MAYBE 1069.50/297.07 MAYBE 1069.50/297.07 1069.50/297.07 We are left with following problem, upon which TcT provides the 1069.50/297.07 certificate MAYBE. 1069.50/297.07 1069.50/297.07 Strict Trs: 1069.50/297.07 { a__zeros() -> cons(0(), zeros()) 1069.50/297.07 , a__zeros() -> zeros() 1069.50/297.07 , a__U11(X1, X2) -> U11(X1, X2) 1069.50/297.07 , a__U11(tt(), V1) -> a__U12(a__isNatIListKind(V1), V1) 1069.50/297.07 , a__U12(X1, X2) -> U12(X1, X2) 1069.50/297.07 , a__U12(tt(), V1) -> a__U13(a__isNatList(V1)) 1069.50/297.07 , a__isNatIListKind(X) -> isNatIListKind(X) 1069.50/297.07 , a__isNatIListKind(cons(V1, V2)) -> a__U51(a__isNatKind(V1), V2) 1069.50/297.07 , a__isNatIListKind(zeros()) -> tt() 1069.50/297.07 , a__isNatIListKind(nil()) -> tt() 1069.50/297.07 , a__U13(X) -> U13(X) 1069.50/297.07 , a__U13(tt()) -> tt() 1069.50/297.07 , a__isNatList(X) -> isNatList(X) 1069.50/297.07 , a__isNatList(cons(V1, V2)) -> a__U81(a__isNatKind(V1), V1, V2) 1069.50/297.07 , a__isNatList(nil()) -> tt() 1069.50/297.07 , a__U21(X1, X2) -> U21(X1, X2) 1069.50/297.07 , a__U21(tt(), V1) -> a__U22(a__isNatKind(V1), V1) 1069.50/297.07 , a__U22(X1, X2) -> U22(X1, X2) 1069.50/297.07 , a__U22(tt(), V1) -> a__U23(a__isNat(V1)) 1069.50/297.07 , a__isNatKind(X) -> isNatKind(X) 1069.50/297.07 , a__isNatKind(0()) -> tt() 1069.50/297.07 , a__isNatKind(s(V1)) -> a__U71(a__isNatKind(V1)) 1069.50/297.07 , a__isNatKind(length(V1)) -> a__U61(a__isNatIListKind(V1)) 1069.50/297.07 , a__U23(X) -> U23(X) 1069.50/297.07 , a__U23(tt()) -> tt() 1069.50/297.07 , a__isNat(X) -> isNat(X) 1069.50/297.07 , a__isNat(0()) -> tt() 1069.50/297.07 , a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) 1069.50/297.07 , a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1) 1069.50/297.07 , a__U31(X1, X2) -> U31(X1, X2) 1069.50/297.07 , a__U31(tt(), V) -> a__U32(a__isNatIListKind(V), V) 1069.50/297.07 , a__U32(X1, X2) -> U32(X1, X2) 1069.50/297.07 , a__U32(tt(), V) -> a__U33(a__isNatList(V)) 1069.50/297.07 , a__U33(X) -> U33(X) 1069.50/297.07 , a__U33(tt()) -> tt() 1069.50/297.07 , a__U41(X1, X2, X3) -> U41(X1, X2, X3) 1069.50/297.07 , a__U41(tt(), V1, V2) -> a__U42(a__isNatKind(V1), V1, V2) 1069.50/297.07 , a__U42(X1, X2, X3) -> U42(X1, X2, X3) 1069.50/297.07 , a__U42(tt(), V1, V2) -> a__U43(a__isNatIListKind(V2), V1, V2) 1069.50/297.07 , a__U43(X1, X2, X3) -> U43(X1, X2, X3) 1069.50/297.07 , a__U43(tt(), V1, V2) -> a__U44(a__isNatIListKind(V2), V1, V2) 1069.50/297.07 , a__U44(X1, X2, X3) -> U44(X1, X2, X3) 1069.50/297.07 , a__U44(tt(), V1, V2) -> a__U45(a__isNat(V1), V2) 1069.50/297.07 , a__U45(X1, X2) -> U45(X1, X2) 1069.50/297.07 , a__U45(tt(), V2) -> a__U46(a__isNatIList(V2)) 1069.50/297.07 , a__U46(X) -> U46(X) 1069.50/297.07 , a__U46(tt()) -> tt() 1069.50/297.07 , a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V) 1069.50/297.07 , a__isNatIList(X) -> isNatIList(X) 1069.50/297.07 , a__isNatIList(cons(V1, V2)) -> a__U41(a__isNatKind(V1), V1, V2) 1069.50/297.07 , a__isNatIList(zeros()) -> tt() 1069.50/297.07 , a__U51(X1, X2) -> U51(X1, X2) 1069.50/297.07 , a__U51(tt(), V2) -> a__U52(a__isNatIListKind(V2)) 1069.50/297.07 , a__U52(X) -> U52(X) 1069.50/297.07 , a__U52(tt()) -> tt() 1069.50/297.07 , a__U61(X) -> U61(X) 1069.50/297.07 , a__U61(tt()) -> tt() 1069.50/297.07 , a__U71(X) -> U71(X) 1069.50/297.07 , a__U71(tt()) -> tt() 1069.50/297.07 , a__U81(X1, X2, X3) -> U81(X1, X2, X3) 1069.50/297.07 , a__U81(tt(), V1, V2) -> a__U82(a__isNatKind(V1), V1, V2) 1069.50/297.07 , a__U82(X1, X2, X3) -> U82(X1, X2, X3) 1069.50/297.07 , a__U82(tt(), V1, V2) -> a__U83(a__isNatIListKind(V2), V1, V2) 1069.50/297.07 , a__U83(X1, X2, X3) -> U83(X1, X2, X3) 1069.50/297.07 , a__U83(tt(), V1, V2) -> a__U84(a__isNatIListKind(V2), V1, V2) 1069.50/297.07 , a__U84(X1, X2, X3) -> U84(X1, X2, X3) 1069.50/297.07 , a__U84(tt(), V1, V2) -> a__U85(a__isNat(V1), V2) 1069.50/297.07 , a__U85(X1, X2) -> U85(X1, X2) 1069.50/297.07 , a__U85(tt(), V2) -> a__U86(a__isNatList(V2)) 1069.50/297.07 , a__U86(X) -> U86(X) 1069.50/297.07 , a__U86(tt()) -> tt() 1069.50/297.07 , a__U91(X1, X2, X3) -> U91(X1, X2, X3) 1069.50/297.07 , a__U91(tt(), L, N) -> a__U92(a__isNatIListKind(L), L, N) 1069.50/297.07 , a__U92(X1, X2, X3) -> U92(X1, X2, X3) 1069.50/297.07 , a__U92(tt(), L, N) -> a__U93(a__isNat(N), L, N) 1069.50/297.07 , a__U93(X1, X2, X3) -> U93(X1, X2, X3) 1069.50/297.07 , a__U93(tt(), L, N) -> a__U94(a__isNatKind(N), L) 1069.50/297.07 , a__U94(X1, X2) -> U94(X1, X2) 1069.50/297.07 , a__U94(tt(), L) -> s(a__length(mark(L))) 1069.50/297.07 , a__length(X) -> length(X) 1069.50/297.07 , a__length(cons(N, L)) -> a__U91(a__isNatList(L), L, N) 1069.50/297.07 , a__length(nil()) -> 0() 1069.50/297.07 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 1069.50/297.07 , mark(0()) -> 0() 1069.50/297.07 , mark(zeros()) -> a__zeros() 1069.50/297.07 , mark(tt()) -> tt() 1069.50/297.07 , mark(s(X)) -> s(mark(X)) 1069.50/297.07 , mark(length(X)) -> a__length(mark(X)) 1069.50/297.07 , mark(nil()) -> nil() 1069.50/297.07 , mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 1069.50/297.07 , mark(U12(X1, X2)) -> a__U12(mark(X1), X2) 1069.50/297.07 , mark(isNatIListKind(X)) -> a__isNatIListKind(X) 1069.50/297.07 , mark(U13(X)) -> a__U13(mark(X)) 1069.50/297.07 , mark(isNatList(X)) -> a__isNatList(X) 1069.50/297.07 , mark(U21(X1, X2)) -> a__U21(mark(X1), X2) 1069.50/297.07 , mark(U22(X1, X2)) -> a__U22(mark(X1), X2) 1069.50/297.07 , mark(isNatKind(X)) -> a__isNatKind(X) 1069.50/297.07 , mark(U23(X)) -> a__U23(mark(X)) 1069.50/297.07 , mark(isNat(X)) -> a__isNat(X) 1069.50/297.07 , mark(U31(X1, X2)) -> a__U31(mark(X1), X2) 1069.50/297.07 , mark(U32(X1, X2)) -> a__U32(mark(X1), X2) 1069.50/297.07 , mark(U33(X)) -> a__U33(mark(X)) 1069.50/297.07 , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) 1069.50/297.07 , mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3) 1069.50/297.07 , mark(U43(X1, X2, X3)) -> a__U43(mark(X1), X2, X3) 1069.50/297.07 , mark(U44(X1, X2, X3)) -> a__U44(mark(X1), X2, X3) 1069.50/297.07 , mark(U45(X1, X2)) -> a__U45(mark(X1), X2) 1069.50/297.07 , mark(U46(X)) -> a__U46(mark(X)) 1069.50/297.07 , mark(isNatIList(X)) -> a__isNatIList(X) 1069.50/297.07 , mark(U51(X1, X2)) -> a__U51(mark(X1), X2) 1069.50/297.07 , mark(U52(X)) -> a__U52(mark(X)) 1069.50/297.07 , mark(U61(X)) -> a__U61(mark(X)) 1069.50/297.07 , mark(U71(X)) -> a__U71(mark(X)) 1069.50/297.07 , mark(U81(X1, X2, X3)) -> a__U81(mark(X1), X2, X3) 1069.50/297.07 , mark(U82(X1, X2, X3)) -> a__U82(mark(X1), X2, X3) 1069.50/297.07 , mark(U83(X1, X2, X3)) -> a__U83(mark(X1), X2, X3) 1069.50/297.07 , mark(U84(X1, X2, X3)) -> a__U84(mark(X1), X2, X3) 1069.50/297.07 , mark(U85(X1, X2)) -> a__U85(mark(X1), X2) 1069.50/297.07 , mark(U86(X)) -> a__U86(mark(X)) 1069.50/297.07 , mark(U91(X1, X2, X3)) -> a__U91(mark(X1), X2, X3) 1069.50/297.07 , mark(U92(X1, X2, X3)) -> a__U92(mark(X1), X2, X3) 1069.50/297.07 , mark(U93(X1, X2, X3)) -> a__U93(mark(X1), X2, X3) 1069.50/297.07 , mark(U94(X1, X2)) -> a__U94(mark(X1), X2) } 1069.50/297.07 Obligation: 1069.50/297.07 innermost runtime complexity 1069.50/297.07 Answer: 1069.50/297.07 MAYBE 1069.50/297.07 1069.50/297.07 None of the processors succeeded. 1069.50/297.07 1069.50/297.07 Details of failed attempt(s): 1069.50/297.07 ----------------------------- 1069.50/297.07 1) 'empty' failed due to the following reason: 1069.50/297.07 1069.50/297.07 Empty strict component of the problem is NOT empty. 1069.50/297.07 1069.50/297.07 2) 'Best' failed due to the following reason: 1069.50/297.07 1069.50/297.07 None of the processors succeeded. 1069.50/297.07 1069.50/297.07 Details of failed attempt(s): 1069.50/297.07 ----------------------------- 1069.50/297.07 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1069.50/297.07 following reason: 1069.50/297.07 1069.50/297.07 Computation stopped due to timeout after 297.0 seconds. 1069.50/297.07 1069.50/297.07 2) 'Best' failed due to the following reason: 1069.50/297.07 1069.50/297.07 None of the processors succeeded. 1069.50/297.07 1069.50/297.07 Details of failed attempt(s): 1069.50/297.07 ----------------------------- 1069.50/297.07 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1069.50/297.07 seconds)' failed due to the following reason: 1069.50/297.07 1069.50/297.07 Computation stopped due to timeout after 148.0 seconds. 1069.50/297.07 1069.50/297.07 2) 'Best' failed due to the following reason: 1069.50/297.07 1069.50/297.07 None of the processors succeeded. 1069.50/297.07 1069.50/297.07 Details of failed attempt(s): 1069.50/297.07 ----------------------------- 1069.50/297.07 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1069.50/297.07 following reason: 1069.50/297.07 1069.50/297.07 The input cannot be shown compatible 1069.50/297.07 1069.50/297.07 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1069.50/297.07 to the following reason: 1069.50/297.07 1069.50/297.07 The input cannot be shown compatible 1069.50/297.07 1069.50/297.07 1069.50/297.07 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1069.50/297.07 failed due to the following reason: 1069.50/297.07 1069.50/297.07 None of the processors succeeded. 1069.50/297.07 1069.50/297.07 Details of failed attempt(s): 1069.50/297.07 ----------------------------- 1069.50/297.07 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1069.50/297.07 failed due to the following reason: 1069.50/297.07 1069.50/297.07 match-boundness of the problem could not be verified. 1069.50/297.07 1069.50/297.07 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1069.50/297.07 failed due to the following reason: 1069.50/297.07 1069.50/297.07 match-boundness of the problem could not be verified. 1069.50/297.07 1069.50/297.07 1069.50/297.07 1069.50/297.07 1069.50/297.07 1069.50/297.07 Arrrr.. 1070.03/297.41 EOF