let R be the TRS under consideration ap(ap(ap(g,_1),_2),ap(s,_3)) -> ap(ap(ap(g,_1),_2),ap(ap(_1,_2),0)) is in elim_R(R) let r0 be the right-hand side of this rule p0 = 1.0 is a position in r0 we have r0|p0 = ap(_1,_2) ap(f,_4) -> _4 is in R let l'0 be the left-hand side of this rule theta0 = {_1/f, _2/_4} is a mgu of r0|p0 and l'0 ==> ap(ap(ap(g,f),_1),ap(s,_2)) -> ap(ap(ap(g,f),_1),ap(_1,0)) 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 = {_1/s, _2/0} let theta' = {} we have r|p = ap(ap(ap(g,f),_1),ap(_1,0)) and theta'(theta(l)) = theta(r|p) so, theta(l) = ap(ap(ap(g,f),s),ap(s,0)) is non-terminating w.r.t. R Termination disproved by the forward process proof stopped at iteration i=1, depth k=3 2 rule(s) generated