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