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