MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(x, c(x), c(y)) -> f(y, y, f(y, x, y)) , f(c(x), x, y) -> c(y) , f(s(x), y, z) -> f(x, s(c(y)), c(z)) , g(x, y) -> x , g(x, y) -> 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(f) = {3} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [f](x1, x2, x3) = [1] x3 + [7] [c](x1) = [1] x1 + [7] [s](x1) = [1] x1 + [7] [g](x1, x2) = [1] x1 + [1] x2 + [7] The following symbols are considered usable {f, g} The order satisfies the following ordering constraints: [f(x, c(x), c(y))] = [1] y + [14] >= [1] y + [14] = [f(y, y, f(y, x, y))] [f(c(x), x, y)] = [1] y + [7] >= [1] y + [7] = [c(y)] [f(s(x), y, z)] = [1] z + [7] ? [1] z + [14] = [f(x, s(c(y)), c(z))] [g(x, y)] = [1] x + [1] y + [7] > [1] x + [0] = [x] [g(x, y)] = [1] x + [1] y + [7] > [1] y + [0] = [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: { f(x, c(x), c(y)) -> f(y, y, f(y, x, y)) , f(c(x), x, y) -> c(y) , f(s(x), y, z) -> f(x, s(c(y)), c(z)) } Weak Trs: { g(x, y) -> x , g(x, y) -> y } Obligation: innermost runtime complexity Answer: MAYBE The weightgap principle applies (using the following nonconstant growth matrix-interpretation) The following argument positions are usable: Uargs(f) = {3} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [f](x1, x2, x3) = [1] x3 + [7] [c](x1) = [1] x1 + [3] [s](x1) = [1] x1 + [7] [g](x1, x2) = [1] x1 + [1] x2 + [0] The following symbols are considered usable {f, g} The order satisfies the following ordering constraints: [f(x, c(x), c(y))] = [1] y + [10] ? [1] y + [14] = [f(y, y, f(y, x, y))] [f(c(x), x, y)] = [1] y + [7] > [1] y + [3] = [c(y)] [f(s(x), y, z)] = [1] z + [7] ? [1] z + [10] = [f(x, s(c(y)), c(z))] [g(x, y)] = [1] x + [1] y + [0] >= [1] x + [0] = [x] [g(x, y)] = [1] x + [1] y + [0] >= [1] y + [0] = [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: { f(x, c(x), c(y)) -> f(y, y, f(y, x, y)) , f(s(x), y, z) -> f(x, s(c(y)), c(z)) } Weak Trs: { f(c(x), x, y) -> c(y) , g(x, y) -> x , g(x, y) -> 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) '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 input cannot be shown compatible 2) 'bsearch-popstar (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..