let R be the TRS under consideration f(k(a),k(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 = k(a) u(d,c(_2),_3) -> k(_2) is in R let r'0 be the right-hand side of this rule theta0 = {_2/a} is a mgu of l0|p0 and r'0 ==> f(u(d,c(a),_1),k(b),_2) -> f(_2,_2,_2) is in EU_R^1 let l1 be the left-hand side of this rule p1 = 0.1 is a position in l1 we have l1|p1 = c(a) h(d) -> c(a) 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(u(d,h(d),_1),k(b),_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 = k(b) u(d,c(_3),_4) -> k(_3) is in R let r'2 be the right-hand side of this rule theta2 = {_3/b} is a mgu of l2|p2 and r'2 ==> f(u(d,h(d),_1),u(d,c(b),_2),_3) -> f(_3,_3,_3) is in EU_R^3 let l3 be the left-hand side of this rule p3 = 1.1 is a position in l3 we have l3|p3 = c(b) h(d) -> c(b) is in R let r'3 be the right-hand side of this rule theta3 = {} is a mgu of l3|p3 and r'3 ==> f(u(d,h(d),_1),u(d,h(d),_2),_3) -> f(_3,_3,_3) is in EU_R^4 let l be the left-hand side and r be the right-hand side of this rule let p = epsilon let theta = {_2/_1, _3/u(d,h(d),_1)} let theta' = {} we have r|p = f(_3,_3,_3) and theta'(theta(l)) = theta(r|p) so, theta(l) = f(u(d,h(d),_1),u(d,h(d),_1),u(d,h(d),_1)) is non-terminating w.r.t. R Termination disproved by the backward process proof stopped at iteration i=4, depth k=3 105 rule(s) generated