MAYBE 602.49/245.34 MAYBE 602.49/245.34 602.49/245.34 We are left with following problem, upon which TcT provides the 602.49/245.34 certificate MAYBE. 602.49/245.34 602.49/245.34 Strict Trs: 602.49/245.34 { -(x, 0()) -> x 602.49/245.34 , -(0(), s(y)) -> 0() 602.49/245.34 , -(s(x), s(y)) -> -(x, y) 602.49/245.34 , lt(x, 0()) -> false() 602.49/245.34 , lt(0(), s(y)) -> true() 602.49/245.34 , lt(s(x), s(y)) -> lt(x, y) 602.49/245.34 , if(false(), x, y) -> y 602.49/245.34 , if(true(), x, y) -> x 602.49/245.34 , div(x, 0()) -> 0() 602.49/245.34 , div(0(), y) -> 0() 602.49/245.34 , div(s(x), s(y)) -> if(lt(x, y), 0(), s(div(-(x, y), s(y)))) } 602.49/245.34 Obligation: 602.49/245.34 runtime complexity 602.49/245.34 Answer: 602.49/245.34 MAYBE 602.49/245.34 602.49/245.34 None of the processors succeeded. 602.49/245.34 602.49/245.34 Details of failed attempt(s): 602.49/245.34 ----------------------------- 602.49/245.34 1) 'Best' failed due to the following reason: 602.49/245.34 602.49/245.34 None of the processors succeeded. 602.49/245.34 602.49/245.34 Details of failed attempt(s): 602.49/245.34 ----------------------------- 602.49/245.34 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 602.49/245.34 seconds)' failed due to the following reason: 602.49/245.34 602.49/245.34 Computation stopped due to timeout after 148.0 seconds. 602.49/245.34 602.49/245.34 2) 'Best' failed due to the following reason: 602.49/245.34 602.49/245.34 None of the processors succeeded. 602.49/245.34 602.49/245.34 Details of failed attempt(s): 602.49/245.34 ----------------------------- 602.49/245.34 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 602.49/245.34 following reason: 602.49/245.34 602.49/245.34 The processor is inapplicable, reason: 602.49/245.34 Processor only applicable for innermost runtime complexity analysis 602.49/245.34 602.49/245.34 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 602.49/245.34 to the following reason: 602.49/245.34 602.49/245.34 The processor is inapplicable, reason: 602.49/245.34 Processor only applicable for innermost runtime complexity analysis 602.49/245.34 602.49/245.34 602.49/245.34 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 602.49/245.34 failed due to the following reason: 602.49/245.34 602.49/245.34 None of the processors succeeded. 602.49/245.34 602.49/245.34 Details of failed attempt(s): 602.49/245.34 ----------------------------- 602.49/245.34 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 602.49/245.34 failed due to the following reason: 602.49/245.34 602.49/245.34 match-boundness of the problem could not be verified. 602.49/245.34 602.49/245.34 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 602.49/245.34 failed due to the following reason: 602.49/245.34 602.49/245.34 match-boundness of the problem could not be verified. 602.49/245.34 602.49/245.34 602.49/245.34 602.49/245.34 2) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 602.49/245.34 the following reason: 602.49/245.34 602.49/245.34 We add the following weak dependency pairs: 602.49/245.34 602.49/245.34 Strict DPs: 602.49/245.34 { -^#(x, 0()) -> c_1(x) 602.49/245.34 , -^#(0(), s(y)) -> c_2() 602.49/245.34 , -^#(s(x), s(y)) -> c_3(-^#(x, y)) 602.49/245.34 , lt^#(x, 0()) -> c_4() 602.49/245.34 , lt^#(0(), s(y)) -> c_5() 602.49/245.34 , lt^#(s(x), s(y)) -> c_6(lt^#(x, y)) 602.49/245.34 , if^#(false(), x, y) -> c_7(y) 602.49/245.34 , if^#(true(), x, y) -> c_8(x) 602.49/245.34 , div^#(x, 0()) -> c_9() 602.49/245.34 , div^#(0(), y) -> c_10() 602.49/245.34 , div^#(s(x), s(y)) -> 602.49/245.34 c_11(if^#(lt(x, y), 0(), s(div(-(x, y), s(y))))) } 602.49/245.34 602.49/245.34 and mark the set of starting terms. 602.49/245.34 602.49/245.34 We are left with following problem, upon which TcT provides the 602.49/245.34 certificate MAYBE. 602.49/245.34 602.49/245.34 Strict DPs: 602.49/245.34 { -^#(x, 0()) -> c_1(x) 602.49/245.34 , -^#(0(), s(y)) -> c_2() 602.49/245.34 , -^#(s(x), s(y)) -> c_3(-^#(x, y)) 602.49/245.34 , lt^#(x, 0()) -> c_4() 602.49/245.34 , lt^#(0(), s(y)) -> c_5() 602.49/245.34 , lt^#(s(x), s(y)) -> c_6(lt^#(x, y)) 602.49/245.34 , if^#(false(), x, y) -> c_7(y) 602.49/245.34 , if^#(true(), x, y) -> c_8(x) 602.49/245.34 , div^#(x, 0()) -> c_9() 602.49/245.34 , div^#(0(), y) -> c_10() 602.49/245.34 , div^#(s(x), s(y)) -> 602.49/245.34 c_11(if^#(lt(x, y), 0(), s(div(-(x, y), s(y))))) } 602.49/245.34 Strict Trs: 602.49/245.34 { -(x, 0()) -> x 602.49/245.34 , -(0(), s(y)) -> 0() 602.49/245.34 , -(s(x), s(y)) -> -(x, y) 602.49/245.34 , lt(x, 0()) -> false() 602.49/245.34 , lt(0(), s(y)) -> true() 602.49/245.34 , lt(s(x), s(y)) -> lt(x, y) 602.49/245.34 , if(false(), x, y) -> y 602.49/245.34 , if(true(), x, y) -> x 602.49/245.34 , div(x, 0()) -> 0() 602.49/245.34 , div(0(), y) -> 0() 602.49/245.34 , div(s(x), s(y)) -> if(lt(x, y), 0(), s(div(-(x, y), s(y)))) } 602.49/245.34 Obligation: 602.49/245.34 runtime complexity 602.49/245.34 Answer: 602.49/245.34 MAYBE 602.49/245.34 602.49/245.34 We estimate the number of application of {2,4,5,9,10} by 602.49/245.34 applications of Pre({2,4,5,9,10}) = {1,3,6,7,8}. Here rules are 602.49/245.34 labeled as follows: 602.49/245.34 602.49/245.34 DPs: 602.49/245.34 { 1: -^#(x, 0()) -> c_1(x) 602.49/245.34 , 2: -^#(0(), s(y)) -> c_2() 602.49/245.34 , 3: -^#(s(x), s(y)) -> c_3(-^#(x, y)) 602.49/245.34 , 4: lt^#(x, 0()) -> c_4() 602.49/245.34 , 5: lt^#(0(), s(y)) -> c_5() 602.49/245.34 , 6: lt^#(s(x), s(y)) -> c_6(lt^#(x, y)) 602.49/245.34 , 7: if^#(false(), x, y) -> c_7(y) 602.49/245.34 , 8: if^#(true(), x, y) -> c_8(x) 602.49/245.34 , 9: div^#(x, 0()) -> c_9() 602.49/245.34 , 10: div^#(0(), y) -> c_10() 602.49/245.34 , 11: div^#(s(x), s(y)) -> 602.49/245.34 c_11(if^#(lt(x, y), 0(), s(div(-(x, y), s(y))))) } 602.49/245.34 602.49/245.34 We are left with following problem, upon which TcT provides the 602.49/245.34 certificate MAYBE. 602.49/245.34 602.49/245.34 Strict DPs: 602.49/245.34 { -^#(x, 0()) -> c_1(x) 602.49/245.34 , -^#(s(x), s(y)) -> c_3(-^#(x, y)) 602.49/245.34 , lt^#(s(x), s(y)) -> c_6(lt^#(x, y)) 602.49/245.34 , if^#(false(), x, y) -> c_7(y) 602.49/245.34 , if^#(true(), x, y) -> c_8(x) 602.49/245.34 , div^#(s(x), s(y)) -> 602.49/245.34 c_11(if^#(lt(x, y), 0(), s(div(-(x, y), s(y))))) } 602.49/245.34 Strict Trs: 602.49/245.34 { -(x, 0()) -> x 602.49/245.34 , -(0(), s(y)) -> 0() 602.49/245.34 , -(s(x), s(y)) -> -(x, y) 602.49/245.34 , lt(x, 0()) -> false() 602.49/245.34 , lt(0(), s(y)) -> true() 602.49/245.34 , lt(s(x), s(y)) -> lt(x, y) 602.49/245.34 , if(false(), x, y) -> y 602.49/245.34 , if(true(), x, y) -> x 602.49/245.34 , div(x, 0()) -> 0() 602.49/245.34 , div(0(), y) -> 0() 602.49/245.34 , div(s(x), s(y)) -> if(lt(x, y), 0(), s(div(-(x, y), s(y)))) } 602.49/245.34 Weak DPs: 602.49/245.34 { -^#(0(), s(y)) -> c_2() 602.49/245.34 , lt^#(x, 0()) -> c_4() 602.49/245.34 , lt^#(0(), s(y)) -> c_5() 602.49/245.34 , div^#(x, 0()) -> c_9() 602.49/245.34 , div^#(0(), y) -> c_10() } 602.49/245.34 Obligation: 602.49/245.34 runtime complexity 602.49/245.34 Answer: 602.49/245.34 MAYBE 602.49/245.34 602.49/245.34 Empty strict component of the problem is NOT empty. 602.49/245.34 602.49/245.34 602.49/245.34 Arrrr.. 602.80/245.65 EOF