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: 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: The weightgap principle applies (using the following nonconstant growth matrix-interpretation) The following argument positions are usable: Uargs(cond) = {1, 3}, Uargs(s) = {1} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [cond](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [3] [true] = [3] [gr](x1, x2) = [5] [add](x1, x2) = [1] x2 + [6] [0] = [7] [false] = [4] [s](x1) = [1] x1 + [1] The following symbols are considered usable {cond, gr, add} The order satisfies the following ordering constraints: [cond(true(), x, y)] = [1] x + [1] y + [6] ? [1] x + [1] y + [14] = [cond(gr(x, y), x, add(x, y))] [gr(0(), x)] = [5] > [4] = [false()] [gr(s(x), 0())] = [5] > [3] = [true()] [gr(s(x), s(y))] = [5] >= [5] = [gr(x, y)] [add(0(), x)] = [1] x + [6] > [1] x + [0] = [x] [add(s(x), y)] = [1] y + [6] ? [1] y + [7] = [s(add(x, y))] Further, it can be verified that all rules not oriented are covered by the weightgap condition. 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(s(x), s(y)) -> gr(x, y) , add(s(x), y) -> s(add(x, y)) } Weak Trs: { gr(0(), x) -> false() , gr(s(x), 0()) -> true() , add(0(), x) -> x } 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) '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 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 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. Arrrr..