let R be the TRS under consideration b(_1) -> 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 = _1 a(b(_2)) -> b(c(b(a(a(_2))))) is in R let l'0 be the left-hand side of this rule theta0 = {_1/a(b(_2))} is a mgu of r0|p0 and l'0 ==> b(a(b(_1))) -> a(b(c(b(a(a(_1)))))) is in EU_R^1 let r1 be the right-hand side of this rule p1 = 0.0.0 is a position in r1 we have r1|p1 = b(a(a(_1))) b(_2) -> a(_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 ==> b(a(b(_1))) -> a(b(c(a(a(a(_1)))))) is in EU_R^2 let r2 be the right-hand side of this rule p2 = 0.0.0 is a position in r2 we have r2|p2 = a(a(a(_1))) a(_2) -> _2 is in R let l'2 be the left-hand side of this rule theta2 = {_2/a(a(_1))} is a mgu of r2|p2 and l'2 ==> b(a(b(_1))) -> a(b(c(a(a(_1))))) is in EU_R^3 let r3 be the right-hand side of this rule p3 = 0.0.0 is a position in r3 we have r3|p3 = a(a(_1)) a(_2) -> _2 is in R let l'3 be the left-hand side of this rule theta3 = {_2/a(_1)} is a mgu of r3|p3 and l'3 ==> b(a(b(_1))) -> a(b(c(a(_1)))) is in EU_R^4 let r4 be the right-hand side of this rule p4 = 0.0.0 is a position in r4 we have r4|p4 = a(_1) a(_2) -> _2 is in R let l'4 be the left-hand side of this rule theta4 = {_1/_2} is a mgu of r4|p4 and l'4 ==> b(a(b(_1))) -> a(b(c(_1))) is in EU_R^5 let r5 be the right-hand side of this rule p5 = epsilon is a position in r5 we have r5|p5 = a(b(c(_1))) a(b(_2)) -> b(c(b(a(a(_2))))) is in R let l'5 be the left-hand side of this rule theta5 = {_2/c(_1)} is a mgu of r5|p5 and l'5 ==> b(a(b(_1))) -> b(c(b(a(a(c(_1)))))) is in EU_R^6 let r6 be the right-hand side of this rule p6 = 0.0.0.0.0 is a position in r6 we have r6|p6 = c(_1) c(c(_2)) -> _2 is in R let l'6 be the left-hand side of this rule theta6 = {_1/c(_2)} is a mgu of r6|p6 and l'6 ==> b(a(b(c(_1)))) -> b(c(b(a(a(_1))))) is in EU_R^7 let r7 be the right-hand side of this rule p7 = 0.0.0.0 is a position in r7 we have r7|p7 = a(_1) a(b(_2)) -> b(c(b(a(a(_2))))) is in R let l'7 be the left-hand side of this rule theta7 = {_1/b(_2)} is a mgu of r7|p7 and l'7 ==> b(a(b(c(b(_1))))) -> b(c(b(a(b(c(b(a(a(_1))))))))) is in EU_R^8 let l be the left-hand side and r be the right-hand side of this rule let p = 0.0 let theta = {} let theta' = {_1/a(a(_1))} we have r|p = b(a(b(c(b(a(a(_1))))))) and theta'(theta(l)) = theta(r|p) so, theta(l) = b(a(b(c(b(_1))))) is non-terminating w.r.t. R Termination disproved by the forward process proof stopped at iteration i=8, depth k=6 3225 rule(s) generated