let R be the TRS under consideration f(g(_1,_2),_1,_3) -> f(_3,_3,_3) is in elim_R(R) let r0 be the right-hand side of this rule p0 = 1 is a position in r0 we have r0|p0 = _3 g(_4,_5) -> _4 is in R let l'0 be the left-hand side of this rule theta0 = {_3/g(_4,_5)} is a mgu of r0|p0 and l'0 ==> f(g(_1,_2),_1,g(_3,_4)) -> f(g(_3,_4),_3,g(_3,_4)) 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/_3, _2/_4} let theta' = {} we have r|p = f(g(_3,_4),_3,g(_3,_4)) and theta'(theta(l)) = theta(r|p) so, theta(l) = f(g(_3,_4),_3,g(_3,_4)) 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