let R be the TRS under consideration a(b(_1)) -> a(c(b(b(a(a(_1)))))) is in elim_R(R) let r0 be the right-hand side of this rule p0 = 0.0 is a position in r0 we have r0|p0 = b(b(a(a(_1)))) b(_2) -> _2 is in R let l'0 be the left-hand side of this rule theta0 = {_2/b(a(a(_1)))} is a mgu of r0|p0 and l'0 ==> a(b(_1)) -> a(c(b(a(a(_1))))) is in EU_R^1 let r1 be the right-hand side of this rule p1 = 0.0 is a position in r1 we have r1|p1 = b(a(a(_1))) b(_2) -> _2 is in R let l'1 be the left-hand side of this rule theta1 = {_2/a(a(_1))} is a mgu of r1|p1 and l'1 ==> a(b(_1)) -> a(c(a(a(_1)))) is in EU_R^2 let r2 be the right-hand side of this rule p2 = 0.0 is a position in r2 we have r2|p2 = a(a(_1)) a(_2) -> _2 is in R let l'2 be the left-hand side of this rule theta2 = {_2/a(_1)} is a mgu of r2|p2 and l'2 ==> a(b(_1)) -> a(c(a(_1))) is in EU_R^3 let l3 be the left-hand side of this rule p3 = 0 is a position in l3 we have l3|p3 = b(_1) c(c(_2)) -> _2 is in R let r'3 be the right-hand side of this rule theta3 = {_2/b(_1)} is a mgu of l3|p3 and r'3 ==> a(c(c(b(_1)))) -> a(c(a(_1))) is in EU_R^4 let l4 be the left-hand side of this rule p4 = 0.0 is a position in l4 we have l4|p4 = c(b(_1)) a(_2) -> _2 is in R let r'4 be the right-hand side of this rule theta4 = {_2/c(b(_1))} is a mgu of l4|p4 and r'4 ==> a(c(a(c(b(_1))))) -> a(c(a(_1))) is in EU_R^5 let r5 be the right-hand side of this rule p5 = 0.0 is a position in r5 we have r5|p5 = a(_1) a(b(_2)) -> a(c(b(b(a(a(_2)))))) is in R let l'5 be the left-hand side of this rule theta5 = {_1/b(_2)} is a mgu of r5|p5 and l'5 ==> a(c(a(c(b(b(_1)))))) -> a(c(a(c(b(b(a(a(_1)))))))) is in EU_R^6 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/a(a(_1))} we have r|p = a(c(a(c(b(b(a(a(_1)))))))) and theta'(theta(l)) = theta(r|p) so, theta(l) = a(c(a(c(b(b(_1)))))) is non-terminating w.r.t. R Termination disproved by the forward+backward process proof stopped at iteration i=6, depth k=6 2756 rule(s) generated