MAYBE 777.58/297.15 MAYBE 777.58/297.15 777.58/297.15 We are left with following problem, upon which TcT provides the 777.58/297.15 certificate MAYBE. 777.58/297.15 777.58/297.15 Strict Trs: 777.58/297.15 { active(and(X1, X2)) -> and(X1, active(X2)) 777.58/297.15 , active(and(X1, X2)) -> and(active(X1), X2) 777.58/297.15 , active(and(tt(), T)) -> mark(T) 777.58/297.15 , active(isNatIList(IL)) -> mark(isNatList(IL)) 777.58/297.15 , active(isNatIList(zeros())) -> mark(tt()) 777.58/297.15 , active(isNatIList(cons(N, IL))) -> 777.58/297.15 mark(and(isNat(N), isNatIList(IL))) 777.58/297.15 , active(isNatList(cons(N, L))) -> 777.58/297.15 mark(and(isNat(N), isNatList(L))) 777.58/297.15 , active(isNatList(nil())) -> mark(tt()) 777.58/297.15 , active(isNatList(take(N, IL))) -> 777.58/297.15 mark(and(isNat(N), isNatIList(IL))) 777.58/297.15 , active(isNat(0())) -> mark(tt()) 777.58/297.15 , active(isNat(s(N))) -> mark(isNat(N)) 777.58/297.15 , active(isNat(length(L))) -> mark(isNatList(L)) 777.58/297.15 , active(s(X)) -> s(active(X)) 777.58/297.15 , active(length(X)) -> length(active(X)) 777.58/297.15 , active(length(cons(N, L))) -> 777.58/297.15 mark(uLength(and(isNat(N), isNatList(L)), L)) 777.58/297.15 , active(zeros()) -> mark(cons(0(), zeros())) 777.58/297.15 , active(cons(X1, X2)) -> cons(active(X1), X2) 777.58/297.15 , active(take(X1, X2)) -> take(X1, active(X2)) 777.58/297.15 , active(take(X1, X2)) -> take(active(X1), X2) 777.58/297.15 , active(take(0(), IL)) -> mark(uTake1(isNatIList(IL))) 777.58/297.15 , active(take(s(M), cons(N, IL))) -> 777.58/297.15 mark(uTake2(and(isNat(M), and(isNat(N), isNatIList(IL))), 777.58/297.15 M, 777.58/297.15 N, 777.58/297.15 IL)) 777.58/297.15 , active(uTake1(X)) -> uTake1(active(X)) 777.58/297.15 , active(uTake1(tt())) -> mark(nil()) 777.58/297.15 , active(uTake2(X1, X2, X3, X4)) -> uTake2(active(X1), X2, X3, X4) 777.58/297.15 , active(uTake2(tt(), M, N, IL)) -> mark(cons(N, take(M, IL))) 777.58/297.15 , active(uLength(X1, X2)) -> uLength(active(X1), X2) 777.58/297.15 , active(uLength(tt(), L)) -> mark(s(length(L))) 777.58/297.15 , and(X1, mark(X2)) -> mark(and(X1, X2)) 777.58/297.15 , and(mark(X1), X2) -> mark(and(X1, X2)) 777.58/297.15 , and(ok(X1), ok(X2)) -> ok(and(X1, X2)) 777.58/297.15 , isNatIList(ok(X)) -> ok(isNatIList(X)) 777.58/297.15 , isNatList(ok(X)) -> ok(isNatList(X)) 777.58/297.15 , isNat(ok(X)) -> ok(isNat(X)) 777.58/297.15 , s(mark(X)) -> mark(s(X)) 777.58/297.15 , s(ok(X)) -> ok(s(X)) 777.58/297.15 , length(mark(X)) -> mark(length(X)) 777.58/297.15 , length(ok(X)) -> ok(length(X)) 777.58/297.15 , cons(mark(X1), X2) -> mark(cons(X1, X2)) 777.58/297.15 , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 777.58/297.15 , take(X1, mark(X2)) -> mark(take(X1, X2)) 777.58/297.15 , take(mark(X1), X2) -> mark(take(X1, X2)) 777.58/297.15 , take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 777.58/297.15 , uTake1(mark(X)) -> mark(uTake1(X)) 777.58/297.15 , uTake1(ok(X)) -> ok(uTake1(X)) 777.58/297.15 , uTake2(mark(X1), X2, X3, X4) -> mark(uTake2(X1, X2, X3, X4)) 777.58/297.15 , uTake2(ok(X1), ok(X2), ok(X3), ok(X4)) -> 777.58/297.15 ok(uTake2(X1, X2, X3, X4)) 777.58/297.15 , uLength(mark(X1), X2) -> mark(uLength(X1, X2)) 777.58/297.15 , uLength(ok(X1), ok(X2)) -> ok(uLength(X1, X2)) 777.58/297.15 , proper(and(X1, X2)) -> and(proper(X1), proper(X2)) 777.58/297.15 , proper(tt()) -> ok(tt()) 777.58/297.15 , proper(isNatIList(X)) -> isNatIList(proper(X)) 777.58/297.15 , proper(isNatList(X)) -> isNatList(proper(X)) 777.58/297.15 , proper(isNat(X)) -> isNat(proper(X)) 777.58/297.15 , proper(0()) -> ok(0()) 777.58/297.15 , proper(s(X)) -> s(proper(X)) 777.58/297.15 , proper(length(X)) -> length(proper(X)) 777.58/297.15 , proper(zeros()) -> ok(zeros()) 777.58/297.15 , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 777.58/297.15 , proper(nil()) -> ok(nil()) 777.58/297.15 , proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 777.58/297.15 , proper(uTake1(X)) -> uTake1(proper(X)) 777.58/297.15 , proper(uTake2(X1, X2, X3, X4)) -> 777.58/297.15 uTake2(proper(X1), proper(X2), proper(X3), proper(X4)) 777.58/297.15 , proper(uLength(X1, X2)) -> uLength(proper(X1), proper(X2)) 777.58/297.15 , top(mark(X)) -> top(proper(X)) 777.58/297.15 , top(ok(X)) -> top(active(X)) } 777.58/297.15 Obligation: 777.58/297.15 innermost runtime complexity 777.58/297.15 Answer: 777.58/297.15 MAYBE 777.58/297.15 777.58/297.15 None of the processors succeeded. 777.58/297.15 777.58/297.15 Details of failed attempt(s): 777.58/297.15 ----------------------------- 777.58/297.15 1) 'empty' failed due to the following reason: 777.58/297.15 777.58/297.15 Empty strict component of the problem is NOT empty. 777.58/297.15 777.58/297.15 2) 'Best' failed due to the following reason: 777.58/297.15 777.58/297.15 None of the processors succeeded. 777.58/297.15 777.58/297.15 Details of failed attempt(s): 777.58/297.15 ----------------------------- 777.58/297.15 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 777.58/297.15 following reason: 777.58/297.15 777.58/297.15 Computation stopped due to timeout after 297.0 seconds. 777.58/297.15 777.58/297.15 2) 'Best' failed due to the following reason: 777.58/297.15 777.58/297.15 None of the processors succeeded. 777.58/297.15 777.58/297.15 Details of failed attempt(s): 777.58/297.15 ----------------------------- 777.58/297.15 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 777.58/297.15 seconds)' failed due to the following reason: 777.58/297.15 777.58/297.15 Computation stopped due to timeout after 148.0 seconds. 777.58/297.15 777.58/297.15 2) 'Best' failed due to the following reason: 777.58/297.15 777.58/297.15 None of the processors succeeded. 777.58/297.15 777.58/297.15 Details of failed attempt(s): 777.58/297.15 ----------------------------- 777.58/297.15 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 777.58/297.15 following reason: 777.58/297.15 777.58/297.15 The input cannot be shown compatible 777.58/297.15 777.58/297.15 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 777.58/297.15 to the following reason: 777.58/297.15 777.58/297.15 The input cannot be shown compatible 777.58/297.15 777.58/297.15 777.58/297.15 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 777.58/297.15 failed due to the following reason: 777.58/297.15 777.58/297.15 None of the processors succeeded. 777.58/297.15 777.58/297.15 Details of failed attempt(s): 777.58/297.15 ----------------------------- 777.58/297.15 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 777.58/297.15 failed due to the following reason: 777.58/297.15 777.58/297.15 match-boundness of the problem could not be verified. 777.58/297.15 777.58/297.15 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 777.58/297.15 failed due to the following reason: 777.58/297.15 777.58/297.15 match-boundness of the problem could not be verified. 777.58/297.15 777.58/297.15 777.58/297.15 777.58/297.15 777.58/297.15 777.58/297.15 Arrrr.. 777.68/297.22 EOF