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