MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { c() -> f(g(c())) , f(g(X)) -> g(X) } Obligation: innermost runtime complexity Answer: MAYBE We add following dependency tuples: Strict DPs: { c^#() -> c_1(f^#(g(c())), c^#()) , f^#(g(X)) -> c_2() } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { c^#() -> c_1(f^#(g(c())), c^#()) , f^#(g(X)) -> c_2() } Weak Trs: { c() -> f(g(c())) , f(g(X)) -> g(X) } 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: c^#() -> c_1(f^#(g(c())), c^#()) , 2: f^#(g(X)) -> c_2() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { c^#() -> c_1(f^#(g(c())), c^#()) } Weak DPs: { f^#(g(X)) -> c_2() } Weak Trs: { c() -> f(g(c())) , f(g(X)) -> 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^#(g(X)) -> c_2() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { c^#() -> c_1(f^#(g(c())), c^#()) } Weak Trs: { c() -> f(g(c())) , f(g(X)) -> 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: { c^#() -> c_1(f^#(g(c())), c^#()) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { c^#() -> c_1(c^#()) } Weak Trs: { c() -> f(g(c())) , f(g(X)) -> 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: { c^#() -> c_1(c^#()) } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..