let R be the TRS under consideration 0(q0(0(_1))) -> 0(0(q0(_1))) is in elim_R(R) let l0 be the left-hand side of this rule p0 = 0 is a position in l0 we have l0|p0 = q0(0(_1)) q0(h(_2)) -> q0(0(h(_2))) is in R let r'0 be the right-hand side of this rule theta0 = {_1/h(_2)} is a mgu of l0|p0 and r'0 ==> 0(q0(h(_1))) -> 0(0(q0(h(_1)))) is in EU_R^1 let l be the left-hand side and r be the right-hand side of this rule let p = 0 let theta = {} let theta' = {} we have r|p = 0(q0(h(_1))) and theta'(theta(l)) = theta(r|p) so, theta(l) = 0(q0(h(_1))) is non-terminating w.r.t. R Termination disproved by the backward process proof stopped at iteration i=1, depth k=3 45 rule(s) generated