MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(X1, X2) -> n__f(X1, X2) , f(g(X), Y) -> f(X, n__f(g(X), activate(Y))) , activate(X) -> X , activate(n__f(X1, X2)) -> f(X1, X2) } Obligation: innermost runtime complexity Answer: MAYBE We add following dependency tuples: Strict DPs: { f^#(X1, X2) -> c_1() , f^#(g(X), Y) -> c_2(f^#(X, n__f(g(X), activate(Y))), activate^#(Y)) , activate^#(X) -> c_3() , activate^#(n__f(X1, X2)) -> c_4(f^#(X1, X2)) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(X1, X2) -> c_1() , f^#(g(X), Y) -> c_2(f^#(X, n__f(g(X), activate(Y))), activate^#(Y)) , activate^#(X) -> c_3() , activate^#(n__f(X1, X2)) -> c_4(f^#(X1, X2)) } Weak Trs: { f(X1, X2) -> n__f(X1, X2) , f(g(X), Y) -> f(X, n__f(g(X), activate(Y))) , activate(X) -> X , activate(n__f(X1, X2)) -> f(X1, X2) } Obligation: innermost runtime complexity Answer: MAYBE We estimate the number of application of {1,3} by applications of Pre({1,3}) = {2,4}. Here rules are labeled as follows: DPs: { 1: f^#(X1, X2) -> c_1() , 2: f^#(g(X), Y) -> c_2(f^#(X, n__f(g(X), activate(Y))), activate^#(Y)) , 3: activate^#(X) -> c_3() , 4: activate^#(n__f(X1, X2)) -> c_4(f^#(X1, X2)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(g(X), Y) -> c_2(f^#(X, n__f(g(X), activate(Y))), activate^#(Y)) , activate^#(n__f(X1, X2)) -> c_4(f^#(X1, X2)) } Weak DPs: { f^#(X1, X2) -> c_1() , activate^#(X) -> c_3() } Weak Trs: { f(X1, X2) -> n__f(X1, X2) , f(g(X), Y) -> f(X, n__f(g(X), activate(Y))) , activate(X) -> X , activate(n__f(X1, X2)) -> f(X1, X2) } 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^#(X1, X2) -> c_1() , activate^#(X) -> c_3() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(g(X), Y) -> c_2(f^#(X, n__f(g(X), activate(Y))), activate^#(Y)) , activate^#(n__f(X1, X2)) -> c_4(f^#(X1, X2)) } Weak Trs: { f(X1, X2) -> n__f(X1, X2) , f(g(X), Y) -> f(X, n__f(g(X), activate(Y))) , activate(X) -> X , activate(n__f(X1, X2)) -> f(X1, X2) } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..