let R be the TRS under consideration f(0,1,g(_1,_2),_3) -> f(g(_1,_2),g(_1,_2),g(_1,_2),h(_1)) is in elim_R(R) let l0 be the left-hand side of this rule p0 = 0 is a position in l0 we have l0|p0 = 0 g(0,1) -> 0 is in R let r'0 be the right-hand side of this rule theta0 = {} is a mgu of l0|p0 and r'0 ==> f(g(0,1),1,g(_1,_2),_3) -> f(g(_1,_2),g(_1,_2),g(_1,_2),h(_1)) is in EU_R^1 let l1 be the left-hand side of this rule p1 = 1 is a position in l1 we have l1|p1 = 1 g(0,1) -> 1 is in R let r'1 be the right-hand side of this rule theta1 = {} is a mgu of l1|p1 and r'1 ==> f(g(0,1),g(0,1),g(_1,_2),_3) -> f(g(_1,_2),g(_1,_2),g(_1,_2),h(_1)) 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 = {_1/0, _2/1, _3/h(0)} let theta' = {} we have r|p = f(g(_1,_2),g(_1,_2),g(_1,_2),h(_1)) and theta'(theta(l)) = theta(r|p) so, theta(l) = f(g(0,1),g(0,1),g(0,1),h(0)) is non-terminating w.r.t. R Termination disproved by the backward process proof stopped at iteration i=2, depth k=2 6 rule(s) generated