MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(0(), 1(), X) -> f(g(X, X), X, X) , g(X, Y) -> X , g(X, Y) -> Y } Obligation: innermost runtime complexity Answer: MAYBE We add following dependency tuples: Strict DPs: { f^#(0(), 1(), X) -> c_1(f^#(g(X, X), X, X), g^#(X, X)) , g^#(X, Y) -> c_2() , g^#(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: { f^#(0(), 1(), X) -> c_1(f^#(g(X, X), X, X), g^#(X, X)) , g^#(X, Y) -> c_2() , g^#(X, Y) -> c_3() } Weak Trs: { f(0(), 1(), X) -> f(g(X, X), X, X) , g(X, Y) -> X , g(X, Y) -> Y } Obligation: innermost runtime complexity Answer: MAYBE We estimate the number of application of {2,3} by applications of Pre({2,3}) = {1}. Here rules are labeled as follows: DPs: { 1: f^#(0(), 1(), X) -> c_1(f^#(g(X, X), X, X), g^#(X, X)) , 2: g^#(X, Y) -> c_2() , 3: g^#(X, Y) -> c_3() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(0(), 1(), X) -> c_1(f^#(g(X, X), X, X), g^#(X, X)) } Weak DPs: { g^#(X, Y) -> c_2() , g^#(X, Y) -> c_3() } Weak Trs: { f(0(), 1(), X) -> f(g(X, X), X, X) , 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. { g^#(X, Y) -> c_2() , g^#(X, Y) -> c_3() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(0(), 1(), X) -> c_1(f^#(g(X, X), X, X), g^#(X, X)) } Weak Trs: { f(0(), 1(), X) -> f(g(X, X), X, X) , g(X, Y) -> X , g(X, Y) -> Y } 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^#(0(), 1(), X) -> c_1(f^#(g(X, X), X, X), g^#(X, X)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(0(), 1(), X) -> c_1(f^#(g(X, X), X, X)) } Weak Trs: { f(0(), 1(), X) -> f(g(X, X), X, X) , g(X, Y) -> X , g(X, Y) -> Y } Obligation: innermost runtime complexity Answer: MAYBE We replace rewrite rules by usable rules: Weak Usable Rules: { g(X, Y) -> X , g(X, Y) -> Y } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(0(), 1(), X) -> c_1(f^#(g(X, X), X, X)) } Weak Trs: { g(X, Y) -> X , g(X, Y) -> Y } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..