MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { cond1(s(x), y) -> cond2(gr(s(x), y), s(x), y) , cond2(true(), x, y) -> cond1(y, y) , cond2(false(), x, y) -> cond1(p(x), y) , gr(s(x), s(y)) -> gr(x, y) , gr(s(x), 0()) -> true() , gr(0(), x) -> false() , p(s(x)) -> x , p(0()) -> 0() , neq(s(x), s(y)) -> neq(x, y) , neq(s(x), 0()) -> true() , neq(0(), s(x)) -> true() , neq(0(), 0()) -> false() } Obligation: runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem (timeout of 30 seconds) (timeout of 60 seconds)' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'Fastest' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due to the following reason: The processor is inapplicable, reason: Processor only applicable for innermost runtime complexity analysis 2) 'bsearch-popstar (timeout of 60 seconds)' failed due to the following reason: The processor is inapplicable, reason: Processor only applicable for innermost runtime complexity analysis 3) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 2) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 2) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed due to the following reason: We add the following weak dependency pairs: Strict DPs: { cond1^#(s(x), y) -> c_1(cond2^#(gr(s(x), y), s(x), y)) , cond2^#(true(), x, y) -> c_2(cond1^#(y, y)) , cond2^#(false(), x, y) -> c_3(cond1^#(p(x), y)) , gr^#(s(x), s(y)) -> c_4(gr^#(x, y)) , gr^#(s(x), 0()) -> c_5() , gr^#(0(), x) -> c_6() , p^#(s(x)) -> c_7(x) , p^#(0()) -> c_8() , neq^#(s(x), s(y)) -> c_9(neq^#(x, y)) , neq^#(s(x), 0()) -> c_10() , neq^#(0(), s(x)) -> c_11() , neq^#(0(), 0()) -> c_12() } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { cond1^#(s(x), y) -> c_1(cond2^#(gr(s(x), y), s(x), y)) , cond2^#(true(), x, y) -> c_2(cond1^#(y, y)) , cond2^#(false(), x, y) -> c_3(cond1^#(p(x), y)) , gr^#(s(x), s(y)) -> c_4(gr^#(x, y)) , gr^#(s(x), 0()) -> c_5() , gr^#(0(), x) -> c_6() , p^#(s(x)) -> c_7(x) , p^#(0()) -> c_8() , neq^#(s(x), s(y)) -> c_9(neq^#(x, y)) , neq^#(s(x), 0()) -> c_10() , neq^#(0(), s(x)) -> c_11() , neq^#(0(), 0()) -> c_12() } Strict Trs: { cond1(s(x), y) -> cond2(gr(s(x), y), s(x), y) , cond2(true(), x, y) -> cond1(y, y) , cond2(false(), x, y) -> cond1(p(x), y) , gr(s(x), s(y)) -> gr(x, y) , gr(s(x), 0()) -> true() , gr(0(), x) -> false() , p(s(x)) -> x , p(0()) -> 0() , neq(s(x), s(y)) -> neq(x, y) , neq(s(x), 0()) -> true() , neq(0(), s(x)) -> true() , neq(0(), 0()) -> false() } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {5,6,8,10,11,12} by applications of Pre({5,6,8,10,11,12}) = {4,7,9}. Here rules are labeled as follows: DPs: { 1: cond1^#(s(x), y) -> c_1(cond2^#(gr(s(x), y), s(x), y)) , 2: cond2^#(true(), x, y) -> c_2(cond1^#(y, y)) , 3: cond2^#(false(), x, y) -> c_3(cond1^#(p(x), y)) , 4: gr^#(s(x), s(y)) -> c_4(gr^#(x, y)) , 5: gr^#(s(x), 0()) -> c_5() , 6: gr^#(0(), x) -> c_6() , 7: p^#(s(x)) -> c_7(x) , 8: p^#(0()) -> c_8() , 9: neq^#(s(x), s(y)) -> c_9(neq^#(x, y)) , 10: neq^#(s(x), 0()) -> c_10() , 11: neq^#(0(), s(x)) -> c_11() , 12: neq^#(0(), 0()) -> c_12() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { cond1^#(s(x), y) -> c_1(cond2^#(gr(s(x), y), s(x), y)) , cond2^#(true(), x, y) -> c_2(cond1^#(y, y)) , cond2^#(false(), x, y) -> c_3(cond1^#(p(x), y)) , gr^#(s(x), s(y)) -> c_4(gr^#(x, y)) , p^#(s(x)) -> c_7(x) , neq^#(s(x), s(y)) -> c_9(neq^#(x, y)) } Strict Trs: { cond1(s(x), y) -> cond2(gr(s(x), y), s(x), y) , cond2(true(), x, y) -> cond1(y, y) , cond2(false(), x, y) -> cond1(p(x), y) , gr(s(x), s(y)) -> gr(x, y) , gr(s(x), 0()) -> true() , gr(0(), x) -> false() , p(s(x)) -> x , p(0()) -> 0() , neq(s(x), s(y)) -> neq(x, y) , neq(s(x), 0()) -> true() , neq(0(), s(x)) -> true() , neq(0(), 0()) -> false() } Weak DPs: { gr^#(s(x), 0()) -> c_5() , gr^#(0(), x) -> c_6() , p^#(0()) -> c_8() , neq^#(s(x), 0()) -> c_10() , neq^#(0(), s(x)) -> c_11() , neq^#(0(), 0()) -> c_12() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..