let R be the TRS under consideration f(tt,_1) -> f(isList(_1),_1) is in elim_R(R) let r0 be the right-hand side of this rule p0 = 0 is a position in r0 we have r0|p0 = isList(_1) isList(nil) -> tt is in R let l'0 be the left-hand side of this rule theta0 = {_1/nil} is a mgu of r0|p0 and l'0 ==> f(tt,nil) -> f(tt,nil) is in EU_R^1 let l be the left-hand side and r be the right-hand side of this rule let p = epsilon let theta = {} let theta' = {} we have r|p = f(tt,nil) and theta'(theta(l)) = theta(r|p) so, theta(l) = f(tt,nil) is non-terminating w.r.t. R Termination disproved by the forward process proof stopped at iteration i=1, depth k=2 4 rule(s) generated