MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { h(X, Z) -> f(X, s(X), Z) , f(X, Y, g(X, Y)) -> h(0(), g(X, Y)) , g(X, s(Y)) -> g(X, Y) , g(0(), Y) -> 0() } 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: none TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [h](x1, x2) = [4] [f](x1, x2, x3) = [0] [s](x1) = [1] x1 + [7] [g](x1, x2) = [0] [0] = [5] The following symbols are considered usable {h, f, g} The order satisfies the following ordering constraints: [h(X, Z)] = [4] > [0] = [f(X, s(X), Z)] [f(X, Y, g(X, Y))] = [0] ? [4] = [h(0(), g(X, Y))] [g(X, s(Y))] = [0] >= [0] = [g(X, Y)] [g(0(), Y)] = [0] ? [5] = [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: { f(X, Y, g(X, Y)) -> h(0(), g(X, Y)) , g(X, s(Y)) -> g(X, Y) , g(0(), Y) -> 0() } Weak Trs: { h(X, Z) -> f(X, s(X), Z) } Obligation: runtime complexity Answer: MAYBE The weightgap principle applies (using the following nonconstant growth matrix-interpretation) The following argument positions are usable: none TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [h](x1, x2) = [1] x2 + [4] [f](x1, x2, x3) = [0] [s](x1) = [1] x1 + [7] [g](x1, x2) = [4] [0] = [1] The following symbols are considered usable {h, f, g} The order satisfies the following ordering constraints: [h(X, Z)] = [1] Z + [4] > [0] = [f(X, s(X), Z)] [f(X, Y, g(X, Y))] = [0] ? [8] = [h(0(), g(X, Y))] [g(X, s(Y))] = [4] >= [4] = [g(X, Y)] [g(0(), Y)] = [4] > [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: { f(X, Y, g(X, Y)) -> h(0(), g(X, Y)) , g(X, s(Y)) -> g(X, Y) } Weak Trs: { h(X, Z) -> f(X, s(X), Z) , g(0(), Y) -> 0() } Obligation: runtime complexity Answer: MAYBE The weightgap principle applies (using the following nonconstant growth matrix-interpretation) The following argument positions are usable: none TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [h](x1, x2) = [1] x1 + [4] [f](x1, x2, x3) = [1] x1 + [0] [s](x1) = [1] x1 + [4] [g](x1, x2) = [1] x1 + [1] x2 + [3] [0] = [5] The following symbols are considered usable {h, f, g} The order satisfies the following ordering constraints: [h(X, Z)] = [1] X + [4] > [1] X + [0] = [f(X, s(X), Z)] [f(X, Y, g(X, Y))] = [1] X + [0] ? [9] = [h(0(), g(X, Y))] [g(X, s(Y))] = [1] X + [1] Y + [7] > [1] X + [1] Y + [3] = [g(X, Y)] [g(0(), Y)] = [1] Y + [8] > [5] = [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: { f(X, Y, g(X, Y)) -> h(0(), g(X, Y)) } Weak Trs: { h(X, Z) -> f(X, s(X), Z) , g(X, s(Y)) -> g(X, Y) , g(0(), Y) -> 0() } 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: 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: 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 processor is inapplicable, reason: Processor only applicable for innermost runtime complexity analysis 2) '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 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. 3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed due to the following reason: We add the following weak dependency pairs: Strict DPs: { h^#(X, Z) -> c_1(f^#(X, s(X), Z)) , f^#(X, Y, g(X, Y)) -> c_2(h^#(0(), g(X, Y))) , g^#(X, s(Y)) -> c_3(g^#(X, Y)) , g^#(0(), Y) -> c_4() } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { h^#(X, Z) -> c_1(f^#(X, s(X), Z)) , f^#(X, Y, g(X, Y)) -> c_2(h^#(0(), g(X, Y))) , g^#(X, s(Y)) -> c_3(g^#(X, Y)) , g^#(0(), Y) -> c_4() } Strict Trs: { h(X, Z) -> f(X, s(X), Z) , f(X, Y, g(X, Y)) -> h(0(), g(X, Y)) , g(X, s(Y)) -> g(X, Y) , g(0(), Y) -> 0() } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {4} by applications of Pre({4}) = {3}. Here rules are labeled as follows: DPs: { 1: h^#(X, Z) -> c_1(f^#(X, s(X), Z)) , 2: f^#(X, Y, g(X, Y)) -> c_2(h^#(0(), g(X, Y))) , 3: g^#(X, s(Y)) -> c_3(g^#(X, Y)) , 4: g^#(0(), Y) -> c_4() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { h^#(X, Z) -> c_1(f^#(X, s(X), Z)) , f^#(X, Y, g(X, Y)) -> c_2(h^#(0(), g(X, Y))) , g^#(X, s(Y)) -> c_3(g^#(X, Y)) } Strict Trs: { h(X, Z) -> f(X, s(X), Z) , f(X, Y, g(X, Y)) -> h(0(), g(X, Y)) , g(X, s(Y)) -> g(X, Y) , g(0(), Y) -> 0() } Weak DPs: { g^#(0(), Y) -> c_4() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..