let R be the TRS under consideration h(_1,_2) -> f(_1,_2,_1) is in elim_R(R) let l0 be the left-hand side of this rule p0 = epsilon is a position in l0 we have l0|p0 = h(_1,_2) f(0,1,_3) -> h(_3,_3) is in R let r'0 be the right-hand side of this rule theta0 = {_1/_3, _2/_3} is a mgu of l0|p0 and r'0 ==> f(0,1,_1) -> f(_1,_1,_1) is in EU_R^1 let l1 be the left-hand side of this rule p1 = 0 is a position in l1 we have l1|p1 = 0 g(_2,_3) -> _2 is in R let r'1 be the right-hand side of this rule theta1 = {_2/0} is a mgu of l1|p1 and r'1 ==> f(g(0,_1),1,_2) -> f(_2,_2,_2) is in EU_R^2 let l2 be the left-hand side of this rule p2 = 1 is a position in l2 we have l2|p2 = 1 g(_3,_4) -> _4 is in R let r'2 be the right-hand side of this rule theta2 = {_4/1} is a mgu of l2|p2 and r'2 ==> f(g(0,_1),g(_2,1),_3) -> f(_3,_3,_3) is in EU_R^3 let l be the left-hand side and r be the right-hand side of this rule let p = epsilon let theta = {_1/1, _2/0, _3/g(0,1)} let theta' = {} we have r|p = f(_3,_3,_3) and theta'(theta(l)) = theta(r|p) so, theta(l) = f(g(0,1),g(0,1),g(0,1)) is non-terminating w.r.t. R Termination disproved by the backward process proof stopped at iteration i=3, depth k=2 92 rule(s) generated