MAYBE 1061.12/297.10 MAYBE 1061.12/297.10 1061.12/297.10 We are left with following problem, upon which TcT provides the 1061.12/297.10 certificate MAYBE. 1061.12/297.10 1061.12/297.10 Strict Trs: 1061.12/297.10 { active(zeros()) -> mark(cons(0(), zeros())) 1061.12/297.10 , active(cons(X1, X2)) -> cons(active(X1), X2) 1061.12/297.10 , active(U11(X1, X2)) -> U11(active(X1), X2) 1061.12/297.10 , active(U11(tt(), V1)) -> mark(U12(isNatList(V1))) 1061.12/297.10 , active(U12(X)) -> U12(active(X)) 1061.12/297.10 , active(U12(tt())) -> mark(tt()) 1061.12/297.10 , active(isNatList(cons(V1, V2))) -> 1061.12/297.10 mark(U51(and(isNatKind(V1), isNatIListKind(V2)), V1, V2)) 1061.12/297.10 , active(isNatList(nil())) -> mark(tt()) 1061.12/297.10 , active(isNatList(take(V1, V2))) -> 1061.12/297.10 mark(U61(and(isNatKind(V1), isNatIListKind(V2)), V1, V2)) 1061.12/297.10 , active(U21(X1, X2)) -> U21(active(X1), X2) 1061.12/297.10 , active(U21(tt(), V1)) -> mark(U22(isNat(V1))) 1061.12/297.10 , active(U22(X)) -> U22(active(X)) 1061.12/297.10 , active(U22(tt())) -> mark(tt()) 1061.12/297.10 , active(isNat(0())) -> mark(tt()) 1061.12/297.10 , active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)) 1061.12/297.10 , active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1), V1)) 1061.12/297.10 , active(U31(X1, X2)) -> U31(active(X1), X2) 1061.12/297.10 , active(U31(tt(), V)) -> mark(U32(isNatList(V))) 1061.12/297.10 , active(U32(X)) -> U32(active(X)) 1061.12/297.10 , active(U32(tt())) -> mark(tt()) 1061.12/297.10 , active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 1061.12/297.10 , active(U41(tt(), V1, V2)) -> mark(U42(isNat(V1), V2)) 1061.12/297.10 , active(U42(X1, X2)) -> U42(active(X1), X2) 1061.12/297.10 , active(U42(tt(), V2)) -> mark(U43(isNatIList(V2))) 1061.12/297.10 , active(U43(X)) -> U43(active(X)) 1061.12/297.10 , active(U43(tt())) -> mark(tt()) 1061.12/297.10 , active(isNatIList(V)) -> mark(U31(isNatIListKind(V), V)) 1061.12/297.10 , active(isNatIList(zeros())) -> mark(tt()) 1061.12/297.10 , active(isNatIList(cons(V1, V2))) -> 1061.12/297.10 mark(U41(and(isNatKind(V1), isNatIListKind(V2)), V1, V2)) 1061.12/297.10 , active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 1061.12/297.10 , active(U51(tt(), V1, V2)) -> mark(U52(isNat(V1), V2)) 1061.12/297.10 , active(U52(X1, X2)) -> U52(active(X1), X2) 1061.12/297.10 , active(U52(tt(), V2)) -> mark(U53(isNatList(V2))) 1061.12/297.10 , active(U53(X)) -> U53(active(X)) 1061.12/297.10 , active(U53(tt())) -> mark(tt()) 1061.12/297.10 , active(U61(X1, X2, X3)) -> U61(active(X1), X2, X3) 1061.12/297.10 , active(U61(tt(), V1, V2)) -> mark(U62(isNat(V1), V2)) 1061.12/297.10 , active(U62(X1, X2)) -> U62(active(X1), X2) 1061.12/297.10 , active(U62(tt(), V2)) -> mark(U63(isNatIList(V2))) 1061.12/297.10 , active(U63(X)) -> U63(active(X)) 1061.12/297.10 , active(U63(tt())) -> mark(tt()) 1061.12/297.10 , active(U71(X1, X2)) -> U71(active(X1), X2) 1061.12/297.10 , active(U71(tt(), L)) -> mark(s(length(L))) 1061.12/297.10 , active(s(X)) -> s(active(X)) 1061.12/297.10 , active(length(X)) -> length(active(X)) 1061.12/297.10 , active(length(cons(N, L))) -> 1061.12/297.10 mark(U71(and(and(isNatList(L), isNatIListKind(L)), 1061.12/297.10 and(isNat(N), isNatKind(N))), 1061.12/297.10 L)) 1061.12/297.10 , active(length(nil())) -> mark(0()) 1061.12/297.10 , active(U81(X)) -> U81(active(X)) 1061.12/297.10 , active(U81(tt())) -> mark(nil()) 1061.12/297.10 , active(U91(X1, X2, X3, X4)) -> U91(active(X1), X2, X3, X4) 1061.12/297.10 , active(U91(tt(), IL, M, N)) -> mark(cons(N, take(M, IL))) 1061.12/297.10 , active(take(X1, X2)) -> take(X1, active(X2)) 1061.12/297.10 , active(take(X1, X2)) -> take(active(X1), X2) 1061.12/297.10 , active(take(0(), IL)) -> 1061.12/297.10 mark(U81(and(isNatIList(IL), isNatIListKind(IL)))) 1061.12/297.10 , active(take(s(M), cons(N, IL))) -> 1061.12/297.10 mark(U91(and(and(isNatIList(IL), isNatIListKind(IL)), 1061.12/297.10 and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), 1061.12/297.10 IL, 1061.12/297.10 M, 1061.12/297.10 N)) 1061.12/297.10 , active(and(X1, X2)) -> and(active(X1), X2) 1061.12/297.10 , active(and(tt(), X)) -> mark(X) 1061.12/297.10 , active(isNatIListKind(zeros())) -> mark(tt()) 1061.12/297.10 , active(isNatIListKind(cons(V1, V2))) -> 1061.12/297.10 mark(and(isNatKind(V1), isNatIListKind(V2))) 1061.12/297.10 , active(isNatIListKind(nil())) -> mark(tt()) 1061.12/297.10 , active(isNatIListKind(take(V1, V2))) -> 1061.12/297.10 mark(and(isNatKind(V1), isNatIListKind(V2))) 1061.12/297.10 , active(isNatKind(0())) -> mark(tt()) 1061.12/297.10 , active(isNatKind(s(V1))) -> mark(isNatKind(V1)) 1061.12/297.10 , active(isNatKind(length(V1))) -> mark(isNatIListKind(V1)) 1061.12/297.10 , cons(mark(X1), X2) -> mark(cons(X1, X2)) 1061.12/297.10 , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 1061.12/297.10 , U11(mark(X1), X2) -> mark(U11(X1, X2)) 1061.12/297.10 , U11(ok(X1), ok(X2)) -> ok(U11(X1, X2)) 1061.12/297.10 , U12(mark(X)) -> mark(U12(X)) 1061.12/297.10 , U12(ok(X)) -> ok(U12(X)) 1061.12/297.10 , isNatList(ok(X)) -> ok(isNatList(X)) 1061.12/297.10 , U21(mark(X1), X2) -> mark(U21(X1, X2)) 1061.12/297.10 , U21(ok(X1), ok(X2)) -> ok(U21(X1, X2)) 1061.12/297.10 , U22(mark(X)) -> mark(U22(X)) 1061.12/297.10 , U22(ok(X)) -> ok(U22(X)) 1061.12/297.10 , isNat(ok(X)) -> ok(isNat(X)) 1061.12/297.10 , U31(mark(X1), X2) -> mark(U31(X1, X2)) 1061.12/297.10 , U31(ok(X1), ok(X2)) -> ok(U31(X1, X2)) 1061.12/297.10 , U32(mark(X)) -> mark(U32(X)) 1061.12/297.10 , U32(ok(X)) -> ok(U32(X)) 1061.12/297.10 , U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 1061.12/297.10 , U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 1061.12/297.10 , U42(mark(X1), X2) -> mark(U42(X1, X2)) 1061.12/297.10 , U42(ok(X1), ok(X2)) -> ok(U42(X1, X2)) 1061.12/297.10 , U43(mark(X)) -> mark(U43(X)) 1061.12/297.10 , U43(ok(X)) -> ok(U43(X)) 1061.12/297.10 , isNatIList(ok(X)) -> ok(isNatIList(X)) 1061.12/297.10 , U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 1061.12/297.10 , U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 1061.12/297.10 , U52(mark(X1), X2) -> mark(U52(X1, X2)) 1061.12/297.10 , U52(ok(X1), ok(X2)) -> ok(U52(X1, X2)) 1061.12/297.10 , U53(mark(X)) -> mark(U53(X)) 1061.12/297.10 , U53(ok(X)) -> ok(U53(X)) 1061.12/297.10 , U61(mark(X1), X2, X3) -> mark(U61(X1, X2, X3)) 1061.12/297.10 , U61(ok(X1), ok(X2), ok(X3)) -> ok(U61(X1, X2, X3)) 1061.12/297.10 , U62(mark(X1), X2) -> mark(U62(X1, X2)) 1061.12/297.10 , U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 1061.12/297.10 , U63(mark(X)) -> mark(U63(X)) 1061.12/297.10 , U63(ok(X)) -> ok(U63(X)) 1061.12/297.10 , U71(mark(X1), X2) -> mark(U71(X1, X2)) 1061.12/297.10 , U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 1061.12/297.10 , s(mark(X)) -> mark(s(X)) 1061.12/297.10 , s(ok(X)) -> ok(s(X)) 1061.12/297.10 , length(mark(X)) -> mark(length(X)) 1061.12/297.10 , length(ok(X)) -> ok(length(X)) 1061.12/297.10 , U81(mark(X)) -> mark(U81(X)) 1061.12/297.10 , U81(ok(X)) -> ok(U81(X)) 1061.12/297.10 , U91(mark(X1), X2, X3, X4) -> mark(U91(X1, X2, X3, X4)) 1061.12/297.10 , U91(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U91(X1, X2, X3, X4)) 1061.12/297.10 , take(X1, mark(X2)) -> mark(take(X1, X2)) 1061.12/297.10 , take(mark(X1), X2) -> mark(take(X1, X2)) 1061.12/297.10 , take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 1061.12/297.10 , and(mark(X1), X2) -> mark(and(X1, X2)) 1061.12/297.10 , and(ok(X1), ok(X2)) -> ok(and(X1, X2)) 1061.12/297.10 , isNatIListKind(ok(X)) -> ok(isNatIListKind(X)) 1061.12/297.10 , isNatKind(ok(X)) -> ok(isNatKind(X)) 1061.12/297.10 , proper(zeros()) -> ok(zeros()) 1061.12/297.10 , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 1061.12/297.10 , proper(0()) -> ok(0()) 1061.12/297.10 , proper(U11(X1, X2)) -> U11(proper(X1), proper(X2)) 1061.12/297.10 , proper(tt()) -> ok(tt()) 1061.12/297.10 , proper(U12(X)) -> U12(proper(X)) 1061.12/297.10 , proper(isNatList(X)) -> isNatList(proper(X)) 1061.12/297.10 , proper(U21(X1, X2)) -> U21(proper(X1), proper(X2)) 1061.12/297.10 , proper(U22(X)) -> U22(proper(X)) 1061.12/297.10 , proper(isNat(X)) -> isNat(proper(X)) 1061.12/297.10 , proper(U31(X1, X2)) -> U31(proper(X1), proper(X2)) 1061.12/297.10 , proper(U32(X)) -> U32(proper(X)) 1061.12/297.10 , proper(U41(X1, X2, X3)) -> 1061.12/297.10 U41(proper(X1), proper(X2), proper(X3)) 1061.12/297.10 , proper(U42(X1, X2)) -> U42(proper(X1), proper(X2)) 1061.12/297.10 , proper(U43(X)) -> U43(proper(X)) 1061.12/297.10 , proper(isNatIList(X)) -> isNatIList(proper(X)) 1061.12/297.10 , proper(U51(X1, X2, X3)) -> 1061.12/297.10 U51(proper(X1), proper(X2), proper(X3)) 1061.12/297.10 , proper(U52(X1, X2)) -> U52(proper(X1), proper(X2)) 1061.12/297.10 , proper(U53(X)) -> U53(proper(X)) 1061.12/297.10 , proper(U61(X1, X2, X3)) -> 1061.12/297.10 U61(proper(X1), proper(X2), proper(X3)) 1061.12/297.10 , proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 1061.12/297.10 , proper(U63(X)) -> U63(proper(X)) 1061.12/297.10 , proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 1061.12/297.10 , proper(s(X)) -> s(proper(X)) 1061.12/297.10 , proper(length(X)) -> length(proper(X)) 1061.12/297.10 , proper(U81(X)) -> U81(proper(X)) 1061.12/297.10 , proper(nil()) -> ok(nil()) 1061.12/297.10 , proper(U91(X1, X2, X3, X4)) -> 1061.12/297.10 U91(proper(X1), proper(X2), proper(X3), proper(X4)) 1061.12/297.10 , proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 1061.12/297.10 , proper(and(X1, X2)) -> and(proper(X1), proper(X2)) 1061.12/297.10 , proper(isNatIListKind(X)) -> isNatIListKind(proper(X)) 1061.12/297.10 , proper(isNatKind(X)) -> isNatKind(proper(X)) 1061.12/297.10 , top(mark(X)) -> top(proper(X)) 1061.12/297.10 , top(ok(X)) -> top(active(X)) } 1061.12/297.10 Obligation: 1061.12/297.10 innermost runtime complexity 1061.12/297.10 Answer: 1061.12/297.10 MAYBE 1061.12/297.10 1061.12/297.10 None of the processors succeeded. 1061.12/297.10 1061.12/297.10 Details of failed attempt(s): 1061.12/297.10 ----------------------------- 1061.12/297.10 1) 'empty' failed due to the following reason: 1061.12/297.10 1061.12/297.10 Empty strict component of the problem is NOT empty. 1061.12/297.10 1061.12/297.10 2) 'Best' failed due to the following reason: 1061.12/297.10 1061.12/297.10 None of the processors succeeded. 1061.12/297.10 1061.12/297.10 Details of failed attempt(s): 1061.12/297.10 ----------------------------- 1061.12/297.10 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1061.12/297.10 following reason: 1061.12/297.10 1061.12/297.10 Computation stopped due to timeout after 297.0 seconds. 1061.12/297.10 1061.12/297.10 2) 'Best' failed due to the following reason: 1061.12/297.10 1061.12/297.10 None of the processors succeeded. 1061.12/297.10 1061.12/297.10 Details of failed attempt(s): 1061.12/297.10 ----------------------------- 1061.12/297.10 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1061.12/297.10 seconds)' failed due to the following reason: 1061.12/297.10 1061.12/297.10 Computation stopped due to timeout after 148.0 seconds. 1061.12/297.10 1061.12/297.10 2) 'Best' failed due to the following reason: 1061.12/297.10 1061.12/297.10 None of the processors succeeded. 1061.12/297.10 1061.12/297.10 Details of failed attempt(s): 1061.12/297.10 ----------------------------- 1061.12/297.10 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1061.12/297.10 to the following reason: 1061.12/297.10 1061.12/297.10 The input cannot be shown compatible 1061.12/297.10 1061.12/297.10 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1061.12/297.10 following reason: 1061.12/297.10 1061.12/297.10 The input cannot be shown compatible 1061.12/297.10 1061.12/297.10 1061.12/297.10 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1061.12/297.10 failed due to the following reason: 1061.12/297.10 1061.12/297.10 None of the processors succeeded. 1061.12/297.10 1061.12/297.10 Details of failed attempt(s): 1061.12/297.10 ----------------------------- 1061.12/297.10 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1061.12/297.10 failed due to the following reason: 1061.12/297.10 1061.12/297.10 match-boundness of the problem could not be verified. 1061.12/297.10 1061.12/297.10 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1061.12/297.10 failed due to the following reason: 1061.12/297.10 1061.12/297.10 match-boundness of the problem could not be verified. 1061.12/297.10 1061.12/297.10 1061.12/297.10 1061.12/297.10 1061.12/297.10 1061.12/297.10 Arrrr.. 1062.01/298.05 EOF