let R be the TRS under consideration f(a,n__b,_1) -> f(_1,_1,_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 = a c -> a 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(c,n__b,_1) -> f(_1,_1,_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 = n__b b -> n__b 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(c,b,_1) -> f(_1,_1,_1) 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 = b c -> b is in R let r'2 be the right-hand side of this rule theta2 = {} is a mgu of l2|p2 and r'2 ==> f(c,c,_1) -> f(_1,_1,_1) 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/c} let theta' = {} we have r|p = f(_1,_1,_1) and theta'(theta(l)) = theta(r|p) so, theta(l) = f(c,c,c) is non-terminating w.r.t. R Termination disproved by the backward process proof stopped at iteration i=3, depth k=1 16 rule(s) generated