MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(x, c(x), c(y)) -> f(y, y, f(y, x, y)) , f(c(x), x, y) -> c(y) , f(s(x), y, z) -> f(x, s(c(y)), c(z)) , g(x, y) -> x , g(x, y) -> y } Obligation: innermost runtime complexity Answer: MAYBE We add following dependency tuples: Strict DPs: { f^#(x, c(x), c(y)) -> c_1(f^#(y, y, f(y, x, y)), f^#(y, x, y)) , f^#(c(x), x, y) -> c_2() , f^#(s(x), y, z) -> c_3(f^#(x, s(c(y)), c(z))) , g^#(x, y) -> c_4() , g^#(x, y) -> c_5() } 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(x), c(y)) -> c_1(f^#(y, y, f(y, x, y)), f^#(y, x, y)) , f^#(c(x), x, y) -> c_2() , f^#(s(x), y, z) -> c_3(f^#(x, s(c(y)), c(z))) , g^#(x, y) -> c_4() , g^#(x, y) -> c_5() } Weak Trs: { f(x, c(x), c(y)) -> f(y, y, f(y, x, y)) , f(c(x), x, y) -> c(y) , f(s(x), y, z) -> f(x, s(c(y)), c(z)) , g(x, y) -> x , g(x, y) -> y } Obligation: innermost runtime complexity Answer: MAYBE We estimate the number of application of {2,4,5} by applications of Pre({2,4,5}) = {1,3}. Here rules are labeled as follows: DPs: { 1: f^#(x, c(x), c(y)) -> c_1(f^#(y, y, f(y, x, y)), f^#(y, x, y)) , 2: f^#(c(x), x, y) -> c_2() , 3: f^#(s(x), y, z) -> c_3(f^#(x, s(c(y)), c(z))) , 4: g^#(x, y) -> c_4() , 5: g^#(x, y) -> c_5() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(x, c(x), c(y)) -> c_1(f^#(y, y, f(y, x, y)), f^#(y, x, y)) , f^#(s(x), y, z) -> c_3(f^#(x, s(c(y)), c(z))) } Weak DPs: { f^#(c(x), x, y) -> c_2() , g^#(x, y) -> c_4() , g^#(x, y) -> c_5() } Weak Trs: { f(x, c(x), c(y)) -> f(y, y, f(y, x, y)) , f(c(x), x, y) -> c(y) , f(s(x), y, z) -> f(x, s(c(y)), c(z)) , g(x, y) -> x , g(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^#(c(x), x, y) -> c_2() , g^#(x, y) -> c_4() , g^#(x, y) -> c_5() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(x, c(x), c(y)) -> c_1(f^#(y, y, f(y, x, y)), f^#(y, x, y)) , f^#(s(x), y, z) -> c_3(f^#(x, s(c(y)), c(z))) } Weak Trs: { f(x, c(x), c(y)) -> f(y, y, f(y, x, y)) , f(c(x), x, y) -> c(y) , f(s(x), y, z) -> f(x, s(c(y)), c(z)) , g(x, y) -> x , g(x, y) -> y } Obligation: innermost runtime complexity Answer: MAYBE We replace rewrite rules by usable rules: Weak Usable Rules: { f(x, c(x), c(y)) -> f(y, y, f(y, x, y)) , f(c(x), x, y) -> c(y) , f(s(x), y, z) -> f(x, s(c(y)), c(z)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(x, c(x), c(y)) -> c_1(f^#(y, y, f(y, x, y)), f^#(y, x, y)) , f^#(s(x), y, z) -> c_3(f^#(x, s(c(y)), c(z))) } Weak Trs: { f(x, c(x), c(y)) -> f(y, y, f(y, x, y)) , f(c(x), x, y) -> c(y) , f(s(x), y, z) -> f(x, s(c(y)), c(z)) } 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..