MAYBE 794.43/297.10 MAYBE 794.43/297.10 794.43/297.10 We are left with following problem, upon which TcT provides the 794.43/297.10 certificate MAYBE. 794.43/297.10 794.43/297.10 Strict Trs: 794.43/297.10 { active(from(X)) -> from(active(X)) 794.43/297.10 , active(from(X)) -> mark(cons(X, from(s(X)))) 794.43/297.10 , active(cons(X1, X2)) -> cons(active(X1), X2) 794.43/297.10 , active(s(X)) -> s(active(X)) 794.43/297.10 , active(2ndspos(X1, X2)) -> 2ndspos(X1, active(X2)) 794.43/297.10 , active(2ndspos(X1, X2)) -> 2ndspos(active(X1), X2) 794.43/297.10 , active(2ndspos(s(N), cons(X, cons(Y, Z)))) -> 794.43/297.10 mark(rcons(posrecip(Y), 2ndsneg(N, Z))) 794.43/297.10 , active(2ndspos(0(), Z)) -> mark(rnil()) 794.43/297.10 , active(rcons(X1, X2)) -> rcons(X1, active(X2)) 794.43/297.10 , active(rcons(X1, X2)) -> rcons(active(X1), X2) 794.43/297.10 , active(posrecip(X)) -> posrecip(active(X)) 794.43/297.10 , active(2ndsneg(X1, X2)) -> 2ndsneg(X1, active(X2)) 794.43/297.10 , active(2ndsneg(X1, X2)) -> 2ndsneg(active(X1), X2) 794.43/297.10 , active(2ndsneg(s(N), cons(X, cons(Y, Z)))) -> 794.43/297.10 mark(rcons(negrecip(Y), 2ndspos(N, Z))) 794.43/297.10 , active(2ndsneg(0(), Z)) -> mark(rnil()) 794.43/297.10 , active(negrecip(X)) -> negrecip(active(X)) 794.43/297.10 , active(pi(X)) -> mark(2ndspos(X, from(0()))) 794.43/297.10 , active(pi(X)) -> pi(active(X)) 794.43/297.10 , active(plus(X1, X2)) -> plus(X1, active(X2)) 794.43/297.10 , active(plus(X1, X2)) -> plus(active(X1), X2) 794.43/297.10 , active(plus(s(X), Y)) -> mark(s(plus(X, Y))) 794.43/297.10 , active(plus(0(), Y)) -> mark(Y) 794.43/297.10 , active(times(X1, X2)) -> times(X1, active(X2)) 794.43/297.10 , active(times(X1, X2)) -> times(active(X1), X2) 794.43/297.10 , active(times(s(X), Y)) -> mark(plus(Y, times(X, Y))) 794.43/297.10 , active(times(0(), Y)) -> mark(0()) 794.43/297.10 , active(square(X)) -> mark(times(X, X)) 794.43/297.10 , active(square(X)) -> square(active(X)) 794.43/297.10 , from(mark(X)) -> mark(from(X)) 794.43/297.10 , from(ok(X)) -> ok(from(X)) 794.43/297.10 , cons(mark(X1), X2) -> mark(cons(X1, X2)) 794.43/297.10 , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 794.43/297.10 , s(mark(X)) -> mark(s(X)) 794.43/297.10 , s(ok(X)) -> ok(s(X)) 794.43/297.10 , 2ndspos(X1, mark(X2)) -> mark(2ndspos(X1, X2)) 794.43/297.10 , 2ndspos(mark(X1), X2) -> mark(2ndspos(X1, X2)) 794.43/297.10 , 2ndspos(ok(X1), ok(X2)) -> ok(2ndspos(X1, X2)) 794.43/297.10 , rcons(X1, mark(X2)) -> mark(rcons(X1, X2)) 794.43/297.10 , rcons(mark(X1), X2) -> mark(rcons(X1, X2)) 794.43/297.10 , rcons(ok(X1), ok(X2)) -> ok(rcons(X1, X2)) 794.43/297.10 , posrecip(mark(X)) -> mark(posrecip(X)) 794.43/297.10 , posrecip(ok(X)) -> ok(posrecip(X)) 794.43/297.10 , 2ndsneg(X1, mark(X2)) -> mark(2ndsneg(X1, X2)) 794.43/297.10 , 2ndsneg(mark(X1), X2) -> mark(2ndsneg(X1, X2)) 794.43/297.10 , 2ndsneg(ok(X1), ok(X2)) -> ok(2ndsneg(X1, X2)) 794.43/297.10 , negrecip(mark(X)) -> mark(negrecip(X)) 794.43/297.10 , negrecip(ok(X)) -> ok(negrecip(X)) 794.43/297.10 , pi(mark(X)) -> mark(pi(X)) 794.43/297.10 , pi(ok(X)) -> ok(pi(X)) 794.43/297.10 , plus(X1, mark(X2)) -> mark(plus(X1, X2)) 794.43/297.10 , plus(mark(X1), X2) -> mark(plus(X1, X2)) 794.43/297.10 , plus(ok(X1), ok(X2)) -> ok(plus(X1, X2)) 794.43/297.10 , times(X1, mark(X2)) -> mark(times(X1, X2)) 794.43/297.10 , times(mark(X1), X2) -> mark(times(X1, X2)) 794.43/297.10 , times(ok(X1), ok(X2)) -> ok(times(X1, X2)) 794.43/297.10 , square(mark(X)) -> mark(square(X)) 794.43/297.10 , square(ok(X)) -> ok(square(X)) 794.43/297.10 , proper(from(X)) -> from(proper(X)) 794.43/297.10 , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 794.43/297.10 , proper(s(X)) -> s(proper(X)) 794.43/297.10 , proper(2ndspos(X1, X2)) -> 2ndspos(proper(X1), proper(X2)) 794.43/297.10 , proper(0()) -> ok(0()) 794.43/297.10 , proper(rnil()) -> ok(rnil()) 794.43/297.10 , proper(rcons(X1, X2)) -> rcons(proper(X1), proper(X2)) 794.43/297.10 , proper(posrecip(X)) -> posrecip(proper(X)) 794.43/297.10 , proper(2ndsneg(X1, X2)) -> 2ndsneg(proper(X1), proper(X2)) 794.43/297.10 , proper(negrecip(X)) -> negrecip(proper(X)) 794.43/297.10 , proper(pi(X)) -> pi(proper(X)) 794.43/297.10 , proper(plus(X1, X2)) -> plus(proper(X1), proper(X2)) 794.43/297.10 , proper(times(X1, X2)) -> times(proper(X1), proper(X2)) 794.43/297.10 , proper(square(X)) -> square(proper(X)) 794.43/297.10 , proper(nil()) -> ok(nil()) 794.43/297.10 , top(mark(X)) -> top(proper(X)) 794.43/297.10 , top(ok(X)) -> top(active(X)) } 794.43/297.10 Obligation: 794.43/297.10 innermost runtime complexity 794.43/297.10 Answer: 794.43/297.10 MAYBE 794.43/297.10 794.43/297.10 None of the processors succeeded. 794.43/297.10 794.43/297.10 Details of failed attempt(s): 794.43/297.10 ----------------------------- 794.43/297.10 1) 'empty' failed due to the following reason: 794.43/297.10 794.43/297.10 Empty strict component of the problem is NOT empty. 794.43/297.10 794.43/297.10 2) 'Best' failed due to the following reason: 794.43/297.10 794.43/297.10 None of the processors succeeded. 794.43/297.10 794.43/297.10 Details of failed attempt(s): 794.43/297.10 ----------------------------- 794.43/297.10 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 794.43/297.10 following reason: 794.43/297.10 794.43/297.10 Computation stopped due to timeout after 297.0 seconds. 794.43/297.10 794.43/297.10 2) 'Best' failed due to the following reason: 794.43/297.10 794.43/297.10 None of the processors succeeded. 794.43/297.10 794.43/297.10 Details of failed attempt(s): 794.43/297.10 ----------------------------- 794.43/297.10 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 794.43/297.10 seconds)' failed due to the following reason: 794.43/297.10 794.43/297.10 Computation stopped due to timeout after 148.0 seconds. 794.43/297.10 794.43/297.10 2) 'Best' failed due to the following reason: 794.43/297.10 794.43/297.10 None of the processors succeeded. 794.43/297.10 794.43/297.10 Details of failed attempt(s): 794.43/297.10 ----------------------------- 794.43/297.10 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 794.43/297.10 to the following reason: 794.43/297.10 794.43/297.10 The input cannot be shown compatible 794.43/297.10 794.43/297.10 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 794.43/297.10 following reason: 794.43/297.10 794.43/297.10 The input cannot be shown compatible 794.43/297.10 794.43/297.10 794.43/297.10 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 794.43/297.10 failed due to the following reason: 794.43/297.10 794.43/297.10 None of the processors succeeded. 794.43/297.10 794.43/297.10 Details of failed attempt(s): 794.43/297.10 ----------------------------- 794.43/297.10 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 794.43/297.10 failed due to the following reason: 794.43/297.10 794.43/297.10 match-boundness of the problem could not be verified. 794.43/297.10 794.43/297.10 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 794.43/297.10 failed due to the following reason: 794.43/297.10 794.43/297.10 match-boundness of the problem could not be verified. 794.43/297.10 794.43/297.10 794.43/297.10 794.43/297.10 794.43/297.10 794.43/297.10 Arrrr.. 795.04/297.71 EOF