MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { g(X) -> h(X) , h(d()) -> g(c()) , c() -> d() } 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: We add the following innermost weak dependency pairs: Strict DPs: { g^#(X) -> c_1(h^#(X)) , h^#(d()) -> c_2(g^#(c())) , c^#() -> c_3() } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { g^#(X) -> c_1(h^#(X)) , h^#(d()) -> c_2(g^#(c())) , c^#() -> c_3() } Strict Trs: { g(X) -> h(X) , h(d()) -> g(c()) , c() -> d() } Obligation: innermost runtime complexity Answer: MAYBE We replace rewrite rules by usable rules: Strict Usable Rules: { c() -> d() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { g^#(X) -> c_1(h^#(X)) , h^#(d()) -> c_2(g^#(c())) , c^#() -> c_3() } Strict Trs: { c() -> d() } Obligation: innermost runtime complexity Answer: MAYBE The weightgap principle applies (using the following constant growth matrix-interpretation) The following argument positions are usable: Uargs(g^#) = {1}, Uargs(c_1) = {1}, Uargs(c_2) = {1} TcT has computed the following constructor-restricted matrix interpretation. [c] = [1] [2] [d] = [0] [2] [g^#](x1) = [2 1] x1 + [2] [2 1] [2] [c_1](x1) = [1 0] x1 + [1] [0 1] [1] [h^#](x1) = [1 1] x1 + [2] [1 1] [2] [c_2](x1) = [1 0] x1 + [1] [0 1] [1] [c^#] = [1] [1] [c_3] = [1] [1] The following symbols are considered usable {c, g^#, h^#, c^#} The order satisfies the following ordering constraints: [c()] = [1] [2] > [0] [2] = [d()] [g^#(X)] = [2 1] X + [2] [2 1] [2] ? [1 1] X + [3] [1 1] [3] = [c_1(h^#(X))] [h^#(d())] = [4] [4] ? [7] [7] = [c_2(g^#(c()))] [c^#()] = [1] [1] >= [1] [1] = [c_3()] 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 DPs: { g^#(X) -> c_1(h^#(X)) , h^#(d()) -> c_2(g^#(c())) , c^#() -> c_3() } Weak Trs: { c() -> d() } Obligation: innermost runtime complexity Answer: MAYBE We estimate the number of application of {3} by applications of Pre({3}) = {}. Here rules are labeled as follows: DPs: { 1: g^#(X) -> c_1(h^#(X)) , 2: h^#(d()) -> c_2(g^#(c())) , 3: c^#() -> c_3() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { g^#(X) -> c_1(h^#(X)) , h^#(d()) -> c_2(g^#(c())) } Weak DPs: { c^#() -> c_3() } Weak Trs: { c() -> d() } Obligation: innermost runtime complexity Answer: MAYBE The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed. { c^#() -> c_3() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { g^#(X) -> c_1(h^#(X)) , h^#(d()) -> c_2(g^#(c())) } Weak Trs: { c() -> d() } 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) 'Fastest (timeout of 5 seconds)' failed due to the following reason: Computation stopped due to timeout after 5.0 seconds. 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) 'Polynomial Path Order (PS)' failed due to the following reason: The input cannot be shown compatible 3) 'Polynomial Path Order (PS)' failed due to the following reason: The input cannot be shown compatible 2) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed due to the following reason: Computation stopped due to timeout after 5.0 seconds. 2) '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(g) = {1} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [g](x1) = [1] x1 + [7] [h](x1) = [1] x1 + [7] [c] = [3] [d] = [7] The following symbols are considered usable {g, h, c} The order satisfies the following ordering constraints: [g(X)] = [1] X + [7] >= [1] X + [7] = [h(X)] [h(d())] = [14] > [10] = [g(c())] [c()] = [3] ? [7] = [d()] 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: { g(X) -> h(X) , c() -> d() } Weak Trs: { h(d()) -> g(c()) } Obligation: innermost runtime complexity Answer: MAYBE The weightgap principle applies (using the following nonconstant growth matrix-interpretation) The following argument positions are usable: Uargs(g) = {1} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [g](x1) = [1] x1 + [0] [h](x1) = [1] x1 + [6] [c] = [4] [d] = [2] The following symbols are considered usable {g, h, c} The order satisfies the following ordering constraints: [g(X)] = [1] X + [0] ? [1] X + [6] = [h(X)] [h(d())] = [8] > [4] = [g(c())] [c()] = [4] > [2] = [d()] 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: { g(X) -> h(X) } Weak Trs: { h(d()) -> g(c()) , c() -> d() } 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. 3) '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 Arrrr..