MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(true(), x, y) -> f(gt(x, y), s(x), s(s(y))) , gt(s(u), s(v)) -> gt(u, v) , gt(s(u), 0()) -> true() , gt(0(), v) -> false() } 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) = {1} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [f](x1, x2, x3) = [1] x1 + [1] x2 + [1] [true] = [5] [gt](x1, x2) = [1] [s](x1) = [1] x1 + [0] [0] = [7] [false] = [0] The following symbols are considered usable {f, gt} The order satisfies the following ordering constraints: [f(true(), x, y)] = [1] x + [6] > [1] x + [2] = [f(gt(x, y), s(x), s(s(y)))] [gt(s(u), s(v))] = [1] >= [1] = [gt(u, v)] [gt(s(u), 0())] = [1] ? [5] = [true()] [gt(0(), v)] = [1] > [0] = [false()] 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: { gt(s(u), s(v)) -> gt(u, v) , gt(s(u), 0()) -> true() } Weak Trs: { f(true(), x, y) -> f(gt(x, y), s(x), s(s(y))) , gt(0(), v) -> false() } 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: The weightgap principle applies (using the following nonconstant growth matrix-interpretation) The following argument positions are usable: Uargs(f) = {1} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [f](x1, x2, x3) = [1 4] x1 + [0 4] x2 + [0 4] x3 + [1] [0 0] [0 0] [0 0] [1] [true] = [3] [1] [gt](x1, x2) = [0 0] x2 + [4] [0 1] [0] [s](x1) = [0] [0] [0] = [0] [1] [false] = [4] [0] The following symbols are considered usable {f, gt} The order satisfies the following ordering constraints: [f(true(), x, y)] = [0 4] x + [0 4] y + [8] [0 0] [0 0] [1] > [0 4] y + [5] [0 0] [1] = [f(gt(x, y), s(x), s(s(y)))] [gt(s(u), s(v))] = [4] [0] ? [0 0] v + [4] [0 1] [0] = [gt(u, v)] [gt(s(u), 0())] = [4] [1] > [3] [1] = [true()] [gt(0(), v)] = [0 0] v + [4] [0 1] [0] >= [4] [0] = [false()] 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: { gt(s(u), s(v)) -> gt(u, v) } Weak Trs: { f(true(), x, y) -> f(gt(x, y), s(x), s(s(y))) , gt(s(u), 0()) -> true() , gt(0(), v) -> false() } 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) '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 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..