let R be the TRS under consideration f(0,1,_1) -> f(g(_1,_1),_1,_1) is in elim_R(R) let r0 be the right-hand side of this rule p0 = 0 is a position in r0 we have r0|p0 = g(_1,_1) g(_2,_3) -> _2 is in R let l'0 be the left-hand side of this rule theta0 = {_1/_3, _2/_3} is a mgu of r0|p0 and l'0 ==> f(0,1,_1) -> f(_1,_1,_1) is in EU_R^1 let r1 be the right-hand side of this rule p1 = 0 is a position in r1 we have r1|p1 = _1 g(_2,_3) -> _2 is in R let l'1 be the left-hand side of this rule theta1 = {_1/g(_2,_3)} is a mgu of r1|p1 and l'1 ==> f(0,1,g(_1,_2)) -> f(_1,g(_1,_2),g(_1,_2)) is in EU_R^2 let r2 be the right-hand side of this rule p2 = 1 is a position in r2 we have r2|p2 = g(_1,_2) g(_3,_4) -> _4 is in R let l'2 be the left-hand side of this rule theta2 = {_1/_3, _2/_4} is a mgu of r2|p2 and l'2 ==> f(0,1,g(_1,_2)) -> f(_1,_2,g(_1,_2)) 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 = {_1/0, _2/1} let theta' = {} we have r|p = f(_1,_2,g(_1,_2)) and theta'(theta(l)) = theta(r|p) so, theta(l) = f(0,1,g(0,1)) is non-terminating w.r.t. R Termination disproved by the forward process proof stopped at iteration i=3, depth k=2 10 rule(s) generated