MAYBE 1153.71/297.04 MAYBE 1153.71/297.04 1153.71/297.04 We are left with following problem, upon which TcT provides the 1153.71/297.04 certificate MAYBE. 1153.71/297.04 1153.71/297.04 Strict Trs: 1153.71/297.04 { p(0()) -> 0() 1153.71/297.04 , p(s(x)) -> x 1153.71/297.04 , plus(x, 0()) -> x 1153.71/297.04 , plus(x, s(y)) -> s(plus(x, p(s(y)))) 1153.71/297.04 , plus(0(), y) -> y 1153.71/297.04 , plus(s(x), y) -> s(plus(x, y)) 1153.71/297.04 , plus(s(x), y) -> s(plus(p(s(x)), y)) 1153.71/297.04 , times(0(), y) -> 0() 1153.71/297.04 , times(s(x), y) -> plus(y, times(x, y)) 1153.71/297.04 , times(s(0()), y) -> y 1153.71/297.04 , div(x, y) -> quot(x, y, y) 1153.71/297.04 , div(0(), y) -> 0() 1153.71/297.04 , div(div(x, y), z) -> div(x, times(zero(y), z)) 1153.71/297.04 , quot(x, 0(), s(z)) -> s(div(x, s(z))) 1153.71/297.04 , quot(s(x), s(y), z) -> quot(x, y, z) 1153.71/297.04 , quot(zero(y), s(y), z) -> 0() 1153.71/297.04 , zero(s(x)) -> 1153.71/297.04 if(eq(x, s(0())), plus(zero(0()), 0()), s(plus(0(), zero(0())))) 1153.71/297.04 , zero(times(x, x)) -> x 1153.71/297.04 , zero(div(x, x)) -> x 1153.71/297.04 , zero(quot(x, x, x)) -> x 1153.71/297.04 , zero(divides(x, x)) -> x 1153.71/297.04 , eq(0(), 0()) -> true() 1153.71/297.04 , eq(0(), s(y)) -> false() 1153.71/297.04 , eq(s(x), 0()) -> false() 1153.71/297.04 , eq(s(x), s(y)) -> eq(x, y) 1153.71/297.04 , divides(y, x) -> eq(x, times(div(x, y), y)) 1153.71/297.04 , prime(s(s(x))) -> pr(s(s(x)), s(x)) 1153.71/297.04 , pr(x, s(0())) -> true() 1153.71/297.04 , pr(x, s(s(y))) -> if(divides(s(s(y)), x), x, s(y)) 1153.71/297.04 , if(true(), x, y) -> false() 1153.71/297.04 , if(false(), x, y) -> pr(x, y) } 1153.71/297.04 Obligation: 1153.71/297.04 innermost runtime complexity 1153.71/297.04 Answer: 1153.71/297.04 MAYBE 1153.71/297.04 1153.71/297.04 Arguments of following rules are not normal-forms: 1153.71/297.04 1153.71/297.04 { div(div(x, y), z) -> div(x, times(zero(y), z)) 1153.71/297.04 , zero(div(x, x)) -> x 1153.71/297.04 , zero(divides(x, x)) -> x } 1153.71/297.04 1153.71/297.04 All above mentioned rules can be savely removed. 1153.71/297.04 1153.71/297.04 We are left with following problem, upon which TcT provides the 1153.71/297.04 certificate MAYBE. 1153.71/297.04 1153.71/297.04 Strict Trs: 1153.71/297.04 { p(0()) -> 0() 1153.71/297.04 , p(s(x)) -> x 1153.71/297.04 , plus(x, 0()) -> x 1153.71/297.04 , plus(x, s(y)) -> s(plus(x, p(s(y)))) 1153.71/297.04 , plus(0(), y) -> y 1153.71/297.04 , plus(s(x), y) -> s(plus(x, y)) 1153.71/297.04 , plus(s(x), y) -> s(plus(p(s(x)), y)) 1153.71/297.04 , times(0(), y) -> 0() 1153.71/297.04 , times(s(x), y) -> plus(y, times(x, y)) 1153.71/297.04 , times(s(0()), y) -> y 1153.71/297.04 , div(x, y) -> quot(x, y, y) 1153.71/297.04 , div(0(), y) -> 0() 1153.71/297.04 , quot(x, 0(), s(z)) -> s(div(x, s(z))) 1153.71/297.04 , quot(s(x), s(y), z) -> quot(x, y, z) 1153.71/297.04 , quot(zero(y), s(y), z) -> 0() 1153.71/297.04 , zero(s(x)) -> 1153.71/297.04 if(eq(x, s(0())), plus(zero(0()), 0()), s(plus(0(), zero(0())))) 1153.71/297.04 , zero(times(x, x)) -> x 1153.71/297.04 , zero(quot(x, x, x)) -> x 1153.71/297.04 , eq(0(), 0()) -> true() 1153.71/297.04 , eq(0(), s(y)) -> false() 1153.71/297.04 , eq(s(x), 0()) -> false() 1153.71/297.04 , eq(s(x), s(y)) -> eq(x, y) 1153.71/297.04 , divides(y, x) -> eq(x, times(div(x, y), y)) 1153.71/297.04 , prime(s(s(x))) -> pr(s(s(x)), s(x)) 1153.71/297.04 , pr(x, s(0())) -> true() 1153.71/297.04 , pr(x, s(s(y))) -> if(divides(s(s(y)), x), x, s(y)) 1153.71/297.04 , if(true(), x, y) -> false() 1153.71/297.04 , if(false(), x, y) -> pr(x, y) } 1153.71/297.04 Obligation: 1153.71/297.04 innermost runtime complexity 1153.71/297.04 Answer: 1153.71/297.04 MAYBE 1153.71/297.04 1153.71/297.04 None of the processors succeeded. 1153.71/297.04 1153.71/297.04 Details of failed attempt(s): 1153.71/297.04 ----------------------------- 1153.71/297.04 1) 'empty' failed due to the following reason: 1153.71/297.04 1153.71/297.04 Empty strict component of the problem is NOT empty. 1153.71/297.04 1153.71/297.04 2) 'Best' failed due to the following reason: 1153.71/297.04 1153.71/297.04 None of the processors succeeded. 1153.71/297.04 1153.71/297.04 Details of failed attempt(s): 1153.71/297.04 ----------------------------- 1153.71/297.04 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1153.71/297.04 following reason: 1153.71/297.04 1153.71/297.04 Computation stopped due to timeout after 297.0 seconds. 1153.71/297.04 1153.71/297.04 2) 'Best' failed due to the following reason: 1153.71/297.04 1153.71/297.04 None of the processors succeeded. 1153.71/297.04 1153.71/297.04 Details of failed attempt(s): 1153.71/297.04 ----------------------------- 1153.71/297.04 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1153.71/297.04 seconds)' failed due to the following reason: 1153.71/297.04 1153.71/297.04 Computation stopped due to timeout after 148.0 seconds. 1153.71/297.04 1153.71/297.04 2) 'Best' failed due to the following reason: 1153.71/297.04 1153.71/297.04 None of the processors succeeded. 1153.71/297.04 1153.71/297.04 Details of failed attempt(s): 1153.71/297.04 ----------------------------- 1153.71/297.04 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1153.71/297.04 following reason: 1153.71/297.04 1153.71/297.04 The input cannot be shown compatible 1153.71/297.04 1153.71/297.04 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1153.71/297.04 to the following reason: 1153.71/297.04 1153.71/297.04 The input cannot be shown compatible 1153.71/297.04 1153.71/297.04 1153.71/297.04 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1153.71/297.04 failed due to the following reason: 1153.71/297.04 1153.71/297.04 None of the processors succeeded. 1153.71/297.04 1153.71/297.04 Details of failed attempt(s): 1153.71/297.04 ----------------------------- 1153.71/297.04 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1153.71/297.04 failed due to the following reason: 1153.71/297.04 1153.71/297.04 match-boundness of the problem could not be verified. 1153.71/297.04 1153.71/297.04 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1153.71/297.04 failed due to the following reason: 1153.71/297.04 1153.71/297.04 match-boundness of the problem could not be verified. 1153.71/297.04 1153.71/297.04 1153.71/297.04 1153.71/297.04 1153.71/297.04 1153.71/297.04 Arrrr.. 1154.30/297.57 EOF