MAYBE 114.51/49.15 MAYBE 114.51/49.15 114.51/49.15 We are left with following problem, upon which TcT provides the 114.51/49.15 certificate MAYBE. 114.51/49.15 114.51/49.15 Strict Trs: 114.51/49.15 { cond1(true(), x, y) -> cond2(gr(y, 0()), x, y) 114.51/49.15 , cond2(true(), x, y) -> cond2(gr(y, 0()), x, p(y)) 114.51/49.15 , cond2(false(), x, y) -> cond1(gr(x, 0()), p(x), y) 114.51/49.15 , gr(0(), x) -> false() 114.51/49.15 , gr(s(x), 0()) -> true() 114.51/49.15 , gr(s(x), s(y)) -> gr(x, y) 114.51/49.15 , p(0()) -> 0() 114.51/49.15 , p(s(x)) -> x } 114.51/49.15 Obligation: 114.51/49.15 runtime complexity 114.51/49.15 Answer: 114.51/49.15 MAYBE 114.51/49.15 114.51/49.15 None of the processors succeeded. 114.51/49.15 114.51/49.15 Details of failed attempt(s): 114.51/49.15 ----------------------------- 114.51/49.15 1) 'Best' failed due to the following reason: 114.51/49.15 114.51/49.15 None of the processors succeeded. 114.51/49.15 114.51/49.15 Details of failed attempt(s): 114.51/49.15 ----------------------------- 114.51/49.15 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 114.51/49.15 seconds)' failed due to the following reason: 114.51/49.15 114.51/49.15 None of the processors succeeded. 114.51/49.15 114.51/49.15 Details of failed attempt(s): 114.51/49.15 ----------------------------- 114.51/49.15 1) 'empty' failed due to the following reason: 114.51/49.15 114.51/49.15 Empty strict component of the problem is NOT empty. 114.51/49.15 114.51/49.15 2) 'With Problem ...' failed due to the following reason: 114.51/49.15 114.51/49.15 None of the processors succeeded. 114.51/49.15 114.51/49.15 Details of failed attempt(s): 114.51/49.15 ----------------------------- 114.51/49.15 1) 'empty' failed due to the following reason: 114.51/49.15 114.51/49.15 Empty strict component of the problem is NOT empty. 114.51/49.15 114.51/49.15 2) 'Fastest' failed due to the following reason: 114.51/49.15 114.51/49.15 None of the processors succeeded. 114.51/49.15 114.51/49.15 Details of failed attempt(s): 114.51/49.15 ----------------------------- 114.51/49.15 1) 'With Problem ...' failed due to the following reason: 114.51/49.15 114.51/49.15 None of the processors succeeded. 114.51/49.15 114.51/49.15 Details of failed attempt(s): 114.51/49.15 ----------------------------- 114.51/49.15 1) 'empty' failed due to the following reason: 114.51/49.15 114.51/49.15 Empty strict component of the problem is NOT empty. 114.51/49.15 114.51/49.15 2) 'With Problem ...' failed due to the following reason: 114.51/49.15 114.51/49.15 Empty strict component of the problem is NOT empty. 114.51/49.15 114.51/49.15 114.51/49.15 2) 'With Problem ...' failed due to the following reason: 114.51/49.15 114.51/49.15 None of the processors succeeded. 114.51/49.15 114.51/49.15 Details of failed attempt(s): 114.51/49.15 ----------------------------- 114.51/49.15 1) 'empty' failed due to the following reason: 114.51/49.15 114.51/49.15 Empty strict component of the problem is NOT empty. 114.51/49.15 114.51/49.15 2) 'With Problem ...' failed due to the following reason: 114.51/49.15 114.51/49.15 None of the processors succeeded. 114.51/49.15 114.51/49.15 Details of failed attempt(s): 114.51/49.15 ----------------------------- 114.51/49.15 1) 'empty' failed due to the following reason: 114.51/49.15 114.51/49.15 Empty strict component of the problem is NOT empty. 114.51/49.15 114.51/49.15 2) 'With Problem ...' failed due to the following reason: 114.51/49.15 114.51/49.15 None of the processors succeeded. 114.51/49.15 114.51/49.15 Details of failed attempt(s): 114.51/49.15 ----------------------------- 114.51/49.15 1) 'empty' failed due to the following reason: 114.51/49.15 114.51/49.15 Empty strict component of the problem is NOT empty. 114.51/49.15 114.51/49.15 2) 'With Problem ...' failed due to the following reason: 114.51/49.15 114.51/49.15 Empty strict component of the problem is NOT empty. 114.51/49.15 114.51/49.15 114.51/49.15 114.51/49.15 114.51/49.15 114.51/49.15 114.51/49.15 114.51/49.15 2) 'Best' failed due to the following reason: 114.51/49.15 114.51/49.15 None of the processors succeeded. 114.51/49.15 114.51/49.15 Details of failed attempt(s): 114.51/49.15 ----------------------------- 114.51/49.15 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 114.51/49.15 following reason: 114.51/49.15 114.51/49.15 The processor is inapplicable, reason: 114.51/49.15 Processor only applicable for innermost runtime complexity analysis 114.51/49.15 114.51/49.15 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 114.51/49.15 to the following reason: 114.51/49.15 114.51/49.15 The processor is inapplicable, reason: 114.51/49.15 Processor only applicable for innermost runtime complexity analysis 114.51/49.15 114.51/49.15 114.51/49.15 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 114.51/49.15 failed due to the following reason: 114.51/49.15 114.51/49.15 None of the processors succeeded. 114.51/49.15 114.51/49.15 Details of failed attempt(s): 114.51/49.15 ----------------------------- 114.51/49.15 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 114.51/49.15 failed due to the following reason: 114.51/49.15 114.51/49.15 match-boundness of the problem could not be verified. 114.51/49.15 114.51/49.15 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 114.51/49.15 failed due to the following reason: 114.51/49.15 114.51/49.15 match-boundness of the problem could not be verified. 114.51/49.15 114.51/49.15 114.51/49.15 114.51/49.15 2) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 114.51/49.15 the following reason: 114.51/49.15 114.51/49.15 We add the following weak dependency pairs: 114.51/49.15 114.51/49.15 Strict DPs: 114.51/49.15 { cond1^#(true(), x, y) -> c_1(cond2^#(gr(y, 0()), x, y)) 114.51/49.15 , cond2^#(true(), x, y) -> c_2(cond2^#(gr(y, 0()), x, p(y))) 114.51/49.15 , cond2^#(false(), x, y) -> c_3(cond1^#(gr(x, 0()), p(x), y)) 114.51/49.15 , gr^#(0(), x) -> c_4() 114.51/49.15 , gr^#(s(x), 0()) -> c_5() 114.51/49.15 , gr^#(s(x), s(y)) -> c_6(gr^#(x, y)) 114.51/49.15 , p^#(0()) -> c_7() 114.51/49.15 , p^#(s(x)) -> c_8(x) } 114.51/49.15 114.51/49.15 and mark the set of starting terms. 114.51/49.15 114.51/49.15 We are left with following problem, upon which TcT provides the 114.51/49.15 certificate MAYBE. 114.51/49.15 114.51/49.15 Strict DPs: 114.51/49.15 { cond1^#(true(), x, y) -> c_1(cond2^#(gr(y, 0()), x, y)) 114.51/49.15 , cond2^#(true(), x, y) -> c_2(cond2^#(gr(y, 0()), x, p(y))) 114.51/49.15 , cond2^#(false(), x, y) -> c_3(cond1^#(gr(x, 0()), p(x), y)) 114.51/49.15 , gr^#(0(), x) -> c_4() 114.51/49.15 , gr^#(s(x), 0()) -> c_5() 114.51/49.15 , gr^#(s(x), s(y)) -> c_6(gr^#(x, y)) 114.51/49.15 , p^#(0()) -> c_7() 114.51/49.15 , p^#(s(x)) -> c_8(x) } 114.51/49.15 Strict Trs: 114.51/49.15 { cond1(true(), x, y) -> cond2(gr(y, 0()), x, y) 114.51/49.15 , cond2(true(), x, y) -> cond2(gr(y, 0()), x, p(y)) 114.51/49.15 , cond2(false(), x, y) -> cond1(gr(x, 0()), p(x), y) 114.51/49.15 , gr(0(), x) -> false() 114.51/49.15 , gr(s(x), 0()) -> true() 114.51/49.15 , gr(s(x), s(y)) -> gr(x, y) 114.51/49.15 , p(0()) -> 0() 114.51/49.15 , p(s(x)) -> x } 114.51/49.15 Obligation: 114.51/49.15 runtime complexity 114.51/49.15 Answer: 114.51/49.15 MAYBE 114.51/49.15 114.51/49.15 We estimate the number of application of {4,5,7} by applications of 114.51/49.15 Pre({4,5,7}) = {6,8}. Here rules are labeled as follows: 114.51/49.15 114.51/49.15 DPs: 114.51/49.15 { 1: cond1^#(true(), x, y) -> c_1(cond2^#(gr(y, 0()), x, y)) 114.51/49.15 , 2: cond2^#(true(), x, y) -> c_2(cond2^#(gr(y, 0()), x, p(y))) 114.51/49.15 , 3: cond2^#(false(), x, y) -> c_3(cond1^#(gr(x, 0()), p(x), y)) 114.51/49.15 , 4: gr^#(0(), x) -> c_4() 114.51/49.15 , 5: gr^#(s(x), 0()) -> c_5() 114.51/49.15 , 6: gr^#(s(x), s(y)) -> c_6(gr^#(x, y)) 114.51/49.15 , 7: p^#(0()) -> c_7() 114.51/49.15 , 8: p^#(s(x)) -> c_8(x) } 114.51/49.15 114.51/49.15 We are left with following problem, upon which TcT provides the 114.51/49.15 certificate MAYBE. 114.51/49.15 114.51/49.15 Strict DPs: 114.51/49.15 { cond1^#(true(), x, y) -> c_1(cond2^#(gr(y, 0()), x, y)) 114.51/49.15 , cond2^#(true(), x, y) -> c_2(cond2^#(gr(y, 0()), x, p(y))) 114.51/49.15 , cond2^#(false(), x, y) -> c_3(cond1^#(gr(x, 0()), p(x), y)) 114.51/49.15 , gr^#(s(x), s(y)) -> c_6(gr^#(x, y)) 114.51/49.15 , p^#(s(x)) -> c_8(x) } 114.51/49.15 Strict Trs: 114.51/49.15 { cond1(true(), x, y) -> cond2(gr(y, 0()), x, y) 114.51/49.15 , cond2(true(), x, y) -> cond2(gr(y, 0()), x, p(y)) 114.51/49.15 , cond2(false(), x, y) -> cond1(gr(x, 0()), p(x), y) 114.51/49.15 , gr(0(), x) -> false() 114.51/49.15 , gr(s(x), 0()) -> true() 114.51/49.15 , gr(s(x), s(y)) -> gr(x, y) 114.51/49.15 , p(0()) -> 0() 114.51/49.15 , p(s(x)) -> x } 114.51/49.15 Weak DPs: 114.51/49.15 { gr^#(0(), x) -> c_4() 114.51/49.15 , gr^#(s(x), 0()) -> c_5() 114.51/49.15 , p^#(0()) -> c_7() } 114.51/49.15 Obligation: 114.51/49.15 runtime complexity 114.51/49.15 Answer: 114.51/49.15 MAYBE 114.51/49.15 114.51/49.15 Empty strict component of the problem is NOT empty. 114.51/49.15 114.51/49.15 114.51/49.15 Arrrr.. 114.64/49.29 EOF