MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(X) -> g(n__h(f(X))) , h(X) -> n__h(X) , activate(X) -> X , activate(n__h(X)) -> h(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) '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(g) = {1}, Uargs(n__h) = {1} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [f](x1) = [1] x1 + [3] [g](x1) = [1] x1 + [3] [n__h](x1) = [1] x1 + [7] [h](x1) = [1] x1 + [5] [activate](x1) = [1] x1 + [7] The following symbols are considered usable {f, h, activate} The order satisfies the following ordering constraints: [f(X)] = [1] X + [3] ? [1] X + [13] = [g(n__h(f(X)))] [h(X)] = [1] X + [5] ? [1] X + [7] = [n__h(X)] [activate(X)] = [1] X + [7] > [1] X + [0] = [X] [activate(n__h(X))] = [1] X + [14] > [1] X + [5] = [h(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: { f(X) -> g(n__h(f(X))) , h(X) -> n__h(X) } Weak Trs: { activate(X) -> X , activate(n__h(X)) -> h(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(g) = {1}, Uargs(n__h) = {1} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [f](x1) = [1] x1 + [3] [g](x1) = [1] x1 + [7] [n__h](x1) = [1] x1 + [3] [h](x1) = [1] x1 + [6] [activate](x1) = [1] x1 + [7] The following symbols are considered usable {f, h, activate} The order satisfies the following ordering constraints: [f(X)] = [1] X + [3] ? [1] X + [13] = [g(n__h(f(X)))] [h(X)] = [1] X + [6] > [1] X + [3] = [n__h(X)] [activate(X)] = [1] X + [7] > [1] X + [0] = [X] [activate(n__h(X))] = [1] X + [10] > [1] X + [6] = [h(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: { f(X) -> g(n__h(f(X))) } Weak Trs: { h(X) -> n__h(X) , activate(X) -> X , activate(n__h(X)) -> h(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) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed due to the following reason: Computation stopped due to timeout after 5.0 seconds. 3) '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 2) 'WithProblem (timeout of 60 seconds)' failed due to the following reason: We add the following innermost weak dependency pairs: Strict DPs: { f^#(X) -> c_1(f^#(X)) , h^#(X) -> c_2() , activate^#(X) -> c_3() , activate^#(n__h(X)) -> c_4(h^#(X)) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(X) -> c_1(f^#(X)) , h^#(X) -> c_2() , activate^#(X) -> c_3() , activate^#(n__h(X)) -> c_4(h^#(X)) } Strict Trs: { f(X) -> g(n__h(f(X))) , h(X) -> n__h(X) , activate(X) -> X , activate(n__h(X)) -> h(X) } Obligation: innermost runtime complexity Answer: MAYBE No rule is usable, rules are removed from the input problem. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(X) -> c_1(f^#(X)) , h^#(X) -> c_2() , activate^#(X) -> c_3() , activate^#(n__h(X)) -> c_4(h^#(X)) } Obligation: innermost runtime complexity Answer: MAYBE The weightgap principle applies (using the following constant growth matrix-interpretation) The following argument positions are usable: Uargs(c_1) = {1}, Uargs(c_4) = {1} TcT has computed the following constructor-restricted matrix interpretation. [n__h](x1) = [1 2] x1 + [1] [0 1] [1] [f^#](x1) = [2 2] x1 + [2] [1 1] [2] [c_1](x1) = [1 0] x1 + [1] [0 1] [2] [h^#](x1) = [1 1] x1 + [1] [1 1] [1] [c_2] = [0] [1] [activate^#](x1) = [2 2] x1 + [2] [2 2] [2] [c_3] = [1] [1] [c_4](x1) = [1 0] x1 + [1] [0 1] [1] The following symbols are considered usable {f^#, h^#, activate^#} The order satisfies the following ordering constraints: [f^#(X)] = [2 2] X + [2] [1 1] [2] ? [2 2] X + [3] [1 1] [4] = [c_1(f^#(X))] [h^#(X)] = [1 1] X + [1] [1 1] [1] > [0] [1] = [c_2()] [activate^#(X)] = [2 2] X + [2] [2 2] [2] > [1] [1] = [c_3()] [activate^#(n__h(X))] = [2 6] X + [6] [2 6] [6] > [1 1] X + [2] [1 1] [2] = [c_4(h^#(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 DPs: { f^#(X) -> c_1(f^#(X)) } Weak DPs: { h^#(X) -> c_2() , activate^#(X) -> c_3() , activate^#(n__h(X)) -> c_4(h^#(X)) } 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. { h^#(X) -> c_2() , activate^#(X) -> c_3() , activate^#(n__h(X)) -> c_4(h^#(X)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(X) -> c_1(f^#(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) 'Polynomial Path Order (PS)' failed due to the following reason: The input cannot be shown compatible 2) 'Fastest (timeout of 5 seconds)' failed due to the following reason: Computation stopped due to timeout after 5.0 seconds. 3) 'Polynomial Path Order (PS)' failed due to the following reason: The input cannot be shown compatible Arrrr..