MAYBE 823.60/297.04 MAYBE 823.60/297.04 823.60/297.04 We are left with following problem, upon which TcT provides the 823.60/297.04 certificate MAYBE. 823.60/297.04 823.60/297.04 Strict Trs: 823.60/297.04 { times(x, 0()) -> 0() 823.60/297.04 , times(x, s(y)) -> plus(times(x, y), x) 823.60/297.04 , plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x)) 823.60/297.04 , plus(s(x), s(y)) -> 823.60/297.04 s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))) 823.60/297.04 , plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y)))) 823.60/297.04 , plus(zero(), y) -> y 823.60/297.04 , if(true(), x, y) -> x 823.60/297.04 , if(false(), x, y) -> y 823.60/297.04 , gt(s(x), s(y)) -> gt(x, y) 823.60/297.04 , gt(s(x), zero()) -> true() 823.60/297.04 , gt(zero(), y) -> false() 823.60/297.04 , not(x) -> if(x, false(), true()) 823.60/297.04 , id(x) -> x } 823.60/297.04 Obligation: 823.60/297.04 runtime complexity 823.60/297.04 Answer: 823.60/297.04 MAYBE 823.60/297.04 823.60/297.04 None of the processors succeeded. 823.60/297.04 823.60/297.04 Details of failed attempt(s): 823.60/297.04 ----------------------------- 823.60/297.04 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 823.60/297.04 following reason: 823.60/297.04 823.60/297.04 Computation stopped due to timeout after 297.0 seconds. 823.60/297.04 823.60/297.04 2) 'Best' failed due to the following reason: 823.60/297.04 823.60/297.04 None of the processors succeeded. 823.60/297.04 823.60/297.04 Details of failed attempt(s): 823.60/297.04 ----------------------------- 823.60/297.04 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 823.60/297.04 seconds)' failed due to the following reason: 823.60/297.04 823.60/297.04 Computation stopped due to timeout after 148.0 seconds. 823.60/297.04 823.60/297.04 2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 823.60/297.04 failed due to the following reason: 823.60/297.04 823.60/297.04 None of the processors succeeded. 823.60/297.04 823.60/297.04 Details of failed attempt(s): 823.60/297.04 ----------------------------- 823.60/297.04 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 823.60/297.04 failed due to the following reason: 823.60/297.04 823.60/297.04 match-boundness of the problem could not be verified. 823.60/297.04 823.60/297.04 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 823.60/297.04 failed due to the following reason: 823.60/297.04 823.60/297.04 match-boundness of the problem could not be verified. 823.60/297.04 823.60/297.04 823.60/297.04 3) 'Best' failed due to the following reason: 823.60/297.04 823.60/297.04 None of the processors succeeded. 823.60/297.04 823.60/297.04 Details of failed attempt(s): 823.60/297.04 ----------------------------- 823.60/297.04 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 823.60/297.04 following reason: 823.60/297.04 823.60/297.04 The processor is inapplicable, reason: 823.60/297.04 Processor only applicable for innermost runtime complexity analysis 823.60/297.04 823.60/297.04 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 823.60/297.04 to the following reason: 823.60/297.04 823.60/297.04 The processor is inapplicable, reason: 823.60/297.04 Processor only applicable for innermost runtime complexity analysis 823.60/297.04 823.60/297.04 823.60/297.04 823.60/297.04 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 823.60/297.04 the following reason: 823.60/297.04 823.60/297.04 We add the following weak dependency pairs: 823.60/297.04 823.60/297.04 Strict DPs: 823.60/297.04 { times^#(x, 0()) -> c_1() 823.60/297.04 , times^#(x, s(y)) -> c_2(plus^#(times(x, y), x)) 823.60/297.04 , plus^#(s(x), x) -> c_3(plus^#(if(gt(x, x), id(x), id(x)), s(x))) 823.60/297.04 , plus^#(s(x), s(y)) -> 823.60/297.04 c_4(plus^#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))) 823.60/297.04 , plus^#(id(x), s(y)) -> c_5(plus^#(x, if(gt(s(y), y), y, s(y)))) 823.60/297.04 , plus^#(zero(), y) -> c_6(y) 823.60/297.04 , if^#(true(), x, y) -> c_7(x) 823.60/297.04 , if^#(false(), x, y) -> c_8(y) 823.60/297.04 , gt^#(s(x), s(y)) -> c_9(gt^#(x, y)) 823.60/297.04 , gt^#(s(x), zero()) -> c_10() 823.60/297.04 , gt^#(zero(), y) -> c_11() 823.60/297.04 , not^#(x) -> c_12(if^#(x, false(), true())) 823.60/297.04 , id^#(x) -> c_13(x) } 823.60/297.04 823.60/297.04 and mark the set of starting terms. 823.60/297.04 823.60/297.04 We are left with following problem, upon which TcT provides the 823.60/297.04 certificate MAYBE. 823.60/297.04 823.60/297.04 Strict DPs: 823.60/297.04 { times^#(x, 0()) -> c_1() 823.60/297.04 , times^#(x, s(y)) -> c_2(plus^#(times(x, y), x)) 823.60/297.04 , plus^#(s(x), x) -> c_3(plus^#(if(gt(x, x), id(x), id(x)), s(x))) 823.60/297.04 , plus^#(s(x), s(y)) -> 823.60/297.04 c_4(plus^#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))) 823.60/297.04 , plus^#(id(x), s(y)) -> c_5(plus^#(x, if(gt(s(y), y), y, s(y)))) 823.60/297.04 , plus^#(zero(), y) -> c_6(y) 823.60/297.04 , if^#(true(), x, y) -> c_7(x) 823.60/297.04 , if^#(false(), x, y) -> c_8(y) 823.60/297.04 , gt^#(s(x), s(y)) -> c_9(gt^#(x, y)) 823.60/297.04 , gt^#(s(x), zero()) -> c_10() 823.60/297.04 , gt^#(zero(), y) -> c_11() 823.60/297.04 , not^#(x) -> c_12(if^#(x, false(), true())) 823.60/297.04 , id^#(x) -> c_13(x) } 823.60/297.04 Strict Trs: 823.60/297.04 { times(x, 0()) -> 0() 823.60/297.04 , times(x, s(y)) -> plus(times(x, y), x) 823.60/297.04 , plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x)) 823.60/297.04 , plus(s(x), s(y)) -> 823.60/297.04 s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))) 823.60/297.04 , plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y)))) 823.60/297.04 , plus(zero(), y) -> y 823.60/297.04 , if(true(), x, y) -> x 823.60/297.04 , if(false(), x, y) -> y 823.60/297.04 , gt(s(x), s(y)) -> gt(x, y) 823.60/297.04 , gt(s(x), zero()) -> true() 823.60/297.04 , gt(zero(), y) -> false() 823.60/297.04 , not(x) -> if(x, false(), true()) 823.60/297.04 , id(x) -> x } 823.60/297.04 Obligation: 823.60/297.04 runtime complexity 823.60/297.04 Answer: 823.60/297.04 MAYBE 823.60/297.04 823.60/297.04 We estimate the number of application of {1,10,11} by applications 823.60/297.04 of Pre({1,10,11}) = {6,7,8,9,13}. Here rules are labeled as 823.60/297.04 follows: 823.60/297.04 823.60/297.04 DPs: 823.60/297.04 { 1: times^#(x, 0()) -> c_1() 823.60/297.04 , 2: times^#(x, s(y)) -> c_2(plus^#(times(x, y), x)) 823.60/297.04 , 3: plus^#(s(x), x) -> 823.60/297.04 c_3(plus^#(if(gt(x, x), id(x), id(x)), s(x))) 823.60/297.04 , 4: plus^#(s(x), s(y)) -> 823.60/297.04 c_4(plus^#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))) 823.60/297.04 , 5: plus^#(id(x), s(y)) -> 823.60/297.04 c_5(plus^#(x, if(gt(s(y), y), y, s(y)))) 823.60/297.04 , 6: plus^#(zero(), y) -> c_6(y) 823.60/297.04 , 7: if^#(true(), x, y) -> c_7(x) 823.60/297.04 , 8: if^#(false(), x, y) -> c_8(y) 823.60/297.04 , 9: gt^#(s(x), s(y)) -> c_9(gt^#(x, y)) 823.60/297.04 , 10: gt^#(s(x), zero()) -> c_10() 823.60/297.04 , 11: gt^#(zero(), y) -> c_11() 823.60/297.04 , 12: not^#(x) -> c_12(if^#(x, false(), true())) 823.60/297.04 , 13: id^#(x) -> c_13(x) } 823.60/297.04 823.60/297.04 We are left with following problem, upon which TcT provides the 823.60/297.04 certificate MAYBE. 823.60/297.04 823.60/297.04 Strict DPs: 823.60/297.04 { times^#(x, s(y)) -> c_2(plus^#(times(x, y), x)) 823.60/297.04 , plus^#(s(x), x) -> c_3(plus^#(if(gt(x, x), id(x), id(x)), s(x))) 823.60/297.04 , plus^#(s(x), s(y)) -> 823.60/297.04 c_4(plus^#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))) 823.60/297.04 , plus^#(id(x), s(y)) -> c_5(plus^#(x, if(gt(s(y), y), y, s(y)))) 823.60/297.04 , plus^#(zero(), y) -> c_6(y) 823.60/297.04 , if^#(true(), x, y) -> c_7(x) 823.60/297.04 , if^#(false(), x, y) -> c_8(y) 823.60/297.04 , gt^#(s(x), s(y)) -> c_9(gt^#(x, y)) 823.60/297.04 , not^#(x) -> c_12(if^#(x, false(), true())) 823.60/297.04 , id^#(x) -> c_13(x) } 823.60/297.04 Strict Trs: 823.60/297.04 { times(x, 0()) -> 0() 823.60/297.04 , times(x, s(y)) -> plus(times(x, y), x) 823.60/297.04 , plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x)) 823.60/297.04 , plus(s(x), s(y)) -> 823.60/297.04 s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))) 823.60/297.04 , plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y)))) 823.60/297.04 , plus(zero(), y) -> y 823.60/297.04 , if(true(), x, y) -> x 823.60/297.04 , if(false(), x, y) -> y 823.60/297.04 , gt(s(x), s(y)) -> gt(x, y) 823.60/297.04 , gt(s(x), zero()) -> true() 823.60/297.04 , gt(zero(), y) -> false() 823.60/297.04 , not(x) -> if(x, false(), true()) 823.60/297.04 , id(x) -> x } 823.60/297.04 Weak DPs: 823.60/297.04 { times^#(x, 0()) -> c_1() 823.60/297.04 , gt^#(s(x), zero()) -> c_10() 823.60/297.04 , gt^#(zero(), y) -> c_11() } 823.60/297.04 Obligation: 823.60/297.04 runtime complexity 823.60/297.04 Answer: 823.60/297.04 MAYBE 823.60/297.04 823.60/297.04 Empty strict component of the problem is NOT empty. 823.60/297.04 823.60/297.04 823.60/297.04 Arrrr.. 823.82/297.25 EOF