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