let R be the TRS under consideration hamming -> app(app(cons,app(s,0)),app(app(merge,list1),app(app(merge,list2),list3))) is in elim_R(R) let r0 be the right-hand side of this rule p0 = 1.0.1 is a position in r0 we have r0|p0 = list1 list1 -> app(app(map,app(mult,app(s,app(s,0)))),hamming) is in R let l'0 be the left-hand side of this rule theta0 = {} is a mgu of r0|p0 and l'0 ==> hamming -> app(app(cons,app(s,0)),app(app(merge,app(app(map,app(mult,app(s,app(s,0)))),hamming)),app(app(merge,list2),list3))) is in EU_R^1 let l be the left-hand side and r be the right-hand side of this rule let p = 1.0.1.1 let theta = {} let theta' = {} we have r|p = hamming and theta'(theta(l)) = theta(r|p) so, theta(l) = hamming is non-terminating w.r.t. R Termination disproved by the forward process proof stopped at iteration i=1, depth k=4 71 rule(s) generated