let R be the TRS under consideration ap(f,_1) -> ap(f,app(g,_1)) is in elim_R(R) let l be the left-hand side and r be the right-hand side of this rule let p = epsilon let theta = {} let theta' = {_1/app(g,_1)} we have r|p = ap(f,app(g,_1)) and theta'(theta(l)) = theta(r|p) so, theta(l) = ap(f,_1) is non-terminating w.r.t. R Termination disproved by the forward process proof stopped at iteration i=0, depth k=0 1 rule(s) generated