MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { cond1(true(), x, y, z) -> cond2(gr(y, z), x, y, z) , cond2(true(), x, y, z) -> cond2(gr(y, z), x, p(y), z) , cond2(false(), x, y, z) -> cond1(gr(x, z), p(x), y, z) , gr(0(), x) -> false() , gr(s(x), 0()) -> true() , gr(s(x), s(y)) -> gr(x, y) , p(0()) -> 0() , p(s(x)) -> x } 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) '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 2) '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 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^#(true(), x, y, z) -> c_1(cond2^#(gr(y, z), x, y, z)) , cond2^#(true(), x, y, z) -> c_2(cond2^#(gr(y, z), x, p(y), z)) , cond2^#(false(), x, y, z) -> c_3(cond1^#(gr(x, z), p(x), y, z)) , gr^#(0(), x) -> c_4() , gr^#(s(x), 0()) -> c_5() , gr^#(s(x), s(y)) -> c_6(gr^#(x, y)) , p^#(0()) -> c_7() , p^#(s(x)) -> c_8(x) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { cond1^#(true(), x, y, z) -> c_1(cond2^#(gr(y, z), x, y, z)) , cond2^#(true(), x, y, z) -> c_2(cond2^#(gr(y, z), x, p(y), z)) , cond2^#(false(), x, y, z) -> c_3(cond1^#(gr(x, z), p(x), y, z)) , gr^#(0(), x) -> c_4() , gr^#(s(x), 0()) -> c_5() , gr^#(s(x), s(y)) -> c_6(gr^#(x, y)) , p^#(0()) -> c_7() , p^#(s(x)) -> c_8(x) } Strict Trs: { cond1(true(), x, y, z) -> cond2(gr(y, z), x, y, z) , cond2(true(), x, y, z) -> cond2(gr(y, z), x, p(y), z) , cond2(false(), x, y, z) -> cond1(gr(x, z), p(x), y, z) , gr(0(), x) -> false() , gr(s(x), 0()) -> true() , gr(s(x), s(y)) -> gr(x, y) , p(0()) -> 0() , p(s(x)) -> x } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {4,5,7} by applications of Pre({4,5,7}) = {6,8}. Here rules are labeled as follows: DPs: { 1: cond1^#(true(), x, y, z) -> c_1(cond2^#(gr(y, z), x, y, z)) , 2: cond2^#(true(), x, y, z) -> c_2(cond2^#(gr(y, z), x, p(y), z)) , 3: cond2^#(false(), x, y, z) -> c_3(cond1^#(gr(x, z), p(x), y, z)) , 4: gr^#(0(), x) -> c_4() , 5: gr^#(s(x), 0()) -> c_5() , 6: gr^#(s(x), s(y)) -> c_6(gr^#(x, y)) , 7: p^#(0()) -> c_7() , 8: p^#(s(x)) -> c_8(x) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { cond1^#(true(), x, y, z) -> c_1(cond2^#(gr(y, z), x, y, z)) , cond2^#(true(), x, y, z) -> c_2(cond2^#(gr(y, z), x, p(y), z)) , cond2^#(false(), x, y, z) -> c_3(cond1^#(gr(x, z), p(x), y, z)) , gr^#(s(x), s(y)) -> c_6(gr^#(x, y)) , p^#(s(x)) -> c_8(x) } Strict Trs: { cond1(true(), x, y, z) -> cond2(gr(y, z), x, y, z) , cond2(true(), x, y, z) -> cond2(gr(y, z), x, p(y), z) , cond2(false(), x, y, z) -> cond1(gr(x, z), p(x), y, z) , gr(0(), x) -> false() , gr(s(x), 0()) -> true() , gr(s(x), s(y)) -> gr(x, y) , p(0()) -> 0() , p(s(x)) -> x } Weak DPs: { gr^#(0(), x) -> c_4() , gr^#(s(x), 0()) -> c_5() , p^#(0()) -> c_7() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..