MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { ack(0(), y) -> s(y) , ack(s(x), 0()) -> ack(x, s(0())) , ack(s(x), s(y)) -> ack(x, ack(s(x), y)) } Obligation: runtime complexity Answer: MAYBE 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(ack) = {2}, Uargs(s) = {1} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [ack](x1, x2) = [1] x2 + [0] [0] = [4] [s](x1) = [1] x1 + [4] The following symbols are considered usable {ack} The order satisfies the following ordering constraints: [ack(0(), y)] = [1] y + [0] ? [1] y + [4] = [s(y)] [ack(s(x), 0())] = [4] ? [8] = [ack(x, s(0()))] [ack(s(x), s(y))] = [1] y + [4] > [1] y + [0] = [ack(x, ack(s(x), y))] 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: { ack(0(), y) -> s(y) , ack(s(x), 0()) -> ack(x, s(0())) } Weak Trs: { ack(s(x), s(y)) -> ack(x, ack(s(x), y)) } Obligation: 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 processor is inapplicable, reason: Processor only applicable for innermost runtime complexity analysis 2) 'bsearch-popstar (timeout of 60 seconds)' failed due to the following reason: The processor is inapplicable, reason: Processor only applicable for innermost runtime complexity analysis 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. 3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed due to the following reason: We add the following weak dependency pairs: Strict DPs: { ack^#(0(), y) -> c_1(y) , ack^#(s(x), 0()) -> c_2(ack^#(x, s(0()))) , ack^#(s(x), s(y)) -> c_3(ack^#(x, ack(s(x), y))) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { ack^#(0(), y) -> c_1(y) , ack^#(s(x), 0()) -> c_2(ack^#(x, s(0()))) , ack^#(s(x), s(y)) -> c_3(ack^#(x, ack(s(x), y))) } Strict Trs: { ack(0(), y) -> s(y) , ack(s(x), 0()) -> ack(x, s(0())) , ack(s(x), s(y)) -> ack(x, ack(s(x), y)) } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..