let R be the TRS under consideration app(app(app(subst,_1),_2),_3) -> app(app(_1,_3),app(_2,_3)) is in elim_R(R) let l0 be the left-hand side of this rule p0 = epsilon is a position in l0 we have l0|p0 = app(app(app(subst,_1),_2),_3) app(app(fix,_4),_5) -> app(app(_4,app(fix,_4)),_5) is in R let r'0 be the right-hand side of this rule theta0 = {_2/app(fix,app(subst,_1)), _3/_5, _4/app(subst,_1)} is a mgu of l0|p0 and r'0 ==> app(app(fix,app(subst,_1)),_2) -> app(app(_1,_2),app(app(fix,app(subst,_1)),_2)) is in EU_R^1 let l be the left-hand side and r be the right-hand side of this rule let p = 1 let theta = {} let theta' = {} we have r|p = app(app(fix,app(subst,_1)),_2) and theta'(theta(l)) = theta(r|p) so, theta(l) = app(app(fix,app(subst,_1)),_2) is non-terminating w.r.t. R Termination disproved by the backward process proof stopped at iteration i=1, depth k=3 3 rule(s) generated