let R be the TRS under consideration if(false,_1) -> _2 is in elim_R(R) let l be the left-hand side and r be the right-hand side of this rule let p = epsilon let theta = {_2/if(false,_1)} let theta' = {} we have r|p = _2 and theta'(theta(l)) = theta(r|p) so, theta(l) = if(false,_1) is non-terminating w.r.t. R Termination disproved by the backward process proof stopped at iteration i=0, depth k=0 1 rule(s) generated