(V2))) 760.06/297.14 , U53(tt()) -> tt() 760.06/297.14 , U61(tt(), L) -> s(length(activate(L))) 760.06/297.14 , s(X) -> n__s(X) 760.06/297.14 , length(X) -> n__length(X) 760.06/297.14 , and(X1, X2) -> n__and(X1, X2) 760.06/297.14 , and(tt(), X) -> activate(X) 760.06/297.14 , isNatIListKind(X) -> n__isNatIListKind(X) 760.06/297.14 , isNatIListKind(n__zeros()) -> tt() 760.06/297.14 , isNatIListKind(n__cons(V1, V2)) -> 760.06/297.14 and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))) 760.06/297.14 , isNatIListKind(n__nil()) -> tt() 760.06/297.14 , isNatKind(X) -> n__isNatKind(X) 760.06/297.14 , isNatKind(n__0()) -> tt() 760.06/297.14 , isNatKind(n__length(V1)) -> isNatIListKind(activate(V1)) 760.06/297.14 , isNatKind(n__s(V1)) -> isNatKind(activate(V1)) 760.06/297.14 , nil() -> n__nil() } 760.06/297.14 Obligation: 760.06/297.14 innermost runtime complexity 760.06/297.14 Answer: 760.06/297.14 MAYBE 760.06/297.14 760.06/297.14 None of the processors succeeded. 760.06/297.14 760.06/297.14 Details of failed attempt(s): 760.06/297.14 ----------------------------- 760.06/297.14 1) 'empty' failed due to the following reason: 760.06/297.14 760.06/297.14 Empty strict component of the problem is NOT empty. 760.06/297.14 760.06/297.14 2) 'Best' failed due to the following reason: 760.06/297.14 760.06/297.14 None of the processors succeeded. 760.06/297.14 760.06/297.14 Details of failed attempt(s): 760.06/297.14 ----------------------------- 760.06/297.14 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 760.06/297.14 following reason: 760.06/297.14 760.06/297.14 Computation stopped due to timeout after 297.0 seconds. 760.06/297.14 760.06/297.14 2) 'Best' failed due to the following reason: 760.06/297.14 760.06/297.14 None of the processors succeeded. 760.06/297.14 760.06/297.14 Details of failed attempt(s): 760.06/297.14 ----------------------------- 760.06/297.14 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 760.06/297.14 seconds)' failed due to the following reason: 760.06/297.14 760.06/297.14 Computation stopped due to timeout after 148.0 seconds. 760.06/297.14 760.06/297.14 2) 'Best' failed due to the following reason: 760.06/297.14 760.06/297.14 None of the processors succeeded. 760.06/297.14 760.06/297.14 Details of failed attempt(s): 760.06/297.14 ----------------------------- 760.06/297.14 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 760.06/297.14 to the following reason: 760.06/297.14 760.06/297.14 The input cannot be shown compatible 760.06/297.14 760.06/297.14 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 760.06/297.14 following reason: 760.06/297.14 760.06/297.14 The input cannot be shown compatible 760.06/297.14 760.06/297.14 760.06/297.14 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 760.06/297.14 failed due to the following reason: 760.06/297.14 760.06/297.14 None of the processors succeeded. 760.06/297.14 760.06/297.14 Details of failed attempt(s): 760.06/297.14 ----------------------------- 760.06/297.14 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 760.06/297.14 failed due to the following reason: 760.06/297.14 760.06/297.14 match-boundness of the problem could not be verified. 760.06/297.14 760.06/297.14 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 760.06/297.14 failed due to the following reason: 760.06/297.14 760.06/297.14 match-boundness of the problem could not be verified. 760.06/297.14 760.06/297.14 760.06/297.14 760.06/297.14 760.06/297.14 760.06/297.14 Arrrr.. 760.06/297.19 EOF