MAYBE 126.11/48.58 MAYBE 126.11/48.58 126.11/48.58 We are left with following problem, upon which TcT provides the 126.11/48.58 certificate MAYBE. 126.11/48.58 126.11/48.58 Strict Trs: 126.11/48.58 { cond1(s(x), y) -> cond2(gr(s(x), y), s(x), y) 126.11/48.58 , cond2(true(), x, y) -> cond1(y, y) 126.11/48.58 , cond2(false(), x, y) -> cond1(p(x), y) 126.11/48.58 , gr(s(x), s(y)) -> gr(x, y) 126.11/48.58 , gr(s(x), 0()) -> true() 126.11/48.58 , gr(0(), x) -> false() 126.11/48.58 , p(s(x)) -> x 126.11/48.58 , p(0()) -> 0() 126.11/48.58 , neq(s(x), s(y)) -> neq(x, y) 126.11/48.58 , neq(s(x), 0()) -> true() 126.11/48.58 , neq(0(), s(x)) -> true() 126.11/48.58 , neq(0(), 0()) -> false() } 126.11/48.58 Obligation: 126.11/48.58 runtime complexity 126.11/48.58 Answer: 126.11/48.58 MAYBE 126.11/48.58 126.11/48.58 None of the processors succeeded. 126.11/48.58 126.11/48.58 Details of failed attempt(s): 126.11/48.58 ----------------------------- 126.11/48.58 1) 'Best' failed due to the following reason: 126.11/48.58 126.11/48.58 None of the processors succeeded. 126.11/48.58 126.11/48.58 Details of failed attempt(s): 126.11/48.58 ----------------------------- 126.11/48.58 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 126.11/48.58 seconds)' failed due to the following reason: 126.11/48.58 126.11/48.58 None of the processors succeeded. 126.11/48.58 126.11/48.58 Details of failed attempt(s): 126.11/48.58 ----------------------------- 126.11/48.58 1) 'empty' failed due to the following reason: 126.11/48.58 126.11/48.58 Empty strict component of the problem is NOT empty. 126.11/48.58 126.11/48.58 2) 'With Problem ...' failed due to the following reason: 126.11/48.58 126.11/48.58 None of the processors succeeded. 126.11/48.58 126.11/48.58 Details of failed attempt(s): 126.11/48.58 ----------------------------- 126.11/48.58 1) 'empty' failed due to the following reason: 126.11/48.58 126.11/48.58 Empty strict component of the problem is NOT empty. 126.11/48.58 126.11/48.58 2) 'Fastest' failed due to the following reason: 126.11/48.58 126.11/48.58 None of the processors succeeded. 126.11/48.58 126.11/48.58 Details of failed attempt(s): 126.11/48.58 ----------------------------- 126.11/48.58 1) 'With Problem ...' failed due to the following reason: 126.11/48.58 126.11/48.58 None of the processors succeeded. 126.11/48.58 126.11/48.58 Details of failed attempt(s): 126.11/48.58 ----------------------------- 126.11/48.58 1) 'empty' failed due to the following reason: 126.11/48.58 126.11/48.58 Empty strict component of the problem is NOT empty. 126.11/48.58 126.11/48.58 2) 'With Problem ...' failed due to the following reason: 126.11/48.58 126.11/48.58 Empty strict component of the problem is NOT empty. 126.11/48.58 126.11/48.58 126.11/48.58 2) 'With Problem ...' failed due to the following reason: 126.11/48.58 126.11/48.58 None of the processors succeeded. 126.11/48.58 126.11/48.58 Details of failed attempt(s): 126.11/48.58 ----------------------------- 126.11/48.58 1) 'empty' failed due to the following reason: 126.11/48.58 126.11/48.58 Empty strict component of the problem is NOT empty. 126.11/48.58 126.11/48.58 2) 'With Problem ...' failed due to the following reason: 126.11/48.58 126.11/48.58 None of the processors succeeded. 126.11/48.58 126.11/48.58 Details of failed attempt(s): 126.11/48.58 ----------------------------- 126.11/48.58 1) 'empty' failed due to the following reason: 126.11/48.58 126.11/48.58 Empty strict component of the problem is NOT empty. 126.11/48.58 126.11/48.58 2) 'With Problem ...' failed due to the following reason: 126.11/48.58 126.11/48.58 None of the processors succeeded. 126.11/48.58 126.11/48.58 Details of failed attempt(s): 126.11/48.58 ----------------------------- 126.11/48.58 1) 'empty' failed due to the following reason: 126.11/48.58 126.11/48.58 Empty strict component of the problem is NOT empty. 126.11/48.58 126.11/48.58 2) 'With Problem ...' failed due to the following reason: 126.11/48.58 126.11/48.58 Empty strict component of the problem is NOT empty. 126.11/48.58 126.11/48.58 126.11/48.58 126.11/48.58 126.11/48.58 126.11/48.58 126.11/48.58 126.11/48.58 2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 126.11/48.58 failed due to the following reason: 126.11/48.58 126.11/48.58 None of the processors succeeded. 126.11/48.58 126.11/48.58 Details of failed attempt(s): 126.11/48.58 ----------------------------- 126.11/48.58 1) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 126.11/48.58 failed due to the following reason: 126.11/48.58 126.11/48.58 match-boundness of the problem could not be verified. 126.11/48.58 126.11/48.58 2) 'Bounds with minimal-enrichment and initial automaton 'match'' 126.11/48.58 failed due to the following reason: 126.11/48.58 126.11/48.58 match-boundness of the problem could not be verified. 126.11/48.58 126.11/48.58 126.11/48.58 3) 'Best' failed due to the following reason: 126.11/48.58 126.11/48.58 None of the processors succeeded. 126.11/48.58 126.11/48.58 Details of failed attempt(s): 126.11/48.58 ----------------------------- 126.11/48.58 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 126.11/48.58 to the following reason: 126.11/48.58 126.11/48.58 The processor is inapplicable, reason: 126.11/48.58 Processor only applicable for innermost runtime complexity analysis 126.11/48.58 126.11/48.58 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 126.11/48.58 following reason: 126.11/48.58 126.11/48.58 The processor is inapplicable, reason: 126.11/48.58 Processor only applicable for innermost runtime complexity analysis 126.11/48.58 126.11/48.58 126.11/48.58 126.11/48.58 2) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 126.11/48.58 the following reason: 126.11/48.58 126.11/48.58 We add the following weak dependency pairs: 126.11/48.58 126.11/48.58 Strict DPs: 126.11/48.58 { cond1^#(s(x), y) -> c_1(cond2^#(gr(s(x), y), s(x), y)) 126.11/48.58 , cond2^#(true(), x, y) -> c_2(cond1^#(y, y)) 126.11/48.58 , cond2^#(false(), x, y) -> c_3(cond1^#(p(x), y)) 126.11/48.58 , gr^#(s(x), s(y)) -> c_4(gr^#(x, y)) 126.11/48.58 , gr^#(s(x), 0()) -> c_5() 126.11/48.58 , gr^#(0(), x) -> c_6() 126.11/48.58 , p^#(s(x)) -> c_7(x) 126.11/48.58 , p^#(0()) -> c_8() 126.11/48.58 , neq^#(s(x), s(y)) -> c_9(neq^#(x, y)) 126.11/48.58 , neq^#(s(x), 0()) -> c_10() 126.11/48.58 , neq^#(0(), s(x)) -> c_11() 126.11/48.58 , neq^#(0(), 0()) -> c_12() } 126.11/48.58 126.11/48.58 and mark the set of starting terms. 126.11/48.58 126.11/48.58 We are left with following problem, upon which TcT provides the 126.11/48.58 certificate MAYBE. 126.11/48.58 126.11/48.58 Strict DPs: 126.11/48.58 { cond1^#(s(x), y) -> c_1(cond2^#(gr(s(x), y), s(x), y)) 126.11/48.58 , cond2^#(true(), x, y) -> c_2(cond1^#(y, y)) 126.11/48.58 , cond2^#(false(), x, y) -> c_3(cond1^#(p(x), y)) 126.11/48.58 , gr^#(s(x), s(y)) -> c_4(gr^#(x, y)) 126.11/48.58 , gr^#(s(x), 0()) -> c_5() 126.11/48.58 , gr^#(0(), x) -> c_6() 126.11/48.58 , p^#(s(x)) -> c_7(x) 126.11/48.58 , p^#(0()) -> c_8() 126.11/48.58 , neq^#(s(x), s(y)) -> c_9(neq^#(x, y)) 126.11/48.58 , neq^#(s(x), 0()) -> c_10() 126.11/48.58 , neq^#(0(), s(x)) -> c_11() 126.11/48.58 , neq^#(0(), 0()) -> c_12() } 126.11/48.58 Strict Trs: 126.11/48.58 { cond1(s(x), y) -> cond2(gr(s(x), y), s(x), y) 126.11/48.58 , cond2(true(), x, y) -> cond1(y, y) 126.11/48.58 , cond2(false(), x, y) -> cond1(p(x), y) 126.11/48.58 , gr(s(x), s(y)) -> gr(x, y) 126.11/48.58 , gr(s(x), 0()) -> true() 126.11/48.58 , gr(0(), x) -> false() 126.11/48.58 , p(s(x)) -> x 126.11/48.58 , p(0()) -> 0() 126.11/48.58 , neq(s(x), s(y)) -> neq(x, y) 126.11/48.58 , neq(s(x), 0()) -> true() 126.11/48.58 , neq(0(), s(x)) -> true() 126.11/48.58 , neq(0(), 0()) -> false() } 126.11/48.58 Obligation: 126.11/48.58 runtime complexity 126.11/48.58 Answer: 126.11/48.58 MAYBE 126.11/48.58 126.11/48.58 We estimate the number of application of {5,6,8,10,11,12} by 126.11/48.58 applications of Pre({5,6,8,10,11,12}) = {4,7,9}. Here rules are 126.11/48.58 labeled as follows: 126.11/48.58 126.11/48.58 DPs: 126.11/48.58 { 1: cond1^#(s(x), y) -> c_1(cond2^#(gr(s(x), y), s(x), y)) 126.11/48.58 , 2: cond2^#(true(), x, y) -> c_2(cond1^#(y, y)) 126.11/48.58 , 3: cond2^#(false(), x, y) -> c_3(cond1^#(p(x), y)) 126.11/48.58 , 4: gr^#(s(x), s(y)) -> c_4(gr^#(x, y)) 126.11/48.58 , 5: gr^#(s(x), 0()) -> c_5() 126.11/48.58 , 6: gr^#(0(), x) -> c_6() 126.11/48.58 , 7: p^#(s(x)) -> c_7(x) 126.11/48.58 , 8: p^#(0()) -> c_8() 126.11/48.58 , 9: neq^#(s(x), s(y)) -> c_9(neq^#(x, y)) 126.11/48.58 , 10: neq^#(s(x), 0()) -> c_10() 126.11/48.58 , 11: neq^#(0(), s(x)) -> c_11() 126.11/48.58 , 12: neq^#(0(), 0()) -> c_12() } 126.11/48.58 126.11/48.58 We are left with following problem, upon which TcT provides the 126.11/48.58 certificate MAYBE. 126.11/48.58 126.11/48.58 Strict DPs: 126.11/48.58 { cond1^#(s(x), y) -> c_1(cond2^#(gr(s(x), y), s(x), y)) 126.11/48.58 , cond2^#(true(), x, y) -> c_2(cond1^#(y, y)) 126.11/48.58 , cond2^#(false(), x, y) -> c_3(cond1^#(p(x), y)) 126.11/48.58 , gr^#(s(x), s(y)) -> c_4(gr^#(x, y)) 126.11/48.58 , p^#(s(x)) -> c_7(x) 126.11/48.58 , neq^#(s(x), s(y)) -> c_9(neq^#(x, y)) } 126.11/48.58 Strict Trs: 126.11/48.58 { cond1(s(x), y) -> cond2(gr(s(x), y), s(x), y) 126.11/48.58 , cond2(true(), x, y) -> cond1(y, y) 126.11/48.58 , cond2(false(), x, y) -> cond1(p(x), y) 126.11/48.58 , gr(s(x), s(y)) -> gr(x, y) 126.11/48.58 , gr(s(x), 0()) -> true() 126.11/48.58 , gr(0(), x) -> false() 126.11/48.58 , p(s(x)) -> x 126.11/48.58 , p(0()) -> 0() 126.11/48.58 , neq(s(x), s(y)) -> neq(x, y) 126.11/48.58 , neq(s(x), 0()) -> true() 126.11/48.58 , neq(0(), s(x)) -> true() 126.11/48.58 , neq(0(), 0()) -> false() } 126.11/48.58 Weak DPs: 126.11/48.58 { gr^#(s(x), 0()) -> c_5() 126.11/48.58 , gr^#(0(), x) -> c_6() 126.11/48.58 , p^#(0()) -> c_8() 126.11/48.58 , neq^#(s(x), 0()) -> c_10() 126.11/48.58 , neq^#(0(), s(x)) -> c_11() 126.11/48.58 , neq^#(0(), 0()) -> c_12() } 126.11/48.58 Obligation: 126.11/48.58 runtime complexity 126.11/48.58 Answer: 126.11/48.58 MAYBE 126.11/48.58 126.11/48.58 Empty strict component of the problem is NOT empty. 126.11/48.58 126.11/48.58 126.11/48.58 Arrrr.. 126.39/48.75 EOF