MAYBE 1032.64/297.03 MAYBE 1032.64/297.03 1032.64/297.03 We are left with following problem, upon which TcT provides the 1032.64/297.03 certificate MAYBE. 1032.64/297.03 1032.64/297.03 Strict Trs: 1032.64/297.03 { minus(x, 0()) -> x 1032.64/297.03 , minus(minus(x, y), z) -> minus(x, plus(y, z)) 1032.64/297.03 , minus(s(x), s(y)) -> minus(x, y) 1032.64/297.03 , quot(0(), s(y)) -> 0() 1032.64/297.03 , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 1032.64/297.03 , plus(0(), y) -> y 1032.64/297.03 , plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x)) 1032.64/297.03 , plus(s(x), y) -> s(plus(x, y)) 1032.64/297.03 , plus(s(x), s(y)) -> 1032.64/297.03 s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))) 1032.64/297.03 , plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y)))) 1032.64/297.03 , plus(zero(), y) -> y 1032.64/297.03 , app(l, nil()) -> l 1032.64/297.03 , app(nil(), k) -> k 1032.64/297.03 , app(cons(x, l), k) -> cons(x, app(l, k)) 1032.64/297.03 , sum(app(l, cons(x, cons(y, k)))) -> 1032.64/297.03 sum(app(l, sum(cons(x, cons(y, k))))) 1032.64/297.03 , sum(cons(x, nil())) -> cons(x, nil()) 1032.64/297.03 , sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)) 1032.64/297.03 , if(true(), x, y) -> x 1032.64/297.03 , if(false(), x, y) -> y 1032.64/297.03 , gt(s(x), s(y)) -> gt(x, y) 1032.64/297.03 , gt(s(x), zero()) -> true() 1032.64/297.03 , gt(zero(), y) -> false() 1032.64/297.03 , not(x) -> if(x, false(), true()) 1032.64/297.03 , id(x) -> x } 1032.64/297.03 Obligation: 1032.64/297.03 innermost runtime complexity 1032.64/297.03 Answer: 1032.64/297.03 MAYBE 1032.64/297.03 1032.64/297.03 Arguments of following rules are not normal-forms: 1032.64/297.03 1032.64/297.03 { plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y)))) } 1032.64/297.03 1032.64/297.03 All above mentioned rules can be savely removed. 1032.64/297.03 1032.64/297.03 We are left with following problem, upon which TcT provides the 1032.64/297.03 certificate MAYBE. 1032.64/297.03 1032.64/297.03 Strict Trs: 1032.64/297.03 { minus(x, 0()) -> x 1032.64/297.03 , minus(minus(x, y), z) -> minus(x, plus(y, z)) 1032.64/297.03 , minus(s(x), s(y)) -> minus(x, y) 1032.64/297.03 , quot(0(), s(y)) -> 0() 1032.64/297.03 , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 1032.64/297.03 , plus(0(), y) -> y 1032.64/297.03 , plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x)) 1032.64/297.03 , plus(s(x), y) -> s(plus(x, y)) 1032.64/297.03 , plus(s(x), s(y)) -> 1032.64/297.03 s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))) 1032.64/297.03 , plus(zero(), y) -> y 1032.64/297.03 , app(l, nil()) -> l 1032.64/297.03 , app(nil(), k) -> k 1032.64/297.03 , app(cons(x, l), k) -> cons(x, app(l, k)) 1032.64/297.03 , sum(app(l, cons(x, cons(y, k)))) -> 1032.64/297.03 sum(app(l, sum(cons(x, cons(y, k))))) 1032.64/297.03 , sum(cons(x, nil())) -> cons(x, nil()) 1032.64/297.03 , sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)) 1032.64/297.03 , if(true(), x, y) -> x 1032.64/297.03 , if(false(), x, y) -> y 1032.64/297.03 , gt(s(x), s(y)) -> gt(x, y) 1032.64/297.03 , gt(s(x), zero()) -> true() 1032.64/297.03 , gt(zero(), y) -> false() 1032.64/297.03 , not(x) -> if(x, false(), true()) 1032.64/297.03 , id(x) -> x } 1032.64/297.03 Obligation: 1032.64/297.03 innermost runtime complexity 1032.64/297.03 Answer: 1032.64/297.03 MAYBE 1032.64/297.03 1032.64/297.03 None of the processors succeeded. 1032.64/297.03 1032.64/297.03 Details of failed attempt(s): 1032.64/297.03 ----------------------------- 1032.64/297.03 1) 'empty' failed due to the following reason: 1032.64/297.03 1032.64/297.03 Empty strict component of the problem is NOT empty. 1032.64/297.03 1032.64/297.03 2) 'Best' failed due to the following reason: 1032.64/297.03 1032.64/297.03 None of the processors succeeded. 1032.64/297.03 1032.64/297.03 Details of failed attempt(s): 1032.64/297.03 ----------------------------- 1032.64/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1032.64/297.03 following reason: 1032.64/297.03 1032.64/297.03 Computation stopped due to timeout after 297.0 seconds. 1032.64/297.03 1032.64/297.03 2) 'Best' failed due to the following reason: 1032.64/297.03 1032.64/297.03 None of the processors succeeded. 1032.64/297.03 1032.64/297.03 Details of failed attempt(s): 1032.64/297.03 ----------------------------- 1032.64/297.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1032.64/297.03 seconds)' failed due to the following reason: 1032.64/297.03 1032.64/297.03 Computation stopped due to timeout after 148.0 seconds. 1032.64/297.03 1032.64/297.03 2) 'Best' failed due to the following reason: 1032.64/297.03 1032.64/297.03 None of the processors succeeded. 1032.64/297.03 1032.64/297.03 Details of failed attempt(s): 1032.64/297.03 ----------------------------- 1032.64/297.03 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1032.64/297.03 to the following reason: 1032.64/297.03 1032.64/297.03 The input cannot be shown compatible 1032.64/297.03 1032.64/297.03 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1032.64/297.03 following reason: 1032.64/297.03 1032.64/297.03 The input cannot be shown compatible 1032.64/297.03 1032.64/297.03 1032.64/297.03 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1032.64/297.03 failed due to the following reason: 1032.64/297.03 1032.64/297.03 None of the processors succeeded. 1032.64/297.03 1032.64/297.03 Details of failed attempt(s): 1032.64/297.03 ----------------------------- 1032.64/297.03 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1032.64/297.03 failed due to the following reason: 1032.64/297.03 1032.64/297.03 match-boundness of the problem could not be verified. 1032.64/297.03 1032.64/297.03 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1032.64/297.03 failed due to the following reason: 1032.64/297.03 1032.64/297.03 match-boundness of the problem could not be verified. 1032.64/297.03 1032.64/297.03 1032.64/297.03 1032.64/297.03 1032.64/297.03 1032.64/297.03 Arrrr.. 1032.76/297.11 EOF