let R be the TRS under consideration c(a(b(a(_1)))) -> c(c(a(_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 = c(a(_1)) c(a(b(a(_2)))) -> a(b(a(b(c(c(a(_2))))))) is in R let l'0 be the left-hand side of this rule theta0 = {_1/b(a(_2))} is a mgu of r0|p0 and l'0 ==> c(a(b(a(b(a(_1)))))) -> c(a(b(a(b(c(c(a(_1)))))))) is in EU_R^1 let r1 be the right-hand side of this rule p1 = 0.0.0.0.0.0 is a position in r1 we have r1|p1 = c(a(_1)) c(a(b(a(_2)))) -> a(b(a(b(c(c(a(_2))))))) is in R let l'1 be the left-hand side of this rule theta1 = {_1/b(a(_2))} is a mgu of r1|p1 and l'1 ==> c(a(b(a(b(a(b(a(_1)))))))) -> c(a(b(a(b(c(a(b(a(b(c(c(a(_1))))))))))))) is in EU_R^2 let r2 be the right-hand side of this rule p2 = 0.0.0.0.0 is a position in r2 we have r2|p2 = c(a(b(a(b(c(c(a(_1)))))))) c(a(b(a(_2)))) -> a(b(a(b(c(c(a(_2))))))) is in R let l'2 be the left-hand side of this rule theta2 = {_2/b(c(c(a(_1))))} is a mgu of r2|p2 and l'2 ==> c(a(b(a(b(a(b(a(_1)))))))) -> c(a(b(a(b(a(b(a(b(c(c(a(b(c(c(a(_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/b(c(c(a(b(c(c(a(_1))))))))} we have r|p = c(a(b(a(b(a(b(a(b(c(c(a(b(c(c(a(_1)))))))))))))))) and theta'(theta(l)) = theta(r|p) so, theta(l) = c(a(b(a(b(a(b(a(_1)))))))) is non-terminating w.r.t. R Termination disproved by the forward process proof stopped at iteration i=3, depth k=13 7 rule(s) generated