MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(a(), g(y)) -> g(g(y)) , f(g(x), a()) -> f(x, g(a())) , f(g(x), g(y)) -> h(g(y), x, g(y)) , h(a(), y, z) -> z , h(g(x), y, z) -> f(y, h(x, y, z)) } 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) = {2} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [f](x1, x2) = [1] x2 + [0] [a] = [5] [g](x1) = [0] [h](x1, x2, x3) = [1] x3 + [0] The following symbols are considered usable {f, h} The order satisfies the following ordering constraints: [f(a(), g(y))] = [0] >= [0] = [g(g(y))] [f(g(x), a())] = [5] > [0] = [f(x, g(a()))] [f(g(x), g(y))] = [0] >= [0] = [h(g(y), x, g(y))] [h(a(), y, z)] = [1] z + [0] >= [1] z + [0] = [z] [h(g(x), y, z)] = [1] z + [0] >= [1] z + [0] = [f(y, h(x, y, z))] 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(a(), g(y)) -> g(g(y)) , f(g(x), g(y)) -> h(g(y), x, g(y)) , h(a(), y, z) -> z , h(g(x), y, z) -> f(y, h(x, y, z)) } Weak Trs: { f(g(x), a()) -> f(x, g(a())) } 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) = {2} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [f](x1, x2) = [1] x2 + [1] [a] = [7] [g](x1) = [0] [h](x1, x2, x3) = [1] x3 + [0] The following symbols are considered usable {f, h} The order satisfies the following ordering constraints: [f(a(), g(y))] = [1] > [0] = [g(g(y))] [f(g(x), a())] = [8] > [1] = [f(x, g(a()))] [f(g(x), g(y))] = [1] > [0] = [h(g(y), x, g(y))] [h(a(), y, z)] = [1] z + [0] >= [1] z + [0] = [z] [h(g(x), y, z)] = [1] z + [0] ? [1] z + [1] = [f(y, h(x, y, z))] 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: { h(a(), y, z) -> z , h(g(x), y, z) -> f(y, h(x, y, z)) } Weak Trs: { f(a(), g(y)) -> g(g(y)) , f(g(x), a()) -> f(x, g(a())) , f(g(x), g(y)) -> h(g(y), x, g(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) = {2} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [f](x1, x2) = [1] x2 + [4] [a] = [5] [g](x1) = [4] [h](x1, x2, x3) = [1] x3 + [4] The following symbols are considered usable {f, h} The order satisfies the following ordering constraints: [f(a(), g(y))] = [8] > [4] = [g(g(y))] [f(g(x), a())] = [9] > [8] = [f(x, g(a()))] [f(g(x), g(y))] = [8] >= [8] = [h(g(y), x, g(y))] [h(a(), y, z)] = [1] z + [4] > [1] z + [0] = [z] [h(g(x), y, z)] = [1] z + [4] ? [1] z + [8] = [f(y, h(x, y, z))] 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: { h(g(x), y, z) -> f(y, h(x, y, z)) } Weak Trs: { f(a(), g(y)) -> g(g(y)) , f(g(x), a()) -> f(x, g(a())) , f(g(x), g(y)) -> h(g(y), x, g(y)) , h(a(), y, z) -> z } 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..