MAYBE 772.50/297.15 MAYBE 772.50/297.15 772.50/297.15 We are left with following problem, upon which TcT provides the 772.50/297.15 certificate MAYBE. 772.50/297.15 772.50/297.15 Strict Trs: 772.50/297.15 { active(zeros()) -> mark(cons(0(), zeros())) 772.50/297.15 , active(cons(X1, X2)) -> cons(active(X1), X2) 772.50/297.15 , active(U11(X1, X2)) -> U11(active(X1), X2) 772.50/297.15 , active(U11(tt(), L)) -> mark(s(length(L))) 772.50/297.15 , active(s(X)) -> s(active(X)) 772.50/297.15 , active(length(X)) -> length(active(X)) 772.50/297.15 , active(length(cons(N, L))) -> 772.50/297.15 mark(U11(and(isNatList(L), isNat(N)), L)) 772.50/297.15 , active(length(nil())) -> mark(0()) 772.50/297.15 , active(U21(X)) -> U21(active(X)) 772.50/297.15 , active(U21(tt())) -> mark(nil()) 772.50/297.15 , active(U31(X1, X2, X3, X4)) -> U31(active(X1), X2, X3, X4) 772.50/297.15 , active(U31(tt(), IL, M, N)) -> mark(cons(N, take(M, IL))) 772.50/297.15 , active(take(X1, X2)) -> take(X1, active(X2)) 772.50/297.15 , active(take(X1, X2)) -> take(active(X1), X2) 772.50/297.15 , active(take(0(), IL)) -> mark(U21(isNatIList(IL))) 772.50/297.15 , active(take(s(M), cons(N, IL))) -> 772.50/297.15 mark(U31(and(isNatIList(IL), and(isNat(M), isNat(N))), IL, M, N)) 772.50/297.15 , active(and(X1, X2)) -> and(active(X1), X2) 772.50/297.15 , active(and(tt(), X)) -> mark(X) 772.50/297.15 , active(isNat(0())) -> mark(tt()) 772.50/297.15 , active(isNat(s(V1))) -> mark(isNat(V1)) 772.50/297.15 , active(isNat(length(V1))) -> mark(isNatList(V1)) 772.50/297.15 , active(isNatList(cons(V1, V2))) -> 772.50/297.15 mark(and(isNat(V1), isNatList(V2))) 772.50/297.15 , active(isNatList(nil())) -> mark(tt()) 772.50/297.15 , active(isNatList(take(V1, V2))) -> 772.50/297.15 mark(and(isNat(V1), isNatIList(V2))) 772.50/297.15 , active(isNatIList(V)) -> mark(isNatList(V)) 772.50/297.15 , active(isNatIList(zeros())) -> mark(tt()) 772.50/297.15 , active(isNatIList(cons(V1, V2))) -> 772.50/297.15 mark(and(isNat(V1), isNatIList(V2))) 772.50/297.15 , cons(mark(X1), X2) -> mark(cons(X1, X2)) 772.50/297.15 , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 772.50/297.15 , U11(mark(X1), X2) -> mark(U11(X1, X2)) 772.50/297.15 , U11(ok(X1), ok(X2)) -> ok(U11(X1, X2)) 772.50/297.15 , s(mark(X)) -> mark(s(X)) 772.50/297.15 , s(ok(X)) -> ok(s(X)) 772.50/297.15 , length(mark(X)) -> mark(length(X)) 772.50/297.15 , length(ok(X)) -> ok(length(X)) 772.50/297.15 , U21(mark(X)) -> mark(U21(X)) 772.50/297.15 , U21(ok(X)) -> ok(U21(X)) 772.50/297.15 , U31(mark(X1), X2, X3, X4) -> mark(U31(X1, X2, X3, X4)) 772.50/297.15 , U31(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U31(X1, X2, X3, X4)) 772.50/297.15 , take(X1, mark(X2)) -> mark(take(X1, X2)) 772.50/297.15 , take(mark(X1), X2) -> mark(take(X1, X2)) 772.50/297.15 , take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 772.50/297.15 , and(mark(X1), X2) -> mark(and(X1, X2)) 772.50/297.15 , and(ok(X1), ok(X2)) -> ok(and(X1, X2)) 772.50/297.15 , isNat(ok(X)) -> ok(isNat(X)) 772.50/297.15 , isNatList(ok(X)) -> ok(isNatList(X)) 772.50/297.15 , isNatIList(ok(X)) -> ok(isNatIList(X)) 772.50/297.15 , proper(zeros()) -> ok(zeros()) 772.50/297.15 , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 772.50/297.15 , proper(0()) -> ok(0()) 772.50/297.15 , proper(U11(X1, X2)) -> U11(proper(X1), proper(X2)) 772.50/297.15 , proper(tt()) -> ok(tt()) 772.50/297.15 , proper(s(X)) -> s(proper(X)) 772.50/297.15 , proper(length(X)) -> length(proper(X)) 772.50/297.15 , proper(U21(X)) -> U21(proper(X)) 772.50/297.15 , proper(nil()) -> ok(nil()) 772.50/297.15 , proper(U31(X1, X2, X3, X4)) -> 772.50/297.15 U31(proper(X1), proper(X2), proper(X3), proper(X4)) 772.50/297.15 , proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 772.50/297.15 , proper(and(X1, X2)) -> and(proper(X1), proper(X2)) 772.50/297.15 , proper(isNat(X)) -> isNat(proper(X)) 772.50/297.15 , proper(isNatList(X)) -> isNatList(proper(X)) 772.50/297.15 , proper(isNatIList(X)) -> isNatIList(proper(X)) 772.50/297.15 , top(mark(X)) -> top(proper(X)) 772.50/297.15 , top(ok(X)) -> top(active(X)) } 772.50/297.15 Obligation: 772.50/297.15 innermost runtime complexity 772.50/297.15 Answer: 772.50/297.15 MAYBE 772.50/297.15 772.50/297.15 None of the processors succeeded. 772.50/297.15 772.50/297.15 Details of failed attempt(s): 772.50/297.15 ----------------------------- 772.50/297.15 1) 'empty' failed due to the following reason: 772.50/297.15 772.50/297.15 Empty strict component of the problem is NOT empty. 772.50/297.15 772.50/297.15 2) 'Best' failed due to the following reason: 772.50/297.15 772.50/297.15 None of the processors succeeded. 772.50/297.15 772.50/297.15 Details of failed attempt(s): 772.50/297.15 ----------------------------- 772.50/297.15 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 772.50/297.15 following reason: 772.50/297.15 772.50/297.15 Computation stopped due to timeout after 297.0 seconds. 772.50/297.15 772.50/297.15 2) 'Best' failed due to the following reason: 772.50/297.15 772.50/297.15 None of the processors succeeded. 772.50/297.15 772.50/297.15 Details of failed attempt(s): 772.50/297.15 ----------------------------- 772.50/297.15 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 772.50/297.15 seconds)' failed due to the following reason: 772.50/297.15 772.50/297.15 Computation stopped due to timeout after 148.0 seconds. 772.50/297.15 772.50/297.15 2) 'Best' failed due to the following reason: 772.50/297.15 772.50/297.15 None of the processors succeeded. 772.50/297.15 772.50/297.15 Details of failed attempt(s): 772.50/297.15 ----------------------------- 772.50/297.15 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 772.50/297.15 to the following reason: 772.50/297.15 772.50/297.15 The input cannot be shown compatible 772.50/297.15 772.50/297.15 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 772.50/297.15 following reason: 772.50/297.15 772.50/297.15 The input cannot be shown compatible 772.50/297.15 772.50/297.15 772.50/297.15 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 772.50/297.15 failed due to the following reason: 772.50/297.15 772.50/297.15 None of the processors succeeded. 772.50/297.15 772.50/297.15 Details of failed attempt(s): 772.50/297.15 ----------------------------- 772.50/297.15 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 772.50/297.15 failed due to the following reason: 772.50/297.15 772.50/297.15 match-boundness of the problem could not be verified. 772.50/297.15 772.50/297.15 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 772.50/297.15 failed due to the following reason: 772.50/297.15 772.50/297.15 match-boundness of the problem could not be verified. 772.50/297.15 772.50/297.15 772.50/297.15 772.50/297.15 772.50/297.15 772.50/297.15 Arrrr.. 772.60/297.21 EOF