MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { g(x, x) -> f(f(x, x), x) , f(x, x) -> g(x, x) , f(x, y) -> y } Obligation: innermost runtime complexity Answer: MAYBE We add following dependency tuples: Strict DPs: { g^#(x, x) -> c_1(f^#(f(x, x), x), f^#(x, x)) , f^#(x, x) -> c_2(g^#(x, x)) , f^#(x, y) -> 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, x) -> c_1(f^#(f(x, x), x), f^#(x, x)) , f^#(x, x) -> c_2(g^#(x, x)) , f^#(x, y) -> c_3() } Weak Trs: { g(x, x) -> f(f(x, x), x) , f(x, x) -> g(x, x) , f(x, y) -> y } Obligation: innermost runtime complexity Answer: MAYBE We estimate the number of application of {3} by applications of Pre({3}) = {1}. Here rules are labeled as follows: DPs: { 1: g^#(x, x) -> c_1(f^#(f(x, x), x), f^#(x, x)) , 2: f^#(x, x) -> c_2(g^#(x, x)) , 3: f^#(x, y) -> c_3() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { g^#(x, x) -> c_1(f^#(f(x, x), x), f^#(x, x)) , f^#(x, x) -> c_2(g^#(x, x)) } Weak DPs: { f^#(x, y) -> c_3() } Weak Trs: { g(x, x) -> f(f(x, x), x) , f(x, x) -> g(x, x) , f(x, y) -> y } 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^#(x, y) -> c_3() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { g^#(x, x) -> c_1(f^#(f(x, x), x), f^#(x, x)) , f^#(x, x) -> c_2(g^#(x, x)) } Weak Trs: { g(x, x) -> f(f(x, x), x) , f(x, x) -> g(x, x) , f(x, y) -> y } 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..