MAYBE 976.30/297.02 MAYBE 976.30/297.02 976.30/297.02 We are left with following problem, upon which TcT provides the 976.30/297.02 certificate MAYBE. 976.30/297.02 976.30/297.02 Strict Trs: 976.30/297.02 { app(l, nil()) -> l 976.30/297.02 , app(nil(), k) -> k 976.30/297.02 , app(cons(x, l), k) -> cons(x, app(l, k)) 976.30/297.02 , sum(app(l, cons(x, cons(y, k)))) -> 976.30/297.02 sum(app(l, sum(cons(x, cons(y, k))))) 976.30/297.02 , sum(cons(x, nil())) -> cons(x, nil()) 976.30/297.02 , sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)) 976.30/297.02 , sum(plus(cons(0(), x), cons(y, l))) -> 976.30/297.02 pred(sum(cons(s(x), cons(y, l)))) 976.30/297.02 , plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x)) 976.30/297.02 , plus(s(x), s(y)) -> 976.30/297.02 s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))) 976.30/297.02 , plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y)))) 976.30/297.02 , plus(zero(), y) -> y 976.30/297.02 , pred(cons(s(x), nil())) -> cons(x, nil()) 976.30/297.02 , if(true(), x, y) -> x 976.30/297.02 , if(false(), x, y) -> y 976.30/297.02 , gt(s(x), s(y)) -> gt(x, y) 976.30/297.02 , gt(s(x), zero()) -> true() 976.30/297.02 , gt(zero(), y) -> false() 976.30/297.02 , not(x) -> if(x, false(), true()) 976.30/297.02 , id(x) -> x } 976.30/297.02 Obligation: 976.30/297.02 innermost runtime complexity 976.30/297.02 Answer: 976.30/297.02 MAYBE 976.30/297.02 976.30/297.02 Arguments of following rules are not normal-forms: 976.30/297.02 976.30/297.02 { plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y)))) } 976.30/297.02 976.30/297.02 All above mentioned rules can be savely removed. 976.30/297.02 976.30/297.02 We are left with following problem, upon which TcT provides the 976.30/297.02 certificate MAYBE. 976.30/297.02 976.30/297.02 Strict Trs: 976.30/297.02 { app(l, nil()) -> l 976.30/297.02 , app(nil(), k) -> k 976.30/297.02 , app(cons(x, l), k) -> cons(x, app(l, k)) 976.30/297.02 , sum(app(l, cons(x, cons(y, k)))) -> 976.30/297.02 sum(app(l, sum(cons(x, cons(y, k))))) 976.30/297.02 , sum(cons(x, nil())) -> cons(x, nil()) 976.30/297.02 , sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)) 976.30/297.02 , sum(plus(cons(0(), x), cons(y, l))) -> 976.30/297.02 pred(sum(cons(s(x), cons(y, l)))) 976.30/297.02 , plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x)) 976.30/297.02 , plus(s(x), s(y)) -> 976.30/297.02 s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))) 976.30/297.02 , plus(zero(), y) -> y 976.30/297.02 , pred(cons(s(x), nil())) -> cons(x, nil()) 976.30/297.02 , if(true(), x, y) -> x 976.30/297.02 , if(false(), x, y) -> y 976.30/297.02 , gt(s(x), s(y)) -> gt(x, y) 976.30/297.02 , gt(s(x), zero()) -> true() 976.30/297.02 , gt(zero(), y) -> false() 976.30/297.02 , not(x) -> if(x, false(), true()) 976.30/297.02 , id(x) -> x } 976.30/297.02 Obligation: 976.30/297.02 innermost runtime complexity 976.30/297.02 Answer: 976.30/297.02 MAYBE 976.30/297.02 976.30/297.02 None of the processors succeeded. 976.30/297.02 976.30/297.02 Details of failed attempt(s): 976.30/297.02 ----------------------------- 976.30/297.02 1) 'empty' failed due to the following reason: 976.30/297.02 976.30/297.02 Empty strict component of the problem is NOT empty. 976.30/297.02 976.30/297.02 2) 'Best' failed due to the following reason: 976.30/297.02 976.30/297.02 None of the processors succeeded. 976.30/297.02 976.30/297.02 Details of failed attempt(s): 976.30/297.02 ----------------------------- 976.30/297.02 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 976.30/297.02 following reason: 976.30/297.02 976.30/297.02 Computation stopped due to timeout after 297.0 seconds. 976.30/297.02 976.30/297.02 2) 'Best' failed due to the following reason: 976.30/297.02 976.30/297.02 None of the processors succeeded. 976.30/297.02 976.30/297.02 Details of failed attempt(s): 976.30/297.02 ----------------------------- 976.30/297.02 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 976.30/297.02 seconds)' failed due to the following reason: 976.30/297.02 976.30/297.02 Computation stopped due to timeout after 148.0 seconds. 976.30/297.02 976.30/297.02 2) 'Best' failed due to the following reason: 976.30/297.02 976.30/297.02 None of the processors succeeded. 976.30/297.02 976.30/297.02 Details of failed attempt(s): 976.30/297.02 ----------------------------- 976.30/297.02 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 976.30/297.02 following reason: 976.30/297.02 976.30/297.02 The input cannot be shown compatible 976.30/297.02 976.30/297.02 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 976.30/297.02 to the following reason: 976.30/297.02 976.30/297.02 The input cannot be shown compatible 976.30/297.02 976.30/297.02 976.30/297.02 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 976.30/297.02 failed due to the following reason: 976.30/297.02 976.30/297.02 None of the processors succeeded. 976.30/297.02 976.30/297.02 Details of failed attempt(s): 976.30/297.02 ----------------------------- 976.30/297.02 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 976.30/297.02 failed due to the following reason: 976.30/297.02 976.30/297.02 match-boundness of the problem could not be verified. 976.30/297.02 976.30/297.02 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 976.30/297.02 failed due to the following reason: 976.30/297.02 976.30/297.02 match-boundness of the problem could not be verified. 976.30/297.02 976.30/297.02 976.30/297.02 976.30/297.02 976.30/297.02 976.30/297.02 Arrrr.. 976.41/297.19 EOF