MAYBE 735.40/297.12 MAYBE 735.40/297.12 735.40/297.12 We are left with following problem, upon which TcT provides the 735.40/297.12 certificate MAYBE. 735.40/297.12 735.40/297.12 Strict Trs: 735.40/297.12 { plus(x, 0()) -> x 735.40/297.12 , plus(0(), y) -> y 735.40/297.12 , plus(s(x), y) -> s(plus(x, y)) 735.40/297.12 , times(0(), y) -> 0() 735.40/297.12 , times(s(x), y) -> plus(y, times(x, y)) 735.40/297.12 , times(s(0()), y) -> y 735.40/297.12 , div(x, y) -> quot(x, y, y) 735.40/297.12 , div(0(), y) -> 0() 735.40/297.12 , div(div(x, y), z) -> div(x, times(y, z)) 735.40/297.12 , quot(x, 0(), s(z)) -> s(div(x, s(z))) 735.40/297.12 , quot(0(), s(y), z) -> 0() 735.40/297.12 , quot(s(x), s(y), z) -> quot(x, y, z) 735.40/297.12 , eq(0(), 0()) -> true() 735.40/297.12 , eq(0(), s(y)) -> false() 735.40/297.12 , eq(s(x), 0()) -> false() 735.40/297.12 , eq(s(x), s(y)) -> eq(x, y) 735.40/297.12 , divides(y, x) -> eq(x, times(div(x, y), y)) 735.40/297.12 , prime(s(s(x))) -> pr(s(s(x)), s(x)) 735.40/297.12 , pr(x, s(0())) -> true() 735.40/297.12 , pr(x, s(s(y))) -> if(divides(s(s(y)), x), x, s(y)) 735.40/297.12 , if(true(), x, y) -> false() 735.40/297.12 , if(false(), x, y) -> pr(x, y) } 735.40/297.12 Obligation: 735.40/297.12 innermost runtime complexity 735.40/297.12 Answer: 735.40/297.12 MAYBE 735.40/297.12 735.40/297.12 Arguments of following rules are not normal-forms: 735.40/297.12 735.40/297.12 { div(div(x, y), z) -> div(x, times(y, z)) } 735.40/297.12 735.40/297.12 All above mentioned rules can be savely removed. 735.40/297.12 735.40/297.12 We are left with following problem, upon which TcT provides the 735.40/297.12 certificate MAYBE. 735.40/297.12 735.40/297.12 Strict Trs: 735.40/297.12 { plus(x, 0()) -> x 735.40/297.12 , plus(0(), y) -> y 735.40/297.12 , plus(s(x), y) -> s(plus(x, y)) 735.40/297.12 , times(0(), y) -> 0() 735.40/297.12 , times(s(x), y) -> plus(y, times(x, y)) 735.40/297.12 , times(s(0()), y) -> y 735.40/297.12 , div(x, y) -> quot(x, y, y) 735.40/297.12 , div(0(), y) -> 0() 735.40/297.12 , quot(x, 0(), s(z)) -> s(div(x, s(z))) 735.40/297.12 , quot(0(), s(y), z) -> 0() 735.40/297.12 , quot(s(x), s(y), z) -> quot(x, y, z) 735.40/297.12 , eq(0(), 0()) -> true() 735.40/297.12 , eq(0(), s(y)) -> false() 735.40/297.12 , eq(s(x), 0()) -> false() 735.40/297.12 , eq(s(x), s(y)) -> eq(x, y) 735.40/297.12 , divides(y, x) -> eq(x, times(div(x, y), y)) 735.40/297.12 , prime(s(s(x))) -> pr(s(s(x)), s(x)) 735.40/297.12 , pr(x, s(0())) -> true() 735.40/297.12 , pr(x, s(s(y))) -> if(divides(s(s(y)), x), x, s(y)) 735.40/297.12 , if(true(), x, y) -> false() 735.40/297.12 , if(false(), x, y) -> pr(x, y) } 735.40/297.12 Obligation: 735.40/297.12 innermost runtime complexity 735.40/297.12 Answer: 735.40/297.12 MAYBE 735.40/297.12 735.40/297.12 None of the processors succeeded. 735.40/297.12 735.40/297.12 Details of failed attempt(s): 735.40/297.12 ----------------------------- 735.40/297.12 1) 'empty' failed due to the following reason: 735.40/297.12 735.40/297.12 Empty strict component of the problem is NOT empty. 735.40/297.12 735.40/297.12 2) 'Best' failed due to the following reason: 735.40/297.12 735.40/297.12 None of the processors succeeded. 735.40/297.12 735.40/297.12 Details of failed attempt(s): 735.40/297.12 ----------------------------- 735.40/297.12 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 735.40/297.12 following reason: 735.40/297.12 735.40/297.12 Computation stopped due to timeout after 297.0 seconds. 735.40/297.12 735.40/297.12 2) 'Best' failed due to the following reason: 735.40/297.12 735.40/297.12 None of the processors succeeded. 735.40/297.12 735.40/297.12 Details of failed attempt(s): 735.40/297.12 ----------------------------- 735.40/297.12 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 735.40/297.12 seconds)' failed due to the following reason: 735.40/297.12 735.40/297.12 Computation stopped due to timeout after 148.0 seconds. 735.40/297.12 735.40/297.12 2) 'Best' failed due to the following reason: 735.40/297.12 735.40/297.12 None of the processors succeeded. 735.40/297.12 735.40/297.12 Details of failed attempt(s): 735.40/297.12 ----------------------------- 735.40/297.12 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 735.40/297.12 to the following reason: 735.40/297.12 735.40/297.12 The input cannot be shown compatible 735.40/297.12 735.40/297.12 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 735.40/297.12 following reason: 735.40/297.12 735.40/297.12 The input cannot be shown compatible 735.40/297.12 735.40/297.12 735.40/297.12 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 735.40/297.12 failed due to the following reason: 735.40/297.12 735.40/297.12 None of the processors succeeded. 735.40/297.12 735.40/297.12 Details of failed attempt(s): 735.40/297.12 ----------------------------- 735.40/297.12 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 735.40/297.12 failed due to the following reason: 735.40/297.12 735.40/297.12 match-boundness of the problem could not be verified. 735.40/297.12 735.40/297.12 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 735.40/297.12 failed due to the following reason: 735.40/297.12 735.40/297.12 match-boundness of the problem could not be verified. 735.40/297.12 735.40/297.12 735.40/297.12 735.40/297.12 735.40/297.12 735.40/297.12 Arrrr.. 735.51/297.22 EOF