MAYBE 982.29/297.72 MAYBE 982.29/297.72 982.29/297.72 We are left with following problem, upon which TcT provides the 982.29/297.72 certificate MAYBE. 982.29/297.72 982.29/297.72 Strict Trs: 982.29/297.72 { zeros() -> cons(0(), n__zeros()) 982.29/297.72 , zeros() -> n__zeros() 982.29/297.72 , cons(X1, X2) -> n__cons(X1, X2) 982.29/297.72 , 0() -> n__0() 982.29/297.72 , U11(tt(), V1) -> U12(isNatList(activate(V1))) 982.29/297.72 , U12(tt()) -> tt() 982.29/297.72 , isNatList(n__take(V1, V2)) -> 982.29/297.72 U61(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), 982.29/297.72 activate(V1), 982.29/297.72 activate(V2)) 982.29/297.72 , isNatList(n__cons(V1, V2)) -> 982.29/297.72 U51(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), 982.29/297.72 activate(V1), 982.29/297.72 activate(V2)) 982.29/297.72 , isNatList(n__nil()) -> tt() 982.29/297.72 , activate(X) -> X 982.29/297.72 , activate(n__zeros()) -> zeros() 982.29/297.72 , activate(n__take(X1, X2)) -> take(X1, X2) 982.29/297.72 , activate(n__0()) -> 0() 982.29/297.72 , activate(n__length(X)) -> length(X) 982.29/297.72 , activate(n__s(X)) -> s(X) 982.29/297.72 , activate(n__cons(X1, X2)) -> cons(X1, X2) 982.29/297.72 , activate(n__isNatIListKind(X)) -> isNatIListKind(X) 982.29/297.72 , activate(n__nil()) -> nil() 982.29/297.72 , activate(n__and(X1, X2)) -> and(X1, X2) 982.29/297.72 , activate(n__isNatKind(X)) -> isNatKind(X) 982.29/297.72 , U21(tt(), V1) -> U22(isNat(activate(V1))) 982.29/297.72 , U22(tt()) -> tt() 982.29/297.72 , isNat(n__0()) -> tt() 982.29/297.72 , isNat(n__length(V1)) -> 982.29/297.72 U11(isNatIListKind(activate(V1)), activate(V1)) 982.29/297.72 , isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) 982.29/297.72 , U31(tt(), V) -> U32(isNatList(activate(V))) 982.29/297.72 , U32(tt()) -> tt() 982.29/297.72 , U41(tt(), V1, V2) -> U42(isNat(activate(V1)), activate(V2)) 982.29/297.72 , U42(tt(), V2) -> U43(isNatIList(activate(V2))) 982.29/297.72 , U43(tt()) -> tt() 982.29/297.72 , isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)) 982.29/297.72 , isNatIList(n__zeros()) -> tt() 982.29/297.72 , isNatIList(n__cons(V1, V2)) -> 982.29/297.72 U41(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), 982.29/297.72 activate(V1), 982.29/297.72 activate(V2)) 982.29/297.72 , U51(tt(), V1, V2) -> U52(isNat(activate(V1)), activate(V2)) 982.29/297.72 , U52(tt(), V2) -> U53(isNatList(activate(V2))) 982.29/297.72 , U53(tt()) -> tt() 982.29/297.72 , U61(tt(), V1, V2) -> U62(isNat(activate(V1)), activate(V2)) 982.29/297.72 , U62(tt(), V2) -> U63(isNatIList(activate(V2))) 982.29/297.72 , U63(tt()) -> tt() 982.29/297.72 , U71(tt(), L) -> s(length(activate(L))) 982.29/297.72 , s(X) -> n__s(X) 982.29/297.72 , length(X) -> n__length(X) 982.29/297.72 , length(cons(N, L)) -> 982.29/297.72 U71(and(and(isNatList(activate(L)), 982.29/297.72 n__isNatIListKind(activate(L))), 982.29/297.72 n__and(isNat(N), n__isNatKind(N))), 982.29/297.72 activate(L)) 982.29/297.72 , length(nil()) -> 0() 982.29/297.72 , U81(tt()) -> nil() 982.29/297.72 , nil() -> n__nil() 982.29/297.72 , U91(tt(), IL, M, N) -> 982.29/297.72 cons(activate(N), n__take(activate(M), activate(IL))) 982.29/297.72 , and(X1, X2) -> n__and(X1, X2) 982.29/297.72 , and(tt(), X) -> activate(X) 982.29/297.72 , isNatIListKind(X) -> n__isNatIListKind(X) 982.29/297.72 , isNatIListKind(n__zeros()) -> tt() 982.29/297.72 , isNatIListKind(n__take(V1, V2)) -> 982.29/297.72 and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))) 982.29/297.72 , isNatIListKind(n__cons(V1, V2)) -> 982.29/297.72 and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))) 982.29/297.72 , isNatIListKind(n__nil()) -> tt() 982.29/297.72 , isNatKind(X) -> n__isNatKind(X) 982.29/297.72 , isNatKind(n__0()) -> tt() 982.29/297.72 , isNatKind(n__length(V1)) -> isNatIListKind(activate(V1)) 982.29/297.72 , isNatKind(n__s(V1)) -> isNatKind(activate(V1)) 982.29/297.72 , take(X1, X2) -> n__take(X1, X2) 982.29/297.72 , take(0(), IL) -> U81(and(isNatIList(IL), n__isNatIListKind(IL))) 982.29/297.72 , take(s(M), cons(N, IL)) -> 982.29/297.72 U91(and(and(isNatIList(activate(IL)), 982.29/297.72 n__isNatIListKind(activate(IL))), 982.29/297.72 n__and(and(isNat(M), n__isNatKind(M)), 982.29/297.72 n__and(isNat(N), n__isNatKind(N)))), 982.29/297.72 activate(IL), 982.29/297.72 M, 982.29/297.72 N) } 982.29/297.72 Obligation: 982.29/297.72 innermost runtime complexity 982.29/297.72 Answer: 982.29/297.72 MAYBE 982.29/297.72 982.29/297.72 Arguments of following rules are not normal-forms: 982.29/297.72 982.29/297.72 { length(cons(N, L)) -> 982.29/297.72 U71(and(and(isNatList(activate(L)), 982.29/297.72 n__isNatIListKind(activate(L))), 982.29/297.72 n__and(isNat(N), n__isNatKind(N))), 982.29/297.72 activate(L)) 982.29/297.72 , length(nil()) -> 0() 982.29/297.72 , take(0(), IL) -> U81(and(isNatIList(IL), n__isNatIListKind(IL))) 982.29/297.72 , take(s(M), cons(N, IL)) -> 982.29/297.72 U91(and(and(isNatIList(activate(IL)), 982.29/297.72 n__isNatIListKind(activate(IL))), 982.29/297.72 n__and(and(isNat(M), n__isNatKind(M)), 982.29/297.72 n__and(isNat(N), n__isNatKind(N)))), 982.29/297.72 activate(IL), 982.29/297.72 M, 982.29/297.72 N) } 982.29/297.72 982.29/297.72 All above mentioned rules can be savely removed. 982.29/297.72 982.29/297.72 We are left with following problem, upon which TcT provides the 982.29/297.72 certificate MAYBE. 982.29/297.72 982.29/297.72 Strict Trs: 982.29/297.72 { zeros() -> cons(0(), n__zeros()) 982.29/297.72 , zeros() -> n__zeros() 982.29/297.72 , cons(X1, X2) -> n__cons(X1, X2) 982.29/297.72 , 0() -> n__0() 982.29/297.72 , U11(tt(), V1) -> U12(isNatList(activate(V1))) 982.29/297.72 , U12(tt()) -> tt() 982.29/297.72 , isNatList(n__take(V1, V2)) -> 982.29/297.72 U61(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), 982.29/297.72 activate(V1), 982.29/297.72 activate(V2)) 982.29/297.72 , isNatList(n__cons(V1, V2)) -> 982.29/297.72 U51(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), 982.29/297.72 activate(V1), 982.29/297.72 activate(V2)) 982.29/297.72 , isNatList(n__nil()) -> tt() 982.29/297.72 , activate(X) -> X 982.29/297.72 , activate(n__zeros()) -> zeros() 982.29/297.72 , activate(n__take(X1, X2)) -> take(X1, X2) 982.29/297.72 , activate(n__0()) -> 0() 982.29/297.72 , activate(n__length(X)) -> length(X) 982.29/297.72 , activate(n__s(X)) -> s(X) 982.29/297.72 , activate(n__cons(X1, X2)) -> cons(X1, X2) 982.29/297.72 , activate(n__isNatIListKind(X)) -> isNatIListKind(X) 982.29/297.72 , activate(n__nil()) -> nil() 982.29/297.72 , activate(n__and(X1, X2)) -> and(X1, X2) 982.29/297.72 , activate(n__isNatKind(X)) -> isNatKind(X) 982.29/297.72 , U21(tt(), V1) -> U22(isNat(activate(V1))) 982.29/297.72 , U22(tt()) -> tt() 982.29/297.72 , isNat(n__0()) -> tt() 982.29/297.72 , isNat(n__length(V1)) -> 982.29/297.72 U11(isNatIListKind(activate(V1)), activate(V1)) 982.29/297.72 , isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) 982.29/297.72 , U31(tt(), V) -> U32(isNatList(activate(V))) 982.29/297.72 , U32(tt()) -> tt() 982.29/297.72 , U41(tt(), V1, V2) -> U42(isNat(activate(V1)), activate(V2)) 982.29/297.72 , U42(tt(), V2) -> U43(isNatIList(activate(V2))) 982.29/297.72 , U43(tt()) -> tt() 982.29/297.72 , isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)) 982.29/297.72 , isNatIList(n__zeros()) -> tt() 982.29/297.72 , isNatIList(n__cons(V1, V2)) -> 982.29/297.72 U41(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), 982.29/297.72 activate(V1), 982.29/297.72 activate(V2)) 982.29/297.72 , U51(tt(), V1, V2) -> U52(isNat(activate(V1)), activate(V2)) 982.29/297.72 , U52(tt(), V2) -> U53(isNatList(activate(V2))) 982.29/297.72 , U53(tt()) -> tt() 982.29/297.72 , U61(tt(), V1, V2) -> U62(isNat(activate(V1)), activate(V2)) 982.29/297.72 , U62(tt(), V2) -> U63(isNatIList(activate(V2))) 982.29/297.72 , U63(tt()) -> tt() 982.29/297.72 , U71(tt(), L) -> s(length(activate(L))) 982.29/297.72 , s(X) -> n__s(X) 982.29/297.72 , length(X) -> n__length(X) 982.29/297.72 , U81(tt()) -> nil() 982.29/297.72 , nil() -> n__nil() 982.29/297.72 , U91(tt(), IL, M, N) -> 982.29/297.72 cons(activate(N), n__take(activate(M), activate(IL))) 982.29/297.72 , and(X1, X2) -> n__and(X1, X2) 982.29/297.72 , and(tt(), X) -> activate(X) 982.29/297.72 , isNatIListKind(X) -> n__isNatIListKind(X) 982.29/297.72 , isNatIListKind(n__zeros()) -> tt() 982.29/297.72 , isNatIListKind(n__take(V1, V2)) -> 982.29/297.72 and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))) 982.29/297.72 , isNatIListKind(n__cons(V1, V2)) -> 982.29/297.72 and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))) 982.29/297.72 , isNatIListKind(n__nil()) -> tt() 982.29/297.72 , isNatKind(X) -> n__isNatKind(X) 982.29/297.72 , isNatKind(n__0()) -> tt() 982.29/297.72 , isNatKind(n__length(V1)) -> isNatIListKind(activate(V1)) 982.29/297.72 , isNatKind(n__s(V1)) -> isNatKind(activate(V1)) 982.29/297.72 , take(X1, X2) -> n__take(X1, X2) } 982.29/297.72 Obligation: 982.29/297.72 innermost runtime complexity 982.29/297.72 Answer: 982.29/297.72 MAYBE 982.29/297.72 982.29/297.72 None of the processors succeeded. 982.29/297.72 982.29/297.72 Details of failed attempt(s): 982.29/297.72 ----------------------------- 982.29/297.72 1) 'empty' failed due to the following reason: 982.29/297.72 982.29/297.72 Empty strict component of the problem is NOT empty. 982.29/297.72 982.29/297.72 2) 'Best' failed due to the following reason: 982.29/297.72 982.29/297.72 None of the processors succeeded. 982.29/297.72 982.29/297.72 Details of failed attempt(s): 982.29/297.72 ----------------------------- 982.29/297.72 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 982.29/297.72 following reason: 982.29/297.72 982.29/297.72 Computation stopped due to timeout after 297.0 seconds. 982.29/297.72 982.29/297.72 2) 'Best' failed due to the following reason: 982.29/297.72 982.29/297.72 None of the processors succeeded. 982.29/297.72 982.29/297.72 Details of failed attempt(s): 982.29/297.72 ----------------------------- 982.29/297.72 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 982.29/297.72 seconds)' failed due to the following reason: 982.29/297.72 982.29/297.72 Computation stopped due to timeout after 148.0 seconds. 982.29/297.72 982.29/297.72 2) 'Best' failed due to the following reason: 982.29/297.72 982.29/297.72 None of the processors succeeded. 982.29/297.72 982.29/297.72 Details of failed attempt(s): 982.29/297.72 ----------------------------- 982.29/297.72 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 982.29/297.72 to the following reason: 982.29/297.72 982.29/297.72 The input cannot be shown compatible 982.29/297.72 982.29/297.72 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 982.29/297.72 following reason: 982.29/297.72 982.29/297.72 The input cannot be shown compatible 982.29/297.72 982.29/297.72 982.29/297.72 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 982.29/297.72 failed due to the following reason: 982.29/297.72 982.29/297.72 None of the processors succeeded. 982.29/297.72 982.29/297.72 Details of failed attempt(s): 982.29/297.72 ----------------------------- 982.29/297.72 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 982.29/297.72 failed due to the following reason: 982.29/297.72 982.29/297.72 match-boundness of the problem could not be verified. 982.29/297.72 982.29/297.72 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 982.29/297.72 failed due to the following reason: 982.29/297.72 982.29/297.72 match-boundness of the problem could not be verified. 982.29/297.72 982.29/297.72 982.29/297.72 982.29/297.72 982.29/297.72 982.29/297.72 Arrrr.. 982.55/297.94 EOF