let R be the TRS under consideration g(_1) -> h(_1) is in elim_R(R) let r0 be the right-hand side of this rule p0 = epsilon is a position in r0 we have r0|p0 = h(_1) h(d) -> g(c) is in R let l'0 be the left-hand side of this rule theta0 = {_1/d} is a mgu of r0|p0 and l'0 ==> g(d) -> g(c) is in EU_R^1 let r1 be the right-hand side of this rule p1 = 0 is a position in r1 we have r1|p1 = c c -> d is in R let l'1 be the left-hand side of this rule theta1 = {} is a mgu of r1|p1 and l'1 ==> g(d) -> g(d) is in EU_R^2 let l be the left-hand side and r be the right-hand side of this rule let p = epsilon let theta = {} let theta' = {} we have r|p = g(d) and theta'(theta(l)) = theta(r|p) so, theta(l) = g(d) is non-terminating w.r.t. R Termination disproved by the forward process proof stopped at iteration i=2, depth k=1 8 rule(s) generated