Problem: f(g(X),Y) -> f(X,n__f(n__g(X),activate(Y))) f(X1,X2) -> n__f(X1,X2) g(X) -> n__g(X) activate(n__f(X1,X2)) -> f(activate(X1),X2) activate(n__g(X)) -> g(activate(X)) activate(X) -> X Proof: Unfolding Processor: loop length: 5 terms: activate(n__f(n__g(g(X)),x2927)) f(activate(n__g(g(X))),x2927) f(g(activate(g(X))),x2927) f(g(g(X)),x2927) f(g(X),n__f(n__g(g(X)),activate(x2927))) context: f(X,n__f(n__g(X),[])) substitution: X -> X x2927 -> activate(x2927) Qed