MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(x, Cons(x', xs)) -> f(f[Ite][False][Ite](lt0(x, Cons(Nil(), Nil())), x, Cons(x', xs)), f[Ite][False][Ite](lt0(x, Cons(Nil(), Nil())), x, Cons(x', xs))) , f(x, Nil()) -> Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Nil())))))))))))))))))))))))))))))))))))))))))) , lt0(x, Nil()) -> False() , lt0(Cons(x', xs'), Cons(x, xs)) -> lt0(xs', xs) , number42() -> Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Nil())))))))))))))))))))))))))))))))))))))))))) , goal(x, y) -> Cons(f(x, y), Cons(g(x, y), Nil())) , g(x, Cons(x', xs)) -> g[Ite][False][Ite](lt0(x, Cons(Nil(), Nil())), x, Cons(x', xs)) , g(x, Nil()) -> Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Nil())))))))))))))))))))))))))))))))))))))))))) } Weak Trs: { f[Ite][False][Ite](True(), x, y) -> x , f[Ite][False][Ite](True(), x', Cons(x, xs)) -> xs , f[Ite][False][Ite](False(), x, y) -> Cons(Cons(Nil(), Nil()), y) , f[Ite][False][Ite](False(), Cons(x, xs), y) -> xs , g[Ite][False][Ite](True(), x', Cons(x, xs)) -> g(x', xs) , g[Ite][False][Ite](False(), Cons(x, xs), y) -> g(xs, Cons(Cons(Nil(), Nil()), y)) } Obligation: innermost runtime complexity Answer: MAYBE 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) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem (timeout of 60 seconds)' failed due to the following reason: Computation stopped due to timeout after 60.0 seconds. 2) '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: Computation stopped due to timeout after 30.0 seconds. 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 input cannot be shown compatible 2) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due to the following reason: The input cannot be shown compatible 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 minimal-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. Arrrr..