let R be the TRS under consideration f(_1,_1) -> f(i(_1),g(g(_1))) is in elim_R(R) let r0 be the right-hand side of this rule p0 = 1 is a position in r0 we have r0|p0 = g(g(_1)) g(_2) -> i(_2) is in R let l'0 be the left-hand side of this rule theta0 = {_2/g(_1)} is a mgu of r0|p0 and l'0 ==> f(_1,_1) -> f(i(_1),i(g(_1))) is in EU_R^1 let r1 be the right-hand side of this rule p1 = 1.0 is a position in r1 we have r1|p1 = g(_1) g(_2) -> i(_2) is in R let l'1 be the left-hand side of this rule theta1 = {_1/_2} is a mgu of r1|p1 and l'1 ==> f(_1,_1) -> f(i(_1),i(i(_1))) is in EU_R^2 let r2 be the right-hand side of this rule p2 = epsilon is a position in r2 we have r2|p2 = f(i(_1),i(i(_1))) f(_2,i(_2)) -> f(_2,_2) is in R let l'2 be the left-hand side of this rule theta2 = {_2/i(_1)} is a mgu of r2|p2 and l'2 ==> f(_1,_1) -> f(i(_1),i(_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 = {} let theta' = {_1/i(_1)} we have r|p = f(i(_1),i(_1)) and theta'(theta(l)) = theta(r|p) so, theta(l) = f(_1,_1) is non-terminating w.r.t. R Termination disproved by the forward process proof stopped at iteration i=3, depth k=3 22 rule(s) generated