let R be the TRS under consideration sel(s(_1),cons(_2)) -> sel(_1,_3) is in elim_R(R) let l be the left-hand side and r be the right-hand side of this rule let p = 1 let theta = {_3/sel(s(_1),cons(_2))} let theta' = {} we have r|p = _3 and theta'(theta(l)) = theta(r|p) so, theta(l) = sel(s(_1),cons(_2)) is non-terminating w.r.t. R Termination disproved by the forward process proof stopped at iteration i=0, depth k=0 1 rule(s) generated