MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { lt(x, 0()) -> false() , lt(0(), s(x)) -> true() , lt(s(x), s(y)) -> lt(x, y) , minus(x, y) -> help(lt(y, x), x, y) , help(true(), x, y) -> s(minus(x, s(y))) , help(false(), x, y) -> 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(s) = {1}, Uargs(help) = {1} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [lt](x1, x2) = [4] [0] = [0] [s](x1) = [1] x1 + [0] [true] = [1] [false] = [1] [minus](x1, x2) = [1] x1 + [1] x2 + [0] [help](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] The following symbols are considered usable {lt, minus, help} The order satisfies the following ordering constraints: [lt(x, 0())] = [4] > [1] = [false()] [lt(0(), s(x))] = [4] > [1] = [true()] [lt(s(x), s(y))] = [4] >= [4] = [lt(x, y)] [minus(x, y)] = [1] x + [1] y + [0] ? [1] x + [1] y + [4] = [help(lt(y, x), x, y)] [help(true(), x, y)] = [1] x + [1] y + [1] > [1] x + [1] y + [0] = [s(minus(x, s(y)))] [help(false(), x, y)] = [1] x + [1] y + [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: { lt(s(x), s(y)) -> lt(x, y) , minus(x, y) -> help(lt(y, x), x, y) } Weak Trs: { lt(x, 0()) -> false() , lt(0(), s(x)) -> true() , help(true(), x, y) -> s(minus(x, s(y))) , help(false(), x, y) -> 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: The weightgap principle applies (using the following nonconstant growth matrix-interpretation) The following argument positions are usable: Uargs(s) = {1}, Uargs(help) = {1} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [lt](x1, x2) = [0 0] x1 + [0] [0 1] [0] [0] = [0] [1] [s](x1) = [1 0] x1 + [0] [0 0] [0] [true] = [0] [1] [false] = [0] [0] [minus](x1, x2) = [0 4] x2 + [1] [0 0] [4] [help](x1, x2, x3) = [1 1] x1 + [0] [0 0] [4] The following symbols are considered usable {lt, minus, help} The order satisfies the following ordering constraints: [lt(x, 0())] = [0 0] x + [0] [0 1] [0] >= [0] [0] = [false()] [lt(0(), s(x))] = [0] [1] >= [0] [1] = [true()] [lt(s(x), s(y))] = [0] [0] ? [0 0] x + [0] [0 1] [0] = [lt(x, y)] [minus(x, y)] = [0 4] y + [1] [0 0] [4] > [0 1] y + [0] [0 0] [4] = [help(lt(y, x), x, y)] [help(true(), x, y)] = [1] [4] >= [1] [0] = [s(minus(x, s(y)))] [help(false(), x, y)] = [0] [4] >= [0] [1] = [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: { lt(s(x), s(y)) -> lt(x, y) } Weak Trs: { lt(x, 0()) -> false() , lt(0(), s(x)) -> true() , minus(x, y) -> help(lt(y, x), x, y) , help(true(), x, y) -> s(minus(x, s(y))) , help(false(), x, y) -> 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) '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 perSymbol-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 2) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. Arrrr..