MAYBE 1136.84/297.06 MAYBE 1136.84/297.06 1136.84/297.06 We are left with following problem, upon which TcT provides the 1136.84/297.06 certificate MAYBE. 1136.84/297.06 1136.84/297.06 Strict Trs: 1136.84/297.06 { zeros() -> cons(0(), n__zeros()) 1136.84/297.06 , zeros() -> n__zeros() 1136.84/297.06 , cons(X1, X2) -> n__cons(X1, X2) 1136.84/297.06 , 0() -> n__0() 1136.84/297.06 , U101(tt(), V1, V2) -> 1136.84/297.06 U102(isNatKind(activate(V1)), activate(V1), activate(V2)) 1136.84/297.06 , U102(tt(), V1, V2) -> 1136.84/297.06 U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 1136.84/297.06 , isNatKind(n__0()) -> tt() 1136.84/297.06 , isNatKind(n__length(V1)) -> U71(isNatIListKind(activate(V1))) 1136.84/297.06 , isNatKind(n__s(V1)) -> U81(isNatKind(activate(V1))) 1136.84/297.06 , activate(X) -> X 1136.84/297.06 , activate(n__zeros()) -> zeros() 1136.84/297.06 , activate(n__take(X1, X2)) -> take(X1, X2) 1136.84/297.06 , activate(n__0()) -> 0() 1136.84/297.06 , activate(n__length(X)) -> length(X) 1136.84/297.06 , activate(n__s(X)) -> s(X) 1136.84/297.06 , activate(n__cons(X1, X2)) -> cons(X1, X2) 1136.84/297.06 , activate(n__nil()) -> nil() 1136.84/297.06 , U103(tt(), V1, V2) -> 1136.84/297.06 U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 1136.84/297.06 , isNatIListKind(n__zeros()) -> tt() 1136.84/297.06 , isNatIListKind(n__take(V1, V2)) -> 1136.84/297.06 U61(isNatKind(activate(V1)), activate(V2)) 1136.84/297.06 , isNatIListKind(n__cons(V1, V2)) -> 1136.84/297.06 U51(isNatKind(activate(V1)), activate(V2)) 1136.84/297.06 , isNatIListKind(n__nil()) -> tt() 1136.84/297.06 , U104(tt(), V1, V2) -> U105(isNat(activate(V1)), activate(V2)) 1136.84/297.06 , U105(tt(), V2) -> U106(isNatIList(activate(V2))) 1136.84/297.06 , isNat(n__0()) -> tt() 1136.84/297.06 , isNat(n__length(V1)) -> 1136.84/297.06 U11(isNatIListKind(activate(V1)), activate(V1)) 1136.84/297.06 , isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) 1136.84/297.06 , U106(tt()) -> tt() 1136.84/297.06 , isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)) 1136.84/297.06 , isNatIList(n__zeros()) -> tt() 1136.84/297.06 , isNatIList(n__cons(V1, V2)) -> 1136.84/297.06 U41(isNatKind(activate(V1)), activate(V1), activate(V2)) 1136.84/297.06 , U11(tt(), V1) -> U12(isNatIListKind(activate(V1)), activate(V1)) 1136.84/297.06 , U12(tt(), V1) -> U13(isNatList(activate(V1))) 1136.84/297.06 , U111(tt(), L, N) -> 1136.84/297.06 U112(isNatIListKind(activate(L)), activate(L), activate(N)) 1136.84/297.06 , U112(tt(), L, N) -> 1136.84/297.06 U113(isNat(activate(N)), activate(L), activate(N)) 1136.84/297.06 , U113(tt(), L, N) -> U114(isNatKind(activate(N)), activate(L)) 1136.84/297.06 , U114(tt(), L) -> s(length(activate(L))) 1136.84/297.06 , s(X) -> n__s(X) 1136.84/297.06 , length(X) -> n__length(X) 1136.84/297.06 , length(cons(N, L)) -> 1136.84/297.06 U111(isNatList(activate(L)), activate(L), N) 1136.84/297.06 , length(nil()) -> 0() 1136.84/297.06 , U13(tt()) -> tt() 1136.84/297.06 , isNatList(n__take(V1, V2)) -> 1136.84/297.06 U101(isNatKind(activate(V1)), activate(V1), activate(V2)) 1136.84/297.06 , isNatList(n__cons(V1, V2)) -> 1136.84/297.06 U91(isNatKind(activate(V1)), activate(V1), activate(V2)) 1136.84/297.06 , isNatList(n__nil()) -> tt() 1136.84/297.06 , U121(tt(), IL) -> U122(isNatIListKind(activate(IL))) 1136.84/297.06 , U122(tt()) -> nil() 1136.84/297.06 , nil() -> n__nil() 1136.84/297.06 , U131(tt(), IL, M, N) -> 1136.84/297.06 U132(isNatIListKind(activate(IL)), 1136.84/297.06 activate(IL), 1136.84/297.06 activate(M), 1136.84/297.06 activate(N)) 1136.84/297.06 , U132(tt(), IL, M, N) -> 1136.84/297.06 U133(isNat(activate(M)), activate(IL), activate(M), activate(N)) 1136.84/297.06 , U133(tt(), IL, M, N) -> 1136.84/297.06 U134(isNatKind(activate(M)), 1136.84/297.06 activate(IL), 1136.84/297.06 activate(M), 1136.84/297.06 activate(N)) 1136.84/297.06 , U134(tt(), IL, M, N) -> 1136.84/297.06 U135(isNat(activate(N)), activate(IL), activate(M), activate(N)) 1136.84/297.06 , U135(tt(), IL, M, N) -> 1136.84/297.06 U136(isNatKind(activate(N)), 1136.84/297.06 activate(IL), 1136.84/297.06 activate(M), 1136.84/297.06 activate(N)) 1136.84/297.06 , U136(tt(), IL, M, N) -> 1136.84/297.06 cons(activate(N), n__take(activate(M), activate(IL))) 1136.84/297.06 , U21(tt(), V1) -> U22(isNatKind(activate(V1)), activate(V1)) 1136.84/297.06 , U22(tt(), V1) -> U23(isNat(activate(V1))) 1136.84/297.06 , U23(tt()) -> tt() 1136.84/297.06 , U31(tt(), V) -> U32(isNatIListKind(activate(V)), activate(V)) 1136.84/297.06 , U32(tt(), V) -> U33(isNatList(activate(V))) 1136.84/297.06 , U33(tt()) -> tt() 1136.84/297.06 , U41(tt(), V1, V2) -> 1136.84/297.06 U42(isNatKind(activate(V1)), activate(V1), activate(V2)) 1136.84/297.06 , U42(tt(), V1, V2) -> 1136.84/297.06 U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 1136.84/297.06 , U43(tt(), V1, V2) -> 1136.84/297.06 U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 1136.84/297.06 , U44(tt(), V1, V2) -> U45(isNat(activate(V1)), activate(V2)) 1136.84/297.06 , U45(tt(), V2) -> U46(isNatIList(activate(V2))) 1136.84/297.06 , U46(tt()) -> tt() 1136.84/297.06 , U51(tt(), V2) -> U52(isNatIListKind(activate(V2))) 1136.84/297.06 , U52(tt()) -> tt() 1136.84/297.06 , U61(tt(), V2) -> U62(isNatIListKind(activate(V2))) 1136.84/297.06 , U62(tt()) -> tt() 1136.84/297.06 , U71(tt()) -> tt() 1136.84/297.06 , U81(tt()) -> tt() 1136.84/297.06 , U91(tt(), V1, V2) -> 1136.84/297.06 U92(isNatKind(activate(V1)), activate(V1), activate(V2)) 1136.84/297.06 , U92(tt(), V1, V2) -> 1136.84/297.06 U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 1136.84/297.06 , U93(tt(), V1, V2) -> 1136.84/297.06 U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 1136.84/297.06 , U94(tt(), V1, V2) -> U95(isNat(activate(V1)), activate(V2)) 1136.84/297.06 , U95(tt(), V2) -> U96(isNatList(activate(V2))) 1136.84/297.06 , U96(tt()) -> tt() 1136.84/297.06 , take(X1, X2) -> n__take(X1, X2) 1136.84/297.06 , take(0(), IL) -> U121(isNatIList(IL), IL) 1136.84/297.06 , take(s(M), cons(N, IL)) -> 1136.84/297.06 U131(isNatIList(activate(IL)), activate(IL), M, N) } 1136.84/297.06 Obligation: 1136.84/297.06 innermost runtime complexity 1136.84/297.06 Answer: 1136.84/297.06 MAYBE 1136.84/297.06 1136.84/297.06 Arguments of following rules are not normal-forms: 1136.84/297.06 1136.84/297.06 { length(cons(N, L)) -> 1136.84/297.06 U111(isNatList(activate(L)), activate(L), N) 1136.84/297.06 , length(nil()) -> 0() 1136.84/297.06 , take(0(), IL) -> U121(isNatIList(IL), IL) 1136.84/297.06 , take(s(M), cons(N, IL)) -> 1136.84/297.06 U131(isNatIList(activate(IL)), activate(IL), M, N) } 1136.84/297.06 1136.84/297.06 All above mentioned rules can be savely removed. 1136.84/297.06 1136.84/297.06 We are left with following problem, upon which TcT provides the 1136.84/297.06 certificate MAYBE. 1136.84/297.06 1136.84/297.06 Strict Trs: 1136.84/297.06 { zeros() -> cons(0(), n__zeros()) 1136.84/297.06 , zeros() -> n__zeros() 1136.84/297.06 , cons(X1, X2) -> n__cons(X1, X2) 1136.84/297.06 , 0() -> n__0() 1136.84/297.06 , U101(tt(), V1, V2) -> 1136.84/297.06 U102(isNatKind(activate(V1)), activate(V1), activate(V2)) 1136.84/297.06 , U102(tt(), V1, V2) -> 1136.84/297.06 U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 1136.84/297.06 , isNatKind(n__0()) -> tt() 1136.84/297.06 , isNatKind(n__length(V1)) -> U71(isNatIListKind(activate(V1))) 1136.84/297.06 , isNatKind(n__s(V1)) -> U81(isNatKind(activate(V1))) 1136.84/297.06 , activate(X) -> X 1136.84/297.06 , activate(n__zeros()) -> zeros() 1136.84/297.06 , activate(n__take(X1, X2)) -> take(X1, X2) 1136.84/297.06 , activate(n__0()) -> 0() 1136.84/297.06 , activate(n__length(X)) -> length(X) 1136.84/297.06 , activate(n__s(X)) -> s(X) 1136.84/297.06 , activate(n__cons(X1, X2)) -> cons(X1, X2) 1136.84/297.06 , activate(n__nil()) -> nil() 1136.84/297.06 , U103(tt(), V1, V2) -> 1136.84/297.06 U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 1136.84/297.06 , isNatIListKind(n__zeros()) -> tt() 1136.84/297.06 , isNatIListKind(n__take(V1, V2)) -> 1136.84/297.06 U61(isNatKind(activate(V1)), activate(V2)) 1136.84/297.06 , isNatIListKind(n__cons(V1, V2)) -> 1136.84/297.06 U51(isNatKind(activate(V1)), activate(V2)) 1136.84/297.06 , isNatIListKind(n__nil()) -> tt() 1136.84/297.06 , U104(tt(), V1, V2) -> U105(isNat(activate(V1)), activate(V2)) 1136.84/297.06 , U105(tt(), V2) -> U106(isNatIList(activate(V2))) 1136.84/297.06 , isNat(n__0()) -> tt() 1136.84/297.06 , isNat(n__length(V1)) -> 1136.84/297.06 U11(isNatIListKind(activate(V1)), activate(V1)) 1136.84/297.06 , isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) 1136.84/297.06 , U106(tt()) -> tt() 1136.84/297.06 , isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)) 1136.84/297.06 , isNatIList(n__zeros()) -> tt() 1136.84/297.06 , isNatIList(n__cons(V1, V2)) -> 1136.84/297.06 U41(isNatKind(activate(V1)), activate(V1), activate(V2)) 1136.84/297.06 , U11(tt(), V1) -> U12(isNatIListKind(activate(V1)), activate(V1)) 1136.84/297.06 , U12(tt(), V1) -> U13(isNatList(activate(V1))) 1136.84/297.06 , U111(tt(), L, N) -> 1136.84/297.06 U112(isNatIListKind(activate(L)), activate(L), activate(N)) 1136.84/297.06 , U112(tt(), L, N) -> 1136.84/297.06 U113(isNat(activate(N)), activate(L), activate(N)) 1136.84/297.06 , U113(tt(), L, N) -> U114(isNatKind(activate(N)), activate(L)) 1136.84/297.06 , U114(tt(), L) -> s(length(activate(L))) 1136.84/297.06 , s(X) -> n__s(X) 1136.84/297.06 , length(X) -> n__length(X) 1136.84/297.06 , U13(tt()) -> tt() 1136.84/297.06 , isNatList(n__take(V1, V2)) -> 1136.84/297.06 U101(isNatKind(activate(V1)), activate(V1), activate(V2)) 1136.84/297.06 , isNatList(n__cons(V1, V2)) -> 1136.84/297.06 U91(isNatKind(activate(V1)), activate(V1), activate(V2)) 1136.84/297.06 , isNatList(n__nil()) -> tt() 1136.84/297.06 , U121(tt(), IL) -> U122(isNatIListKind(activate(IL))) 1136.84/297.06 , U122(tt()) -> nil() 1136.84/297.06 , nil() -> n__nil() 1136.84/297.06 , U131(tt(), IL, M, N) -> 1136.84/297.06 U132(isNatIListKind(activate(IL)), 1136.84/297.06 activate(IL), 1136.84/297.06 activate(M), 1136.84/297.06 activate(N)) 1136.84/297.06 , U132(tt(), IL, M, N) -> 1136.84/297.06 U133(isNat(activate(M)), activate(IL), activate(M), activate(N)) 1136.84/297.06 , U133(tt(), IL, M, N) -> 1136.84/297.06 U134(isNatKind(activate(M)), 1136.84/297.06 activate(IL), 1136.84/297.06 activate(M), 1136.84/297.06 activate(N)) 1136.84/297.06 , U134(tt(), IL, M, N) -> 1136.84/297.06 U135(isNat(activate(N)), activate(IL), activate(M), activate(N)) 1136.84/297.06 , U135(tt(), IL, M, N) -> 1136.84/297.06 U136(isNatKind(activate(N)), 1136.84/297.06 activate(IL), 1136.84/297.06 activate(M), 1136.84/297.06 activate(N)) 1136.84/297.06 , U136(tt(), IL, M, N) -> 1136.84/297.06 cons(activate(N), n__take(activate(M), activate(IL))) 1136.84/297.06 , U21(tt(), V1) -> U22(isNatKind(activate(V1)), activate(V1)) 1136.84/297.06 , U22(tt(), V1) -> U23(isNat(activate(V1))) 1136.84/297.06 , U23(tt()) -> tt() 1136.84/297.06 , U31(tt(), V) -> U32(isNatIListKind(activate(V)), activate(V)) 1136.84/297.06 , U32(tt(), V) -> U33(isNatList(activate(V))) 1136.84/297.06 , U33(tt()) -> tt() 1136.84/297.06 , U41(tt(), V1, V2) -> 1136.84/297.06 U42(isNatKind(activate(V1)), activate(V1), activate(V2)) 1136.84/297.06 , U42(tt(), V1, V2) -> 1136.84/297.06 U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 1136.84/297.06 , U43(tt(), V1, V2) -> 1136.84/297.06 U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 1136.84/297.06 , U44(tt(), V1, V2) -> U45(isNat(activate(V1)), activate(V2)) 1136.84/297.06 , U45(tt(), V2) -> U46(isNatIList(activate(V2))) 1136.84/297.06 , U46(tt()) -> tt() 1136.84/297.06 , U51(tt(), V2) -> U52(isNatIListKind(activate(V2))) 1136.84/297.06 , U52(tt()) -> tt() 1136.84/297.06 , U61(tt(), V2) -> U62(isNatIListKind(activate(V2))) 1136.84/297.06 , U62(tt()) -> tt() 1136.84/297.06 , U71(tt()) -> tt() 1136.84/297.06 , U81(tt()) -> tt() 1136.84/297.06 , U91(tt(), V1, V2) -> 1136.84/297.06 U92(isNatKind(activate(V1)), activate(V1), activate(V2)) 1136.84/297.06 , U92(tt(), V1, V2) -> 1136.84/297.06 U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 1136.84/297.06 , U93(tt(), V1, V2) -> 1136.84/297.06 U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 1136.84/297.06 , U94(tt(), V1, V2) -> U95(isNat(activate(V1)), activate(V2)) 1136.84/297.06 , U95(tt(), V2) -> U96(isNatList(activate(V2))) 1136.84/297.06 , U96(tt()) -> tt() 1136.84/297.06 , take(X1, X2) -> n__take(X1, X2) } 1136.84/297.06 Obligation: 1136.84/297.06 innermost runtime complexity 1136.84/297.06 Answer: 1136.84/297.06 MAYBE 1136.84/297.06 1136.84/297.06 None of the processors succeeded. 1136.84/297.06 1136.84/297.06 Details of failed attempt(s): 1136.84/297.06 ----------------------------- 1136.84/297.06 1) 'empty' failed due to the following reason: 1136.84/297.06 1136.84/297.06 Empty strict component of the problem is NOT empty. 1136.84/297.06 1136.84/297.06 2) 'Best' failed due to the following reason: 1136.84/297.06 1136.84/297.06 None of the processors succeeded. 1136.84/297.06 1136.84/297.06 Details of failed attempt(s): 1136.84/297.06 ----------------------------- 1136.84/297.06 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1136.84/297.06 following reason: 1136.84/297.06 1136.84/297.06 Computation stopped due to timeout after 297.0 seconds. 1136.84/297.06 1136.84/297.06 2) 'Best' failed due to the following reason: 1136.84/297.06 1136.84/297.06 None of the processors succeeded. 1136.84/297.06 1136.84/297.06 Details of failed attempt(s): 1136.84/297.06 ----------------------------- 1136.84/297.06 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1136.84/297.06 seconds)' failed due to the following reason: 1136.84/297.06 1136.84/297.06 Computation stopped due to timeout after 148.0 seconds. 1136.84/297.06 1136.84/297.06 2) 'Best' failed due to the following reason: 1136.84/297.06 1136.84/297.06 None of the processors succeeded. 1136.84/297.06 1136.84/297.06 Details of failed attempt(s): 1136.84/297.06 ----------------------------- 1136.84/297.06 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1136.84/297.06 to the following reason: 1136.84/297.06 1136.84/297.06 The input cannot be shown compatible 1136.84/297.06 1136.84/297.06 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1136.84/297.06 following reason: 1136.84/297.06 1136.84/297.06 The input cannot be shown compatible 1136.84/297.06 1136.84/297.06 1136.84/297.06 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1136.84/297.06 failed due to the following reason: 1136.84/297.06 1136.84/297.06 None of the processors succeeded. 1136.84/297.06 1136.84/297.06 Details of failed attempt(s): 1136.84/297.06 ----------------------------- 1136.84/297.06 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1136.84/297.06 failed due to the following reason: 1136.84/297.06 1136.84/297.06 match-boundness of the problem could not be verified. 1136.84/297.06 1136.84/297.06 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1136.84/297.06 failed due to the following reason: 1136.84/297.06 1136.84/297.06 match-boundness of the problem could not be verified. 1136.84/297.06 1136.84/297.06 1136.84/297.06 1136.84/297.06 1136.84/297.06 1136.84/297.06 Arrrr.. 1137.10/297.11 EOF