MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(f(x)) -> b() , f(g(a())) -> a() , g(x) -> f(g(x)) } Obligation: innermost runtime complexity Answer: MAYBE Arguments of following rules are not normal-forms: { f(g(a())) -> a() } All above mentioned rules can be savely removed. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(f(x)) -> b() , g(x) -> f(g(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: We add the following dependency tuples: Strict DPs: { f^#(f(x)) -> c_1() , g^#(x) -> c_2(f^#(g(x)), g^#(x)) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(f(x)) -> c_1() , g^#(x) -> c_2(f^#(g(x)), g^#(x)) } Weak Trs: { f(f(x)) -> b() , g(x) -> f(g(x)) } Obligation: innermost runtime complexity Answer: MAYBE We estimate the number of application of {1} by applications of Pre({1}) = {2}. Here rules are labeled as follows: DPs: { 1: f^#(f(x)) -> c_1() , 2: g^#(x) -> c_2(f^#(g(x)), g^#(x)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { g^#(x) -> c_2(f^#(g(x)), g^#(x)) } Weak DPs: { f^#(f(x)) -> c_1() } Weak Trs: { f(f(x)) -> b() , g(x) -> f(g(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. { f^#(f(x)) -> c_1() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { g^#(x) -> c_2(f^#(g(x)), g^#(x)) } Weak Trs: { f(f(x)) -> b() , g(x) -> f(g(x)) } Obligation: innermost runtime complexity Answer: MAYBE Due to missing edges in the dependency-graph, the right-hand sides of following rules could be simplified: { g^#(x) -> c_2(f^#(g(x)), g^#(x)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { g^#(x) -> c_1(g^#(x)) } Weak Trs: { f(f(x)) -> b() , g(x) -> f(g(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: { g^#(x) -> c_1(g^#(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) '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(f) = {1} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [f](x1) = [1] x1 + [7] [g](x1) = [1] x1 + [7] [b] = [5] The following symbols are considered usable {f, g} The order satisfies the following ordering constraints: [f(f(x))] = [1] x + [14] > [5] = [b()] [g(x)] = [1] x + [7] ? [1] x + [14] = [f(g(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: { g(x) -> f(g(x)) } Weak Trs: { f(f(x)) -> b() } 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) '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 Arrrr..