let R be the TRS under consideration

a(a(a(_1))) -> b(a(b(_1))) is in elim_R(R)
let r0 be the right-hand side of this rule
p0 = epsilon is a position in r0
we have r0|p0 = b(a(b(_1)))
b(a(b(_2))) -> a(b(a(_2))) is in R
let l'0 be the left-hand side of this rule
theta0 = {_1/_2} is a mgu of r0|p0 and l'0

==> a(a(a(_1))) -> a(b(a(_1))) is in EU_R^1
let r1 be the right-hand side of this rule
p1 = 0 is a position in r1
we have r1|p1 = b(a(_1))
b(a(b(_2))) -> a(b(a(_2))) is in R
let l'1 be the left-hand side of this rule
theta1 = {_1/b(_2)} is a mgu of r1|p1 and l'1

==> a(a(a(b(_1)))) -> a(a(b(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(_1)
a(a(a(_2))) -> b(a(b(_2))) is in R
let l'2 be the left-hand side of this rule
theta2 = {_1/a(a(_2))} is a mgu of r2|p2 and l'2

==> a(a(a(b(a(a(_1)))))) -> a(a(b(b(a(b(_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 = b(a(b(_1)))
b(a(b(_2))) -> a(b(a(_2))) is in R
let l'3 be the left-hand side of this rule
theta3 = {_1/_2} is a mgu of r3|p3 and l'3

==> a(a(a(b(a(a(_1)))))) -> a(a(b(a(b(a(_1)))))) is in EU_R^4
let r4 be the right-hand side of this rule
p4 = 0.0 is a position in r4
we have r4|p4 = b(a(b(a(_1))))
b(a(b(_2))) -> a(b(a(_2))) is in R
let l'4 be the left-hand side of this rule
theta4 = {_2/a(_1)} is a mgu of r4|p4 and l'4

==> a(a(a(b(a(a(_1)))))) -> a(a(a(b(a(a(_1)))))) is in EU_R^5
let l be the left-hand side and r be the right-hand side of this rule
let p = epsilon
let theta = {}
let theta' = {}
we have r|p = a(a(a(b(a(a(_1)))))) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = a(a(a(b(a(a(_1)))))) is non-terminating w.r.t. R

Termination disproved by the forward process
proof stopped at iteration i=5, depth k=6
49 rule(s) generated