let R be the TRS under consideration fact(_1) -> if(zero(_1),s(0),prod(_1,fact(p(_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 = 2.1 let theta = {} let theta' = {_1/p(_1)} we have r|p = fact(p(_1)) and theta'(theta(l)) = theta(r|p) so, theta(l) = fact(_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