MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { g(x, x) -> g(g(x, x), x) , g(x, y) -> y } Obligation: innermost runtime complexity Answer: MAYBE We add following dependency tuples: Strict DPs: { g^#(x, x) -> c_1(g^#(g(x, x), x), g^#(x, x)) , g^#(x, y) -> c_2() } 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(g^#(g(x, x), x), g^#(x, x)) , g^#(x, y) -> c_2() } Weak Trs: { g(x, x) -> g(g(x, x), x) , g(x, y) -> y } Obligation: innermost runtime complexity Answer: MAYBE We estimate the number of application of {2} by applications of Pre({2}) = {1}. Here rules are labeled as follows: DPs: { 1: g^#(x, x) -> c_1(g^#(g(x, x), x), g^#(x, x)) , 2: g^#(x, y) -> c_2() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { g^#(x, x) -> c_1(g^#(g(x, x), x), g^#(x, x)) } Weak DPs: { g^#(x, y) -> c_2() } Weak Trs: { g(x, x) -> g(g(x, x), 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. { g^#(x, y) -> c_2() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { g^#(x, x) -> c_1(g^#(g(x, x), x), g^#(x, x)) } Weak Trs: { g(x, x) -> g(g(x, x), x) , g(x, y) -> y } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..