MAYBE 763.28/297.14 MAYBE 763.28/297.14 763.28/297.14 We are left with following problem, upon which TcT provides the 763.28/297.14 certificate MAYBE. 763.28/297.14 763.28/297.14 Strict Trs: 763.28/297.14 { zeros() -> cons(0(), n__zeros()) 763.28/297.14 , zeros() -> n__zeros() 763.28/297.14 , cons(X1, X2) -> n__cons(X1, X2) 763.28/297.14 , 0() -> n__0() 763.28/297.14 , U11(tt(), V1) -> U12(isNatList(activate(V1))) 763.28/297.14 , U12(tt()) -> tt() 763.28/297.14 , isNatList(n__cons(V1, V2)) -> 763.28/297.14 U51(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), 763.28/297.14 activate(V1), 763.28/297.14 activate(V2)) 763.28/297.14 , isNatList(n__nil()) -> tt() 763.28/297.14 , activate(X) -> X 763.28/297.14 , activate(n__zeros()) -> zeros() 763.28/297.14 , activate(n__0()) -> 0() 763.28/297.14 , activate(n__length(X)) -> length(X) 763.28/297.14 , activate(n__s(X)) -> s(X) 763.28/297.14 , activate(n__cons(X1, X2)) -> cons(X1, X2) 763.28/297.14 , activate(n__isNatIListKind(X)) -> isNatIListKind(X) 763.28/297.14 , activate(n__nil()) -> nil() 763.28/297.14 , activate(n__and(X1, X2)) -> and(X1, X2) 763.28/297.14 , activate(n__isNatKind(X)) -> isNatKind(X) 763.28/297.14 , U21(tt(), V1) -> U22(isNat(activate(V1))) 763.28/297.14 , U22(tt()) -> tt() 763.28/297.14 , isNat(n__0()) -> tt() 763.28/297.14 , isNat(n__length(V1)) -> 763.28/297.14 U11(isNatIListKind(activate(V1)), activate(V1)) 763.28/297.15 , isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) 763.28/297.15 , U31(tt(), V) -> U32(isNatList(activate(V))) 763.28/297.15 , U32(tt()) -> tt() 763.28/297.15 , U41(tt(), V1, V2) -> U42(isNat(activate(V1)), activate(V2)) 763.28/297.15 , U42(tt(), V2) -> U43(isNatIList(activate(V2))) 763.28/297.15 , U43(tt()) -> tt() 763.28/297.15 , isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)) 763.28/297.15 , isNatIList(n__zeros()) -> tt() 763.28/297.15 , isNatIList(n__cons(V1, V2)) -> 763.28/297.15 U41(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), 763.28/297.15 activate(V1), 763.28/297.15 activate(V2)) 763.28/297.15 , U51(tt(), V1, V2) -> U52(isNat(activate(V1)), activate(V2)) 763.28/297.15 , U52(tt(), V2) -> U53(isNatList(activate(V2))) 763.28/297.15 , U53(tt()) -> tt() 763.28/297.15 , U61(tt(), L) -> s(length(activate(L))) 763.28/297.15 , s(X) -> n__s(X) 763.28/297.15 , length(X) -> n__length(X) 763.28/297.15 , length(cons(N, L)) -> 763.28/297.15 U61(and(and(isNatList(activate(L)), 763.28/297.15 n__isNatIListKind(activate(L))), 763.28/297.15 n__and(isNat(N), n__isNatKind(N))), 763.28/297.15 activate(L)) 763.28/297.15 , length(nil()) -> 0() 763.28/297.15 , and(X1, X2) -> n__and(X1, X2) 763.28/297.15 , and(tt(), X) -> activate(X) 763.28/297.15 , isNatIListKind(X) -> n__isNatIListKind(X) 763.28/297.15 , isNatIListKind(n__zeros()) -> tt() 763.28/297.15 , isNatIListKind(n__cons(V1, V2)) -> 763.28/297.15 and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))) 763.28/297.15 , isNatIListKind(n__nil()) -> tt() 763.28/297.15 , isNatKind(X) -> n__isNatKind(X) 763.28/297.15 , isNatKind(n__0()) -> tt() 763.28/297.15 , isNatKind(n__length(V1)) -> isNatIListKind(activate(V1)) 763.28/297.15 , isNatKind(n__s(V1)) -> isNatKind(activate(V1)) 763.28/297.15 , nil() -> n__nil() } 763.28/297.15 Obligation: 763.28/297.15 innermost runtime complexity 763.28/297.15 Answer: 763.28/297.15 MAYBE 763.28/297.15 763.28/297.15 Arguments of following rules are not normal-forms: 763.28/297.15 763.28/297.15 { length(cons(N, L)) -> 763.28/297.15 U61(and(and(isNatList(activate(L)), 763.28/297.15 n__isNatIListKind(activate(L))), 763.28/297.15 n__and(isNat(N), n__isNatKind(N))), 763.28/297.15 activate(L)) 763.28/297.15 , length(nil()) -> 0() } 763.28/297.15 763.28/297.15 All above mentioned rules can be savely removed. 763.28/297.15 763.28/297.15 We are left with following problem, upon which TcT provides the 763.28/297.15 certificate MAYBE. 763.28/297.15 763.28/297.15 Strict Trs: 763.28/297.15 { zeros() -> cons(0(), n__zeros()) 763.28/297.15 , zeros() -> n__zeros() 763.28/297.15 , cons(X1, X2) -> n__cons(X1, X2) 763.28/297.15 , 0() -> n__0() 763.28/297.15 , U11(tt(), V1) -> U12(isNatList(activate(V1))) 763.28/297.15 , U12(tt()) -> tt() 763.28/297.15 , isNatList(n__cons(V1, V2)) -> 763.28/297.15 U51(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), 763.28/297.15 activate(V1), 763.28/297.15 activate(V2)) 763.28/297.15 , isNatList(n__nil()) -> tt() 763.28/297.15 , activate(X) -> X 763.28/297.15 , activate(n__zeros()) -> zeros() 763.28/297.15 , activate(n__0()) -> 0() 763.28/297.15 , activate(n__length(X)) -> length(X) 763.28/297.15 , activate(n__s(X)) -> s(X) 763.28/297.15 , activate(n__cons(X1, X2)) -> cons(X1, X2) 763.28/297.15 , activate(n__isNatIListKind(X)) -> isNatIListKind(X) 763.28/297.15 , activate(n__nil()) -> nil() 763.28/297.15 , activate(n__and(X1, X2)) -> and(X1, X2) 763.28/297.15 , activate(n__isNatKind(X)) -> isNatKind(X) 763.28/297.15 , U21(tt(), V1) -> U22(isNat(activate(V1))) 763.28/297.15 , U22(tt()) -> tt() 763.28/297.15 , isNat(n__0()) -> tt() 763.28/297.15 , isNat(n__length(V1)) -> 763.28/297.15 U11(isNatIListKind(activate(V1)), activate(V1)) 763.28/297.15 , isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) 763.28/297.15 , U31(tt(), V) -> U32(isNatList(activate(V))) 763.28/297.15 , U32(tt()) -> tt() 763.28/297.15 , U41(tt(), V1, V2) -> U42(isNat(activate(V1)), activate(V2)) 763.28/297.15 , U42(tt(), V2) -> U43(isNatIList(activate(V2))) 763.28/297.15 , U43(tt()) -> tt() 763.28/297.15 , isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)) 763.28/297.15 , isNatIList(n__zeros()) -> tt() 763.28/297.15 , isNatIList(n__cons(V1, V2)) -> 763.28/297.15 U41(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), 763.28/297.15 activate(V1), 763.28/297.15 activate(V2)) 763.28/297.15 , U51(tt(), V1, V2) -> U52(isNat(activate(V1)), activate(V2)) 763.28/297.15 , U52(tt(), V2) -> U53(isNatList(activate(V2))) 763.28/297.15 , U53(tt()) -> tt() 763.28/297.15 , U61(tt(), L) -> s(length(activate(L))) 763.28/297.15 , s(X) -> n__s(X) 763.28/297.15 , length(X) -> n__length(X) 763.28/297.15 , and(X1, X2) -> n__and(X1, X2) 763.28/297.15 , and(tt(), X) -> activate(X) 763.28/297.15 , isNatIListKind(X) -> n__isNatIListKind(X) 763.28/297.15 , isNatIListKind(n__zeros()) -> tt() 763.28/297.15 , isNatIListKind(n__cons(V1, V2)) -> 763.28/297.15 and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))) 763.28/297.15 , isNatIListKind(n__nil()) -> tt() 763.28/297.15 , isNatKind(X) -> n__isNatKind(X) 763.28/297.15 , isNatKind(n__0()) -> tt() 763.28/297.15 , isNatKind(n__length(V1)) -> isNatIListKind(activate(V1)) 763.28/297.15 , isNatKind(n__s(V1)) -> isNatKind(activate(V1)) 763.28/297.15 , nil() -> n__nil() } 763.28/297.15 Obligation: 763.28/297.15 innermost runtime complexity 763.28/297.15 Answer: 763.28/297.15 MAYBE 763.28/297.15 763.28/297.15 None of the processors succeeded. 763.28/297.15 763.28/297.15 Details of failed attempt(s): 763.28/297.15 ----------------------------- 763.28/297.15 1) 'empty' failed due to the following reason: 763.28/297.15 763.28/297.15 Empty strict component of the problem is NOT empty. 763.28/297.15 763.28/297.15 2) 'Best' failed due to the following reason: 763.28/297.15 763.28/297.15 None of the processors succeeded. 763.28/297.15 763.28/297.15 Details of failed attempt(s): 763.28/297.15 ----------------------------- 763.28/297.15 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 763.28/297.15 following reason: 763.28/297.15 763.28/297.15 Computation stopped due to timeout after 297.0 seconds. 763.28/297.15 763.28/297.15 2) 'Best' failed due to the following reason: 763.28/297.15 763.28/297.15 None of the processors succeeded. 763.28/297.15 763.28/297.15 Details of failed attempt(s): 763.28/297.15 ----------------------------- 763.28/297.15 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 763.28/297.15 seconds)' failed due to the following reason: 763.28/297.15 763.28/297.15 Computation stopped due to timeout after 148.0 seconds. 763.28/297.15 763.28/297.15 2) 'Best' failed due to the following reason: 763.28/297.15 763.28/297.15 None of the processors succeeded. 763.28/297.15 763.28/297.15 Details of failed attempt(s): 763.28/297.15 ----------------------------- 763.28/297.15 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 763.28/297.15 to the following reason: 763.28/297.15 763.28/297.15 The input cannot be shown compatible 763.28/297.15 763.28/297.15 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 763.28/297.15 following reason: 763.28/297.15 763.28/297.15 The input cannot be shown compatible 763.28/297.15 763.28/297.15 763.28/297.15 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 763.28/297.15 failed due to the following reason: 763.28/297.15 763.28/297.15 None of the processors succeeded. 763.28/297.15 763.28/297.15 Details of failed attempt(s): 763.28/297.15 ----------------------------- 763.28/297.15 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 763.28/297.15 failed due to the following reason: 763.28/297.15 763.28/297.15 match-boundness of the problem could not be verified. 763.28/297.15 763.28/297.15 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 763.28/297.15 failed due to the following reason: 763.28/297.15 763.28/297.15 match-boundness of the problem could not be verified. 763.28/297.15 763.28/297.15 763.28/297.15 763.28/297.15 763.28/297.15 763.28/297.15 Arrrr.. 763.41/297.20 EOF