MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { cond(true(), x, y) -> cond(gr(x, y), p(x), y) , gr(0(), x) -> false() , gr(s(x), 0()) -> true() , gr(s(x), s(y)) -> gr(x, y) , p(0()) -> 0() , p(s(x)) -> x } 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, 2} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [cond](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [1] [true] = [7] [gr](x1, x2) = [7] [p](x1) = [1] x1 + [7] [0] = [7] [false] = [6] [s](x1) = [1] x1 + [7] The following symbols are considered usable {cond, gr, p} The order satisfies the following ordering constraints: [cond(true(), x, y)] = [1] x + [1] y + [8] ? [1] x + [1] y + [15] = [cond(gr(x, y), p(x), y)] [gr(0(), x)] = [7] > [6] = [false()] [gr(s(x), 0())] = [7] >= [7] = [true()] [gr(s(x), s(y))] = [7] >= [7] = [gr(x, y)] [p(0())] = [14] > [7] = [0()] [p(s(x))] = [1] x + [14] > [1] x + [0] = [x] 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(true(), x, y) -> cond(gr(x, y), p(x), y) , gr(s(x), 0()) -> true() , gr(s(x), s(y)) -> gr(x, y) } Weak Trs: { gr(0(), x) -> false() , p(0()) -> 0() , p(s(x)) -> x } 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, 2} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [cond](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [7] [true] = [3] [gr](x1, x2) = [7] [p](x1) = [1] x1 + [0] [0] = [7] [false] = [7] [s](x1) = [1] x1 + [7] The following symbols are considered usable {cond, gr, p} The order satisfies the following ordering constraints: [cond(true(), x, y)] = [1] x + [1] y + [10] ? [1] x + [1] y + [14] = [cond(gr(x, y), p(x), y)] [gr(0(), x)] = [7] >= [7] = [false()] [gr(s(x), 0())] = [7] > [3] = [true()] [gr(s(x), s(y))] = [7] >= [7] = [gr(x, y)] [p(0())] = [7] >= [7] = [0()] [p(s(x))] = [1] x + [7] > [1] x + [0] = [x] 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(true(), x, y) -> cond(gr(x, y), p(x), y) , gr(s(x), s(y)) -> gr(x, y) } Weak Trs: { gr(0(), x) -> false() , gr(s(x), 0()) -> true() , p(0()) -> 0() , p(s(x)) -> x } 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) '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..