MAYBE 553.23/158.70 MAYBE 553.23/158.70 553.23/158.70 We are left with following problem, upon which TcT provides the 553.23/158.70 certificate MAYBE. 553.23/158.70 553.23/158.70 Strict Trs: 553.23/158.70 { half(x) -> if(ge(x, s(s(0()))), x) 553.23/158.70 , if(false(), x) -> 0() 553.23/158.70 , if(true(), x) -> s(half(p(p(x)))) 553.23/158.70 , ge(x, 0()) -> true() 553.23/158.70 , ge(s(x), s(y)) -> ge(x, y) 553.23/158.70 , ge(0(), s(x)) -> false() 553.23/158.70 , p(s(x)) -> x 553.23/158.70 , p(0()) -> 0() 553.23/158.70 , log(s(x)) -> s(log(half(s(x)))) 553.23/158.70 , log(0()) -> 0() } 553.23/158.70 Obligation: 553.23/158.70 runtime complexity 553.23/158.70 Answer: 553.23/158.70 MAYBE 553.23/158.70 553.23/158.70 None of the processors succeeded. 553.23/158.70 553.23/158.70 Details of failed attempt(s): 553.23/158.70 ----------------------------- 553.23/158.70 1) 'Best' failed due to the following reason: 553.23/158.70 553.23/158.70 None of the processors succeeded. 553.23/158.70 553.23/158.70 Details of failed attempt(s): 553.23/158.70 ----------------------------- 553.23/158.70 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 553.23/158.70 seconds)' failed due to the following reason: 553.23/158.70 553.23/158.70 Computation stopped due to timeout after 148.0 seconds. 553.23/158.70 553.23/158.70 2) 'Best' failed due to the following reason: 553.23/158.70 553.23/158.70 None of the processors succeeded. 553.23/158.70 553.23/158.70 Details of failed attempt(s): 553.23/158.70 ----------------------------- 553.23/158.70 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 553.23/158.70 following reason: 553.23/158.70 553.23/158.70 The processor is inapplicable, reason: 553.23/158.70 Processor only applicable for innermost runtime complexity analysis 553.23/158.70 553.23/158.70 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 553.23/158.70 to the following reason: 553.23/158.70 553.23/158.70 The processor is inapplicable, reason: 553.23/158.70 Processor only applicable for innermost runtime complexity analysis 553.23/158.70 553.23/158.70 553.23/158.70 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 553.23/158.70 failed due to the following reason: 553.23/158.70 553.23/158.70 None of the processors succeeded. 553.23/158.70 553.23/158.70 Details of failed attempt(s): 553.23/158.70 ----------------------------- 553.23/158.70 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 553.23/158.70 failed due to the following reason: 553.23/158.70 553.23/158.70 match-boundness of the problem could not be verified. 553.23/158.70 553.23/158.70 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 553.23/158.70 failed due to the following reason: 553.23/158.70 553.23/158.70 match-boundness of the problem could not be verified. 553.23/158.70 553.23/158.70 553.23/158.70 553.23/158.70 2) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 553.23/158.70 the following reason: 553.23/158.70 553.23/158.70 We add the following weak dependency pairs: 553.23/158.70 553.23/158.70 Strict DPs: 553.23/158.70 { half^#(x) -> c_1(if^#(ge(x, s(s(0()))), x)) 553.23/158.70 , if^#(false(), x) -> c_2() 553.23/158.70 , if^#(true(), x) -> c_3(half^#(p(p(x)))) 553.23/158.70 , ge^#(x, 0()) -> c_4() 553.23/158.70 , ge^#(s(x), s(y)) -> c_5(ge^#(x, y)) 553.23/158.70 , ge^#(0(), s(x)) -> c_6() 553.23/158.70 , p^#(s(x)) -> c_7(x) 553.23/158.70 , p^#(0()) -> c_8() 553.23/158.70 , log^#(s(x)) -> c_9(log^#(half(s(x)))) 553.23/158.70 , log^#(0()) -> c_10() } 553.23/158.70 553.23/158.70 and mark the set of starting terms. 553.23/158.70 553.23/158.70 We are left with following problem, upon which TcT provides the 553.23/158.70 certificate MAYBE. 553.23/158.70 553.23/158.70 Strict DPs: 553.23/158.70 { half^#(x) -> c_1(if^#(ge(x, s(s(0()))), x)) 553.23/158.70 , if^#(false(), x) -> c_2() 553.23/158.70 , if^#(true(), x) -> c_3(half^#(p(p(x)))) 553.23/158.70 , ge^#(x, 0()) -> c_4() 553.23/158.70 , ge^#(s(x), s(y)) -> c_5(ge^#(x, y)) 553.23/158.70 , ge^#(0(), s(x)) -> c_6() 553.23/158.70 , p^#(s(x)) -> c_7(x) 553.23/158.70 , p^#(0()) -> c_8() 553.23/158.70 , log^#(s(x)) -> c_9(log^#(half(s(x)))) 553.23/158.70 , log^#(0()) -> c_10() } 553.23/158.70 Strict Trs: 553.23/158.70 { half(x) -> if(ge(x, s(s(0()))), x) 553.23/158.70 , if(false(), x) -> 0() 553.23/158.70 , if(true(), x) -> s(half(p(p(x)))) 553.23/158.70 , ge(x, 0()) -> true() 553.23/158.70 , ge(s(x), s(y)) -> ge(x, y) 553.23/158.70 , ge(0(), s(x)) -> false() 553.23/158.70 , p(s(x)) -> x 553.23/158.70 , p(0()) -> 0() 553.23/158.70 , log(s(x)) -> s(log(half(s(x)))) 553.23/158.70 , log(0()) -> 0() } 553.23/158.70 Obligation: 553.23/158.70 runtime complexity 553.23/158.70 Answer: 553.23/158.70 MAYBE 553.23/158.70 553.23/158.70 We estimate the number of application of {2,4,6,8,10} by 553.23/158.70 applications of Pre({2,4,6,8,10}) = {1,5,7,9}. Here rules are 553.23/158.70 labeled as follows: 553.23/158.70 553.23/158.70 DPs: 553.23/158.70 { 1: half^#(x) -> c_1(if^#(ge(x, s(s(0()))), x)) 553.23/158.70 , 2: if^#(false(), x) -> c_2() 553.23/158.70 , 3: if^#(true(), x) -> c_3(half^#(p(p(x)))) 553.23/158.70 , 4: ge^#(x, 0()) -> c_4() 553.23/158.70 , 5: ge^#(s(x), s(y)) -> c_5(ge^#(x, y)) 553.23/158.70 , 6: ge^#(0(), s(x)) -> c_6() 553.23/158.70 , 7: p^#(s(x)) -> c_7(x) 553.23/158.70 , 8: p^#(0()) -> c_8() 553.23/158.70 , 9: log^#(s(x)) -> c_9(log^#(half(s(x)))) 553.23/158.70 , 10: log^#(0()) -> c_10() } 553.23/158.70 553.23/158.70 We are left with following problem, upon which TcT provides the 553.23/158.70 certificate MAYBE. 553.23/158.70 553.23/158.70 Strict DPs: 553.23/158.70 { half^#(x) -> c_1(if^#(ge(x, s(s(0()))), x)) 553.23/158.70 , if^#(true(), x) -> c_3(half^#(p(p(x)))) 553.23/158.70 , ge^#(s(x), s(y)) -> c_5(ge^#(x, y)) 553.23/158.70 , p^#(s(x)) -> c_7(x) 553.23/158.70 , log^#(s(x)) -> c_9(log^#(half(s(x)))) } 553.23/158.70 Strict Trs: 553.23/158.70 { half(x) -> if(ge(x, s(s(0()))), x) 553.23/158.70 , if(false(), x) -> 0() 553.23/158.70 , if(true(), x) -> s(half(p(p(x)))) 553.23/158.70 , ge(x, 0()) -> true() 553.23/158.70 , ge(s(x), s(y)) -> ge(x, y) 553.23/158.70 , ge(0(), s(x)) -> false() 553.23/158.70 , p(s(x)) -> x 553.23/158.70 , p(0()) -> 0() 553.23/158.70 , log(s(x)) -> s(log(half(s(x)))) 553.23/158.70 , log(0()) -> 0() } 553.23/158.70 Weak DPs: 553.23/158.70 { if^#(false(), x) -> c_2() 553.23/158.70 , ge^#(x, 0()) -> c_4() 553.23/158.70 , ge^#(0(), s(x)) -> c_6() 553.23/158.70 , p^#(0()) -> c_8() 553.23/158.70 , log^#(0()) -> c_10() } 553.23/158.70 Obligation: 553.23/158.70 runtime complexity 553.23/158.70 Answer: 553.23/158.70 MAYBE 553.23/158.70 553.23/158.70 Empty strict component of the problem is NOT empty. 553.23/158.70 553.23/158.70 553.23/158.70 Arrrr.. 553.64/159.16 EOF