MAYBE 959.52/297.03 MAYBE 959.52/297.03 959.52/297.03 We are left with following problem, upon which TcT provides the 959.52/297.03 certificate MAYBE. 959.52/297.03 959.52/297.03 Strict Trs: 959.52/297.03 { g(s(x), s(y)) -> 959.52/297.03 if(and(f(s(x)), f(s(y))), 959.52/297.03 t(g(k(minus(m(x, y), n(x, y)), s(s(0()))), 959.52/297.03 k(n(s(x), s(y)), s(s(0()))))), 959.52/297.03 g(minus(m(x, y), n(x, y)), n(s(x), s(y)))) 959.52/297.03 , if(true(), x, y) -> x 959.52/297.03 , if(false(), x, y) -> y 959.52/297.03 , and(x, false()) -> false() 959.52/297.03 , and(true(), true()) -> true() 959.52/297.03 , f(s(x)) -> h(x) 959.52/297.03 , f(0()) -> true() 959.52/297.03 , t(x) -> p(x, x) 959.52/297.03 , k(s(x), s(y)) -> s(k(minus(x, y), s(y))) 959.52/297.03 , k(0(), s(y)) -> 0() 959.52/297.03 , minus(x, 0()) -> x 959.52/297.03 , minus(s(x), s(y)) -> minus(x, y) 959.52/297.03 , m(x, 0()) -> x 959.52/297.03 , m(s(x), s(y)) -> s(m(x, y)) 959.52/297.03 , m(0(), y) -> y 959.52/297.03 , n(x, 0()) -> 0() 959.52/297.03 , n(s(x), s(y)) -> s(n(x, y)) 959.52/297.03 , n(0(), y) -> 0() 959.52/297.03 , p(s(x), x) -> p(if(gt(x, x), id(x), id(x)), s(x)) 959.52/297.03 , p(s(x), s(y)) -> 959.52/297.03 s(s(p(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))) 959.52/297.03 , p(0(), y) -> y 959.52/297.03 , p(id(x), s(y)) -> s(p(x, if(gt(s(y), y), y, s(y)))) 959.52/297.03 , gt(s(x), s(y)) -> gt(x, y) 959.52/297.03 , gt(s(x), 0()) -> true() 959.52/297.03 , gt(0(), y) -> false() 959.52/297.03 , not(x) -> if(x, false(), true()) 959.52/297.03 , id(x) -> x 959.52/297.03 , h(s(x)) -> f(x) 959.52/297.03 , h(0()) -> false() } 959.52/297.03 Obligation: 959.52/297.03 innermost runtime complexity 959.52/297.03 Answer: 959.52/297.03 MAYBE 959.52/297.03 959.52/297.03 Arguments of following rules are not normal-forms: 959.52/297.03 959.52/297.03 { p(id(x), s(y)) -> s(p(x, if(gt(s(y), y), y, s(y)))) } 959.52/297.03 959.52/297.03 All above mentioned rules can be savely removed. 959.52/297.03 959.52/297.03 We are left with following problem, upon which TcT provides the 959.52/297.03 certificate MAYBE. 959.52/297.03 959.52/297.03 Strict Trs: 959.52/297.03 { g(s(x), s(y)) -> 959.52/297.03 if(and(f(s(x)), f(s(y))), 959.52/297.03 t(g(k(minus(m(x, y), n(x, y)), s(s(0()))), 959.52/297.03 k(n(s(x), s(y)), s(s(0()))))), 959.52/297.03 g(minus(m(x, y), n(x, y)), n(s(x), s(y)))) 959.52/297.03 , if(true(), x, y) -> x 959.52/297.03 , if(false(), x, y) -> y 959.52/297.03 , and(x, false()) -> false() 959.52/297.03 , and(true(), true()) -> true() 959.52/297.03 , f(s(x)) -> h(x) 959.52/297.03 , f(0()) -> true() 959.52/297.03 , t(x) -> p(x, x) 959.52/297.03 , k(s(x), s(y)) -> s(k(minus(x, y), s(y))) 959.52/297.03 , k(0(), s(y)) -> 0() 959.52/297.03 , minus(x, 0()) -> x 959.52/297.03 , minus(s(x), s(y)) -> minus(x, y) 959.52/297.03 , m(x, 0()) -> x 959.52/297.03 , m(s(x), s(y)) -> s(m(x, y)) 959.52/297.03 , m(0(), y) -> y 959.52/297.03 , n(x, 0()) -> 0() 959.52/297.03 , n(s(x), s(y)) -> s(n(x, y)) 959.52/297.03 , n(0(), y) -> 0() 959.52/297.03 , p(s(x), x) -> p(if(gt(x, x), id(x), id(x)), s(x)) 959.52/297.03 , p(s(x), s(y)) -> 959.52/297.03 s(s(p(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))) 959.52/297.03 , p(0(), y) -> y 959.52/297.03 , gt(s(x), s(y)) -> gt(x, y) 959.52/297.03 , gt(s(x), 0()) -> true() 959.52/297.03 , gt(0(), y) -> false() 959.52/297.03 , not(x) -> if(x, false(), true()) 959.52/297.03 , id(x) -> x 959.52/297.03 , h(s(x)) -> f(x) 959.52/297.03 , h(0()) -> false() } 959.52/297.03 Obligation: 959.52/297.03 innermost runtime complexity 959.52/297.03 Answer: 959.52/297.03 MAYBE 959.52/297.03 959.52/297.03 None of the processors succeeded. 959.52/297.03 959.52/297.03 Details of failed attempt(s): 959.52/297.03 ----------------------------- 959.52/297.03 1) 'empty' failed due to the following reason: 959.52/297.03 959.52/297.03 Empty strict component of the problem is NOT empty. 959.52/297.03 959.52/297.03 2) 'Best' failed due to the following reason: 959.52/297.03 959.52/297.03 None of the processors succeeded. 959.52/297.03 959.52/297.03 Details of failed attempt(s): 959.52/297.03 ----------------------------- 959.52/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 959.52/297.03 following reason: 959.52/297.03 959.52/297.03 Computation stopped due to timeout after 297.0 seconds. 959.52/297.03 959.52/297.03 2) 'Best' failed due to the following reason: 959.52/297.03 959.52/297.03 None of the processors succeeded. 959.52/297.03 959.52/297.03 Details of failed attempt(s): 959.52/297.03 ----------------------------- 959.52/297.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 959.52/297.03 seconds)' failed due to the following reason: 959.52/297.03 959.52/297.03 Computation stopped due to timeout after 148.0 seconds. 959.52/297.03 959.52/297.03 2) 'Best' failed due to the following reason: 959.52/297.03 959.52/297.03 None of the processors succeeded. 959.52/297.03 959.52/297.03 Details of failed attempt(s): 959.52/297.03 ----------------------------- 959.52/297.03 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 959.52/297.03 following reason: 959.52/297.03 959.52/297.03 The input cannot be shown compatible 959.52/297.03 959.52/297.03 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 959.52/297.03 to the following reason: 959.52/297.03 959.52/297.03 The input cannot be shown compatible 959.52/297.03 959.52/297.03 959.52/297.03 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 959.52/297.03 failed due to the following reason: 959.52/297.03 959.52/297.03 None of the processors succeeded. 959.52/297.03 959.52/297.03 Details of failed attempt(s): 959.52/297.03 ----------------------------- 959.52/297.03 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 959.52/297.03 failed due to the following reason: 959.52/297.03 959.52/297.03 match-boundness of the problem could not be verified. 959.52/297.03 959.52/297.03 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 959.52/297.03 failed due to the following reason: 959.52/297.03 959.52/297.03 match-boundness of the problem could not be verified. 959.52/297.03 959.52/297.03 959.52/297.03 959.52/297.03 959.52/297.03 959.52/297.03 Arrrr.. 959.73/297.24 EOF