MAYBE 946.24/297.03 MAYBE 946.24/297.03 946.24/297.03 We are left with following problem, upon which TcT provides the 946.24/297.03 certificate MAYBE. 946.24/297.03 946.24/297.03 Strict Trs: 946.24/297.03 { p(0()) -> 0() 946.24/297.03 , p(s(x)) -> x 946.24/297.03 , plus(x, 0()) -> x 946.24/297.03 , plus(x, s(y)) -> s(plus(x, p(s(y)))) 946.24/297.03 , plus(0(), y) -> y 946.24/297.03 , plus(s(x), y) -> s(plus(x, y)) 946.24/297.03 , plus(s(x), y) -> s(plus(p(s(x)), y)) 946.24/297.03 , times(0(), y) -> 0() 946.24/297.03 , times(s(x), y) -> plus(y, times(x, y)) 946.24/297.03 , times(s(0()), y) -> y 946.24/297.03 , div(x, y) -> quot(x, y, y) 946.24/297.03 , div(0(), y) -> 0() 946.24/297.03 , div(div(x, y), z) -> div(x, times(y, z)) 946.24/297.03 , quot(x, 0(), s(z)) -> s(div(x, s(z))) 946.24/297.03 , quot(0(), s(y), z) -> 0() 946.24/297.03 , quot(s(x), s(y), z) -> quot(x, y, z) 946.24/297.03 , eq(0(), 0()) -> true() 946.24/297.03 , eq(0(), s(y)) -> false() 946.24/297.03 , eq(s(x), 0()) -> false() 946.24/297.03 , eq(s(x), s(y)) -> eq(x, y) 946.24/297.03 , divides(y, x) -> eq(x, times(div(x, y), y)) 946.24/297.03 , prime(s(s(x))) -> pr(s(s(x)), s(x)) 946.24/297.03 , pr(x, s(0())) -> true() 946.24/297.03 , pr(x, s(s(y))) -> if(divides(s(s(y)), x), x, s(y)) 946.24/297.03 , if(true(), x, y) -> false() 946.24/297.03 , if(false(), x, y) -> pr(x, y) } 946.24/297.03 Obligation: 946.24/297.03 innermost runtime complexity 946.24/297.03 Answer: 946.24/297.03 MAYBE 946.24/297.03 946.24/297.03 Arguments of following rules are not normal-forms: 946.24/297.03 946.24/297.03 { div(div(x, y), z) -> div(x, times(y, z)) } 946.24/297.03 946.24/297.03 All above mentioned rules can be savely removed. 946.24/297.03 946.24/297.03 We are left with following problem, upon which TcT provides the 946.24/297.03 certificate MAYBE. 946.24/297.03 946.24/297.03 Strict Trs: 946.24/297.03 { p(0()) -> 0() 946.24/297.03 , p(s(x)) -> x 946.24/297.03 , plus(x, 0()) -> x 946.24/297.03 , plus(x, s(y)) -> s(plus(x, p(s(y)))) 946.24/297.03 , plus(0(), y) -> y 946.24/297.03 , plus(s(x), y) -> s(plus(x, y)) 946.24/297.03 , plus(s(x), y) -> s(plus(p(s(x)), y)) 946.24/297.03 , times(0(), y) -> 0() 946.24/297.03 , times(s(x), y) -> plus(y, times(x, y)) 946.24/297.03 , times(s(0()), y) -> y 946.24/297.03 , div(x, y) -> quot(x, y, y) 946.24/297.03 , div(0(), y) -> 0() 946.24/297.03 , quot(x, 0(), s(z)) -> s(div(x, s(z))) 946.24/297.03 , quot(0(), s(y), z) -> 0() 946.24/297.03 , quot(s(x), s(y), z) -> quot(x, y, z) 946.24/297.03 , eq(0(), 0()) -> true() 946.24/297.03 , eq(0(), s(y)) -> false() 946.24/297.03 , eq(s(x), 0()) -> false() 946.24/297.03 , eq(s(x), s(y)) -> eq(x, y) 946.24/297.03 , divides(y, x) -> eq(x, times(div(x, y), y)) 946.24/297.03 , prime(s(s(x))) -> pr(s(s(x)), s(x)) 946.24/297.03 , pr(x, s(0())) -> true() 946.24/297.03 , pr(x, s(s(y))) -> if(divides(s(s(y)), x), x, s(y)) 946.24/297.03 , if(true(), x, y) -> false() 946.24/297.03 , if(false(), x, y) -> pr(x, y) } 946.24/297.03 Obligation: 946.24/297.03 innermost runtime complexity 946.24/297.03 Answer: 946.24/297.03 MAYBE 946.24/297.03 946.24/297.03 None of the processors succeeded. 946.24/297.03 946.24/297.03 Details of failed attempt(s): 946.24/297.03 ----------------------------- 946.24/297.03 1) 'empty' failed due to the following reason: 946.24/297.03 946.24/297.03 Empty strict component of the problem is NOT empty. 946.24/297.03 946.24/297.03 2) 'Best' failed due to the following reason: 946.24/297.03 946.24/297.03 None of the processors succeeded. 946.24/297.03 946.24/297.03 Details of failed attempt(s): 946.24/297.03 ----------------------------- 946.24/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 946.24/297.03 following reason: 946.24/297.03 946.24/297.03 Computation stopped due to timeout after 297.0 seconds. 946.24/297.03 946.24/297.03 2) 'Best' failed due to the following reason: 946.24/297.03 946.24/297.03 None of the processors succeeded. 946.24/297.03 946.24/297.03 Details of failed attempt(s): 946.24/297.03 ----------------------------- 946.24/297.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 946.24/297.03 seconds)' failed due to the following reason: 946.24/297.03 946.24/297.03 Computation stopped due to timeout after 148.0 seconds. 946.24/297.03 946.24/297.03 2) 'Best' failed due to the following reason: 946.24/297.03 946.24/297.03 None of the processors succeeded. 946.24/297.03 946.24/297.03 Details of failed attempt(s): 946.24/297.03 ----------------------------- 946.24/297.03 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 946.24/297.03 following reason: 946.24/297.03 946.24/297.03 The input cannot be shown compatible 946.24/297.03 946.24/297.03 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 946.24/297.03 to the following reason: 946.24/297.03 946.24/297.03 The input cannot be shown compatible 946.24/297.03 946.24/297.03 946.24/297.03 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 946.24/297.03 failed due to the following reason: 946.24/297.03 946.24/297.03 None of the processors succeeded. 946.24/297.03 946.24/297.03 Details of failed attempt(s): 946.24/297.03 ----------------------------- 946.24/297.03 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 946.24/297.03 failed due to the following reason: 946.24/297.03 946.24/297.03 match-boundness of the problem could not be verified. 946.24/297.03 946.24/297.03 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 946.24/297.03 failed due to the following reason: 946.24/297.03 946.24/297.03 match-boundness of the problem could not be verified. 946.24/297.03 946.24/297.03 946.24/297.03 946.24/297.03 946.24/297.03 946.24/297.03 Arrrr.. 946.56/297.32 EOF