let R be the TRS under consideration inf(_1) -> cons(_1,inf(s(_1))) 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 = {} let theta' = {_1/s(_1)} we have r|p = inf(s(_1)) and theta'(theta(l)) = theta(r|p) so, theta(l) = inf(_1) 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