let R be the TRS under consideration f(s(a),s(b),_1) -> f(_1,_1,_1) is in elim_R(R) let r0 be the right-hand side of this rule p0 = 0 is a position in r0 we have r0|p0 = _1 cons(_2,_3) -> _2 is in R let l'0 be the left-hand side of this rule theta0 = {_1/cons(_2,_3)} is a mgu of r0|p0 and l'0 ==> f(s(a),s(b),cons(_1,_2)) -> f(_1,cons(_1,_2),cons(_1,_2)) is in EU_R^1 let r1 be the right-hand side of this rule p1 = 1 is a position in r1 we have r1|p1 = cons(_1,_2) cons(_3,_4) -> _4 is in R let l'1 be the left-hand side of this rule theta1 = {_1/_3, _2/_4} is a mgu of r1|p1 and l'1 ==> f(s(a),s(b),cons(_1,_2)) -> f(_1,_2,cons(_1,_2)) is in EU_R^2 let l be the left-hand side and r be the right-hand side of this rule let p = epsilon let theta = {_1/s(a), _2/s(b)} let theta' = {} we have r|p = f(_1,_2,cons(_1,_2)) and theta'(theta(l)) = theta(r|p) so, theta(l) = f(s(a),s(b),cons(s(a),s(b))) is non-terminating w.r.t. R Termination disproved by the forward process proof stopped at iteration i=2, depth k=2 9 rule(s) generated