let R be the TRS under consideration f(_1,c(_1),c(_2)) -> f(_2,_2,f(_2,_1,_2)) 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 = _2 g(_3,_4) -> _3 is in R let l'0 be the left-hand side of this rule theta0 = {_2/g(_3,_4)} is a mgu of r0|p0 and l'0 ==> f(_1,c(_1),c(g(_2,_3))) -> f(_2,g(_2,_3),f(g(_2,_3),_1,g(_2,_3))) is in EU_R^1 let r1 be the right-hand side of this rule p1 = 1 is a position in r1 we have r1|p1 = g(_2,_3) g(_4,_5) -> _5 is in R let l'1 be the left-hand side of this rule theta1 = {_2/_4, _3/_5} is a mgu of r1|p1 and l'1 ==> f(_1,c(_1),c(g(_2,_3))) -> f(_2,_3,f(g(_2,_3),_1,g(_2,_3))) is in EU_R^2 let r2 be the right-hand side of this rule p2 = 2.0 is a position in r2 we have r2|p2 = g(_2,_3) g(_4,_5) -> _5 is in R let l'2 be the left-hand side of this rule theta2 = {_2/_4, _3/_5} is a mgu of r2|p2 and l'2 ==> f(_1,c(_1),c(g(_2,_3))) -> f(_2,_3,f(_3,_1,g(_2,_3))) is in EU_R^3 let r3 be the right-hand side of this rule p3 = 2 is a position in r3 we have r3|p3 = f(_3,_1,g(_2,_3)) f(c(_4),_4,_5) -> c(_5) is in R let l'3 be the left-hand side of this rule theta3 = {_1/_4, _3/c(_4), _5/g(_2,c(_4))} is a mgu of r3|p3 and l'3 ==> f(_1,c(_1),c(g(_2,c(_1)))) -> f(_2,c(_1),c(g(_2,c(_1)))) 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 = {_1/_2} let theta' = {} we have r|p = f(_2,c(_1),c(g(_2,c(_1)))) and theta'(theta(l)) = theta(r|p) so, theta(l) = f(_2,c(_2),c(g(_2,c(_2)))) is non-terminating w.r.t. R Termination disproved by the forward process proof stopped at iteration i=4, depth k=3 241 rule(s) generated