let R be the TRS under consideration *(_1,+(_2,f(_3))) -> *(g(_1,_3),+(_2,_2)) 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 = *(_1,+(_2,f(_3))) *(_4,+(_5,f(_6))) -> *(g(_4,_6),+(_5,_5)) is in R let r'0 be the right-hand side of this rule theta0 = {_1/g(_4,_6), _2/f(_3), _5/f(_3)} is a mgu of l0|p0 and r'0 ==> *(_1,+(f(_2),f(_3))) -> *(g(g(_1,_3),_2),+(f(_2),f(_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 = epsilon let theta = {} let theta' = {_1/g(g(_1,_3),_2), _2/_2, _3/_2} we have r|p = *(g(g(_1,_3),_2),+(f(_2),f(_2))) and theta'(theta(l)) = theta(r|p) so, theta(l) = *(_1,+(f(_2),f(_3))) is non-terminating w.r.t. R Termination disproved by the backward process proof stopped at iteration i=1, depth k=3 15 rule(s) generated