MAYBE 865.33/297.03 MAYBE 865.33/297.03 865.33/297.03 We are left with following problem, upon which TcT provides the 865.33/297.03 certificate MAYBE. 865.33/297.03 865.33/297.03 Strict Trs: 865.33/297.03 { app(l, nil()) -> l 865.33/297.03 , app(nil(), k) -> k 865.33/297.03 , app(cons(x, l), k) -> cons(x, app(l, k)) 865.33/297.03 , sum(app(l, cons(x, cons(y, k)))) -> 865.33/297.03 sum(app(l, sum(cons(x, cons(y, k))))) 865.33/297.03 , sum(cons(x, nil())) -> cons(x, nil()) 865.33/297.03 , sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)) 865.33/297.03 , plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x)) 865.33/297.03 , plus(s(x), s(y)) -> 865.33/297.03 s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))) 865.33/297.03 , plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y)))) 865.33/297.03 , plus(zero(), y) -> y 865.33/297.03 , if(true(), x, y) -> x 865.33/297.03 , if(false(), x, y) -> y 865.33/297.03 , gt(s(x), s(y)) -> gt(x, y) 865.33/297.03 , gt(s(x), zero()) -> true() 865.33/297.03 , gt(zero(), y) -> false() 865.33/297.03 , not(x) -> if(x, false(), true()) 865.33/297.03 , id(x) -> x } 865.33/297.03 Obligation: 865.33/297.03 runtime complexity 865.33/297.03 Answer: 865.33/297.03 MAYBE 865.33/297.03 865.33/297.03 None of the processors succeeded. 865.33/297.03 865.33/297.03 Details of failed attempt(s): 865.33/297.03 ----------------------------- 865.33/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 865.33/297.03 following reason: 865.33/297.03 865.33/297.03 Computation stopped due to timeout after 297.0 seconds. 865.33/297.03 865.33/297.03 2) 'Best' failed due to the following reason: 865.33/297.03 865.33/297.03 None of the processors succeeded. 865.33/297.03 865.33/297.03 Details of failed attempt(s): 865.33/297.03 ----------------------------- 865.33/297.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 865.33/297.03 seconds)' failed due to the following reason: 865.33/297.03 865.33/297.03 Computation stopped due to timeout after 148.0 seconds. 865.33/297.03 865.33/297.03 2) 'Best' failed due to the following reason: 865.33/297.03 865.33/297.03 None of the processors succeeded. 865.33/297.03 865.33/297.03 Details of failed attempt(s): 865.33/297.03 ----------------------------- 865.33/297.03 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 865.33/297.03 following reason: 865.33/297.03 865.33/297.03 The processor is inapplicable, reason: 865.33/297.03 Processor only applicable for innermost runtime complexity analysis 865.33/297.03 865.33/297.03 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 865.33/297.03 to the following reason: 865.33/297.03 865.33/297.03 The processor is inapplicable, reason: 865.33/297.03 Processor only applicable for innermost runtime complexity analysis 865.33/297.03 865.33/297.03 865.33/297.03 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 865.33/297.03 failed due to the following reason: 865.33/297.03 865.33/297.03 None of the processors succeeded. 865.33/297.03 865.33/297.03 Details of failed attempt(s): 865.33/297.03 ----------------------------- 865.33/297.03 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 865.33/297.03 failed due to the following reason: 865.33/297.03 865.33/297.03 match-boundness of the problem could not be verified. 865.33/297.03 865.33/297.03 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 865.33/297.03 failed due to the following reason: 865.33/297.03 865.33/297.03 match-boundness of the problem could not be verified. 865.33/297.03 865.33/297.03 865.33/297.03 865.33/297.03 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 865.33/297.03 the following reason: 865.33/297.03 865.33/297.03 We add the following weak dependency pairs: 865.33/297.03 865.33/297.03 Strict DPs: 865.33/297.03 { app^#(l, nil()) -> c_1(l) 865.33/297.03 , app^#(nil(), k) -> c_2(k) 865.33/297.03 , app^#(cons(x, l), k) -> c_3(x, app^#(l, k)) 865.33/297.03 , sum^#(app(l, cons(x, cons(y, k)))) -> 865.33/297.03 c_4(sum^#(app(l, sum(cons(x, cons(y, k)))))) 865.33/297.03 , sum^#(cons(x, nil())) -> c_5(x) 865.33/297.03 , sum^#(cons(x, cons(y, l))) -> c_6(sum^#(cons(plus(x, y), l))) 865.33/297.03 , plus^#(s(x), x) -> c_7(plus^#(if(gt(x, x), id(x), id(x)), s(x))) 865.33/297.03 , plus^#(s(x), s(y)) -> 865.33/297.03 c_8(plus^#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))) 865.33/297.03 , plus^#(id(x), s(y)) -> c_9(plus^#(x, if(gt(s(y), y), y, s(y)))) 865.33/297.03 , plus^#(zero(), y) -> c_10(y) 865.33/297.03 , if^#(true(), x, y) -> c_11(x) 865.33/297.03 , if^#(false(), x, y) -> c_12(y) 865.33/297.03 , gt^#(s(x), s(y)) -> c_13(gt^#(x, y)) 865.33/297.03 , gt^#(s(x), zero()) -> c_14() 865.33/297.03 , gt^#(zero(), y) -> c_15() 865.33/297.03 , not^#(x) -> c_16(if^#(x, false(), true())) 865.33/297.03 , id^#(x) -> c_17(x) } 865.33/297.03 865.33/297.03 and mark the set of starting terms. 865.33/297.03 865.33/297.03 We are left with following problem, upon which TcT provides the 865.33/297.03 certificate MAYBE. 865.33/297.03 865.33/297.03 Strict DPs: 865.33/297.03 { app^#(l, nil()) -> c_1(l) 865.33/297.03 , app^#(nil(), k) -> c_2(k) 865.33/297.03 , app^#(cons(x, l), k) -> c_3(x, app^#(l, k)) 865.33/297.03 , sum^#(app(l, cons(x, cons(y, k)))) -> 865.33/297.03 c_4(sum^#(app(l, sum(cons(x, cons(y, k)))))) 865.33/297.03 , sum^#(cons(x, nil())) -> c_5(x) 865.33/297.03 , sum^#(cons(x, cons(y, l))) -> c_6(sum^#(cons(plus(x, y), l))) 865.33/297.03 , plus^#(s(x), x) -> c_7(plus^#(if(gt(x, x), id(x), id(x)), s(x))) 865.33/297.03 , plus^#(s(x), s(y)) -> 865.33/297.03 c_8(plus^#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))) 865.33/297.03 , plus^#(id(x), s(y)) -> c_9(plus^#(x, if(gt(s(y), y), y, s(y)))) 865.33/297.03 , plus^#(zero(), y) -> c_10(y) 865.33/297.03 , if^#(true(), x, y) -> c_11(x) 865.33/297.03 , if^#(false(), x, y) -> c_12(y) 865.33/297.03 , gt^#(s(x), s(y)) -> c_13(gt^#(x, y)) 865.33/297.03 , gt^#(s(x), zero()) -> c_14() 865.33/297.03 , gt^#(zero(), y) -> c_15() 865.33/297.03 , not^#(x) -> c_16(if^#(x, false(), true())) 865.33/297.03 , id^#(x) -> c_17(x) } 865.33/297.03 Strict Trs: 865.33/297.03 { app(l, nil()) -> l 865.33/297.03 , app(nil(), k) -> k 865.33/297.03 , app(cons(x, l), k) -> cons(x, app(l, k)) 865.33/297.03 , sum(app(l, cons(x, cons(y, k)))) -> 865.33/297.03 sum(app(l, sum(cons(x, cons(y, k))))) 865.33/297.03 , sum(cons(x, nil())) -> cons(x, nil()) 865.33/297.03 , sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)) 865.33/297.03 , plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x)) 865.33/297.03 , plus(s(x), s(y)) -> 865.33/297.03 s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))) 865.33/297.03 , plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y)))) 865.33/297.03 , plus(zero(), y) -> y 865.33/297.03 , if(true(), x, y) -> x 865.33/297.03 , if(false(), x, y) -> y 865.33/297.03 , gt(s(x), s(y)) -> gt(x, y) 865.33/297.03 , gt(s(x), zero()) -> true() 865.33/297.03 , gt(zero(), y) -> false() 865.33/297.03 , not(x) -> if(x, false(), true()) 865.33/297.03 , id(x) -> x } 865.33/297.03 Obligation: 865.33/297.03 runtime complexity 865.33/297.03 Answer: 865.33/297.03 MAYBE 865.33/297.03 865.33/297.03 We estimate the number of application of {14,15} by applications of 865.33/297.03 Pre({14,15}) = {1,2,3,5,10,11,12,13,17}. Here rules are labeled as 865.33/297.03 follows: 865.33/297.03 865.33/297.03 DPs: 865.33/297.03 { 1: app^#(l, nil()) -> c_1(l) 865.33/297.03 , 2: app^#(nil(), k) -> c_2(k) 865.33/297.03 , 3: app^#(cons(x, l), k) -> c_3(x, app^#(l, k)) 865.33/297.03 , 4: sum^#(app(l, cons(x, cons(y, k)))) -> 865.33/297.03 c_4(sum^#(app(l, sum(cons(x, cons(y, k)))))) 865.33/297.03 , 5: sum^#(cons(x, nil())) -> c_5(x) 865.33/297.03 , 6: sum^#(cons(x, cons(y, l))) -> c_6(sum^#(cons(plus(x, y), l))) 865.33/297.03 , 7: plus^#(s(x), x) -> 865.33/297.03 c_7(plus^#(if(gt(x, x), id(x), id(x)), s(x))) 865.33/297.03 , 8: plus^#(s(x), s(y)) -> 865.33/297.03 c_8(plus^#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))) 865.33/297.03 , 9: plus^#(id(x), s(y)) -> 865.33/297.03 c_9(plus^#(x, if(gt(s(y), y), y, s(y)))) 865.33/297.03 , 10: plus^#(zero(), y) -> c_10(y) 865.33/297.03 , 11: if^#(true(), x, y) -> c_11(x) 865.33/297.03 , 12: if^#(false(), x, y) -> c_12(y) 865.33/297.03 , 13: gt^#(s(x), s(y)) -> c_13(gt^#(x, y)) 865.33/297.03 , 14: gt^#(s(x), zero()) -> c_14() 865.33/297.03 , 15: gt^#(zero(), y) -> c_15() 865.33/297.03 , 16: not^#(x) -> c_16(if^#(x, false(), true())) 865.33/297.03 , 17: id^#(x) -> c_17(x) } 865.33/297.03 865.33/297.03 We are left with following problem, upon which TcT provides the 865.33/297.03 certificate MAYBE. 865.33/297.03 865.33/297.03 Strict DPs: 865.33/297.03 { app^#(l, nil()) -> c_1(l) 865.33/297.03 , app^#(nil(), k) -> c_2(k) 865.33/297.03 , app^#(cons(x, l), k) -> c_3(x, app^#(l, k)) 865.33/297.03 , sum^#(app(l, cons(x, cons(y, k)))) -> 865.33/297.03 c_4(sum^#(app(l, sum(cons(x, cons(y, k)))))) 865.33/297.03 , sum^#(cons(x, nil())) -> c_5(x) 865.33/297.03 , sum^#(cons(x, cons(y, l))) -> c_6(sum^#(cons(plus(x, y), l))) 865.33/297.03 , plus^#(s(x), x) -> c_7(plus^#(if(gt(x, x), id(x), id(x)), s(x))) 865.33/297.03 , plus^#(s(x), s(y)) -> 865.33/297.03 c_8(plus^#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))) 865.33/297.03 , plus^#(id(x), s(y)) -> c_9(plus^#(x, if(gt(s(y), y), y, s(y)))) 865.33/297.03 , plus^#(zero(), y) -> c_10(y) 865.33/297.03 , if^#(true(), x, y) -> c_11(x) 865.33/297.03 , if^#(false(), x, y) -> c_12(y) 865.33/297.03 , gt^#(s(x), s(y)) -> c_13(gt^#(x, y)) 865.33/297.03 , not^#(x) -> c_16(if^#(x, false(), true())) 865.33/297.03 , id^#(x) -> c_17(x) } 865.33/297.03 Strict Trs: 865.33/297.03 { app(l, nil()) -> l 865.33/297.03 , app(nil(), k) -> k 865.33/297.03 , app(cons(x, l), k) -> cons(x, app(l, k)) 865.33/297.03 , sum(app(l, cons(x, cons(y, k)))) -> 865.33/297.03 sum(app(l, sum(cons(x, cons(y, k))))) 865.33/297.03 , sum(cons(x, nil())) -> cons(x, nil()) 865.33/297.03 , sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)) 865.33/297.03 , plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x)) 865.33/297.03 , plus(s(x), s(y)) -> 865.33/297.03 s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))) 865.33/297.03 , plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y)))) 865.33/297.03 , plus(zero(), y) -> y 865.33/297.03 , if(true(), x, y) -> x 865.33/297.03 , if(false(), x, y) -> y 865.33/297.03 , gt(s(x), s(y)) -> gt(x, y) 865.33/297.03 , gt(s(x), zero()) -> true() 865.33/297.03 , gt(zero(), y) -> false() 865.33/297.03 , not(x) -> if(x, false(), true()) 865.33/297.03 , id(x) -> x } 865.33/297.03 Weak DPs: 865.33/297.03 { gt^#(s(x), zero()) -> c_14() 865.33/297.03 , gt^#(zero(), y) -> c_15() } 865.33/297.03 Obligation: 865.33/297.03 runtime complexity 865.33/297.03 Answer: 865.33/297.03 MAYBE 865.33/297.03 865.33/297.03 Empty strict component of the problem is NOT empty. 865.33/297.03 865.33/297.03 865.33/297.03 Arrrr.. 865.45/297.19 EOF