MAYBE 782.87/297.15 MAYBE 782.87/297.15 782.87/297.15 We are left with following problem, upon which TcT provides the 782.87/297.15 certificate MAYBE. 782.87/297.15 782.87/297.15 Strict Trs: 782.87/297.15 { active(from(X)) -> from(active(X)) 782.87/297.15 , active(from(X)) -> mark(cons(X, from(s(X)))) 782.87/297.15 , active(cons(X1, X2)) -> cons(active(X1), X2) 782.87/297.15 , active(s(X)) -> s(active(X)) 782.87/297.15 , active(2ndspos(X1, X2)) -> 2ndspos(X1, active(X2)) 782.87/297.15 , active(2ndspos(X1, X2)) -> 2ndspos(active(X1), X2) 782.87/297.15 , active(2ndspos(s(N), cons(X, Z))) -> 782.87/297.15 mark(2ndspos(s(N), cons2(X, Z))) 782.87/297.15 , active(2ndspos(s(N), cons2(X, cons(Y, Z)))) -> 782.87/297.15 mark(rcons(posrecip(Y), 2ndsneg(N, Z))) 782.87/297.15 , active(2ndspos(0(), Z)) -> mark(rnil()) 782.87/297.15 , active(cons2(X1, X2)) -> cons2(X1, active(X2)) 782.87/297.15 , active(rcons(X1, X2)) -> rcons(X1, active(X2)) 782.87/297.15 , active(rcons(X1, X2)) -> rcons(active(X1), X2) 782.87/297.15 , active(posrecip(X)) -> posrecip(active(X)) 782.87/297.15 , active(2ndsneg(X1, X2)) -> 2ndsneg(X1, active(X2)) 782.87/297.15 , active(2ndsneg(X1, X2)) -> 2ndsneg(active(X1), X2) 782.87/297.15 , active(2ndsneg(s(N), cons(X, Z))) -> 782.87/297.15 mark(2ndsneg(s(N), cons2(X, Z))) 782.87/297.15 , active(2ndsneg(s(N), cons2(X, cons(Y, Z)))) -> 782.87/297.15 mark(rcons(negrecip(Y), 2ndspos(N, Z))) 782.87/297.15 , active(2ndsneg(0(), Z)) -> mark(rnil()) 782.87/297.15 , active(negrecip(X)) -> negrecip(active(X)) 782.87/297.15 , active(pi(X)) -> mark(2ndspos(X, from(0()))) 782.87/297.15 , active(pi(X)) -> pi(active(X)) 782.87/297.15 , active(plus(X1, X2)) -> plus(X1, active(X2)) 782.87/297.15 , active(plus(X1, X2)) -> plus(active(X1), X2) 782.87/297.15 , active(plus(s(X), Y)) -> mark(s(plus(X, Y))) 782.87/297.15 , active(plus(0(), Y)) -> mark(Y) 782.87/297.15 , active(times(X1, X2)) -> times(X1, active(X2)) 782.87/297.15 , active(times(X1, X2)) -> times(active(X1), X2) 782.87/297.15 , active(times(s(X), Y)) -> mark(plus(Y, times(X, Y))) 782.87/297.15 , active(times(0(), Y)) -> mark(0()) 782.87/297.15 , active(square(X)) -> mark(times(X, X)) 782.87/297.15 , active(square(X)) -> square(active(X)) 782.87/297.15 , from(mark(X)) -> mark(from(X)) 782.87/297.15 , from(ok(X)) -> ok(from(X)) 782.87/297.15 , cons(mark(X1), X2) -> mark(cons(X1, X2)) 782.87/297.15 , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 782.87/297.15 , s(mark(X)) -> mark(s(X)) 782.87/297.15 , s(ok(X)) -> ok(s(X)) 782.87/297.15 , 2ndspos(X1, mark(X2)) -> mark(2ndspos(X1, X2)) 782.87/297.15 , 2ndspos(mark(X1), X2) -> mark(2ndspos(X1, X2)) 782.87/297.15 , 2ndspos(ok(X1), ok(X2)) -> ok(2ndspos(X1, X2)) 782.87/297.15 , cons2(X1, mark(X2)) -> mark(cons2(X1, X2)) 782.87/297.15 , cons2(ok(X1), ok(X2)) -> ok(cons2(X1, X2)) 782.87/297.15 , rcons(X1, mark(X2)) -> mark(rcons(X1, X2)) 782.87/297.15 , rcons(mark(X1), X2) -> mark(rcons(X1, X2)) 782.87/297.15 , rcons(ok(X1), ok(X2)) -> ok(rcons(X1, X2)) 782.87/297.15 , posrecip(mark(X)) -> mark(posrecip(X)) 782.87/297.15 , posrecip(ok(X)) -> ok(posrecip(X)) 782.87/297.15 , 2ndsneg(X1, mark(X2)) -> mark(2ndsneg(X1, X2)) 782.87/297.15 , 2ndsneg(mark(X1), X2) -> mark(2ndsneg(X1, X2)) 782.87/297.15 , 2ndsneg(ok(X1), ok(X2)) -> ok(2ndsneg(X1, X2)) 782.87/297.15 , negrecip(mark(X)) -> mark(negrecip(X)) 782.87/297.15 , negrecip(ok(X)) -> ok(negrecip(X)) 782.87/297.15 , pi(mark(X)) -> mark(pi(X)) 782.87/297.15 , pi(ok(X)) -> ok(pi(X)) 782.87/297.15 , plus(X1, mark(X2)) -> mark(plus(X1, X2)) 782.87/297.15 , plus(mark(X1), X2) -> mark(plus(X1, X2)) 782.87/297.15 , plus(ok(X1), ok(X2)) -> ok(plus(X1, X2)) 782.87/297.15 , times(X1, mark(X2)) -> mark(times(X1, X2)) 782.87/297.15 , times(mark(X1), X2) -> mark(times(X1, X2)) 782.87/297.15 , times(ok(X1), ok(X2)) -> ok(times(X1, X2)) 782.87/297.15 , square(mark(X)) -> mark(square(X)) 782.87/297.15 , square(ok(X)) -> ok(square(X)) 782.87/297.15 , proper(from(X)) -> from(proper(X)) 782.87/297.15 , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 782.87/297.15 , proper(s(X)) -> s(proper(X)) 782.87/297.15 , proper(2ndspos(X1, X2)) -> 2ndspos(proper(X1), proper(X2)) 782.87/297.15 , proper(0()) -> ok(0()) 782.87/297.15 , proper(rnil()) -> ok(rnil()) 782.87/297.15 , proper(cons2(X1, X2)) -> cons2(proper(X1), proper(X2)) 782.87/297.15 , proper(rcons(X1, X2)) -> rcons(proper(X1), proper(X2)) 782.87/297.15 , proper(posrecip(X)) -> posrecip(proper(X)) 782.87/297.15 , proper(2ndsneg(X1, X2)) -> 2ndsneg(proper(X1), proper(X2)) 782.87/297.15 , proper(negrecip(X)) -> negrecip(proper(X)) 782.87/297.15 , proper(pi(X)) -> pi(proper(X)) 782.87/297.15 , proper(plus(X1, X2)) -> plus(proper(X1), proper(X2)) 782.87/297.15 , proper(times(X1, X2)) -> times(proper(X1), proper(X2)) 782.87/297.15 , proper(square(X)) -> square(proper(X)) 782.87/297.15 , proper(nil()) -> ok(nil()) 782.87/297.15 , top(mark(X)) -> top(proper(X)) 782.87/297.15 , top(ok(X)) -> top(active(X)) } 782.87/297.15 Obligation: 782.87/297.15 innermost runtime complexity 782.87/297.15 Answer: 782.87/297.15 MAYBE 782.87/297.15 782.87/297.15 None of the processors succeeded. 782.87/297.15 782.87/297.15 Details of failed attempt(s): 782.87/297.15 ----------------------------- 782.87/297.15 1) 'empty' failed due to the following reason: 782.87/297.15 782.87/297.15 Empty strict component of the problem is NOT empty. 782.87/297.15 782.87/297.15 2) 'Best' failed due to the following reason: 782.87/297.15 782.87/297.15 None of the processors succeeded. 782.87/297.15 782.87/297.15 Details of failed attempt(s): 782.87/297.15 ----------------------------- 782.87/297.15 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 782.87/297.15 following reason: 782.87/297.15 782.87/297.15 Computation stopped due to timeout after 297.0 seconds. 782.87/297.15 782.87/297.15 2) 'Best' failed due to the following reason: 782.87/297.15 782.87/297.15 None of the processors succeeded. 782.87/297.15 782.87/297.15 Details of failed attempt(s): 782.87/297.15 ----------------------------- 782.87/297.15 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 782.87/297.15 seconds)' failed due to the following reason: 782.87/297.15 782.87/297.15 Computation stopped due to timeout after 148.0 seconds. 782.87/297.15 782.87/297.15 2) 'Best' failed due to the following reason: 782.87/297.15 782.87/297.15 None of the processors succeeded. 782.87/297.15 782.87/297.15 Details of failed attempt(s): 782.87/297.15 ----------------------------- 782.87/297.15 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 782.87/297.15 to the following reason: 782.87/297.15 782.87/297.15 The input cannot be shown compatible 782.87/297.15 782.87/297.15 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 782.87/297.15 following reason: 782.87/297.15 782.87/297.15 The input cannot be shown compatible 782.87/297.15 782.87/297.15 782.87/297.15 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 782.87/297.15 failed due to the following reason: 782.87/297.15 782.87/297.15 None of the processors succeeded. 782.87/297.15 782.87/297.15 Details of failed attempt(s): 782.87/297.15 ----------------------------- 782.87/297.15 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 782.87/297.15 failed due to the following reason: 782.87/297.15 782.87/297.15 match-boundness of the problem could not be verified. 782.87/297.15 782.87/297.15 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 782.87/297.15 failed due to the following reason: 782.87/297.15 782.87/297.15 match-boundness of the problem could not be verified. 782.87/297.15 782.87/297.15 782.87/297.15 782.87/297.15 782.87/297.15 782.87/297.15 Arrrr.. 783.49/297.77 EOF