MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(g(x)) -> f(a(g(g(f(x))), g(f(x)))) } Obligation: innermost runtime complexity Answer: MAYBE We add following dependency tuples: Strict DPs: { f^#(g(x)) -> c_1(f^#(a(g(g(f(x))), g(f(x)))), f^#(x), f^#(x)) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(g(x)) -> c_1(f^#(a(g(g(f(x))), g(f(x)))), f^#(x), f^#(x)) } Weak Trs: { f(g(x)) -> f(a(g(g(f(x))), g(f(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: { f^#(g(x)) -> c_1(f^#(a(g(g(f(x))), g(f(x)))), f^#(x), f^#(x)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(g(x)) -> c_1(f^#(x), f^#(x)) } Weak Trs: { f(g(x)) -> f(a(g(g(f(x))), g(f(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^#(g(x)) -> c_1(f^#(x), f^#(x)) } Obligation: innermost runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'matrices' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'matrix interpretation of dimension 4' failed due to the following reason: The input cannot be shown compatible 2) 'matrix interpretation of dimension 3' failed due to the following reason: The input cannot be shown compatible 3) 'matrix interpretation of dimension 3' failed due to the following reason: The input cannot be shown compatible 4) 'matrix interpretation of dimension 2' failed due to the following reason: The input cannot be shown compatible 5) 'matrix interpretation of dimension 2' failed due to the following reason: The input cannot be shown compatible 6) 'matrix interpretation of dimension 1' failed due to the following reason: The input cannot be shown compatible 2) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. Arrrr..