let R be the TRS under consideration

a(a(a(_1))) -> b(b(b(_1))) is in elim_R(R)
let l0 be the left-hand side of this rule
p0 = 0.0 is a position in l0
we have l0|p0 = a(_1)
b(a(a(_2))) -> a(_2) is in R
let r'0 be the right-hand side of this rule
theta0 = {_1/_2} is a mgu of l0|p0 and r'0

==> a(a(b(a(a(_1))))) -> b(b(b(_1))) is in EU_R^1
let l1 be the left-hand side of this rule
p1 = 0 is a position in l1
we have l1|p1 = a(b(a(a(_1))))
b(b(_2)) -> a(b(a(_2))) is in R
let r'1 be the right-hand side of this rule
theta1 = {_2/a(_1)} is a mgu of l1|p1 and r'1

==> a(b(b(a(_1)))) -> b(b(b(_1))) is in EU_R^2
let l2 be the left-hand side of this rule
p2 = 0.0.0 is a position in l2
we have l2|p2 = a(_1)
b(b(_2)) -> a(b(a(_2))) is in R
let r'2 be the right-hand side of this rule
theta2 = {_1/b(a(_2))} is a mgu of l2|p2 and r'2

==> a(b(b(b(b(_1))))) -> b(b(b(b(a(_1))))) is in EU_R^3
let l3 be the left-hand side of this rule
p3 = 0.0 is a position in l3
we have l3|p3 = b(b(b(_1)))
a(a(a(_2))) -> b(b(b(_2))) is in R
let r'3 be the right-hand side of this rule
theta3 = {_1/_2} is a mgu of l3|p3 and r'3

==> a(b(a(a(a(_1))))) -> b(b(b(b(a(_1))))) is in EU_R^4
let l4 be the left-hand side of this rule
p4 = epsilon is a position in l4
we have l4|p4 = a(b(a(a(a(_1)))))
b(b(_2)) -> a(b(a(_2))) is in R
let r'4 be the right-hand side of this rule
theta4 = {_2/a(a(_1))} is a mgu of l4|p4 and r'4

==> b(b(a(a(_1)))) -> b(b(b(b(a(_1))))) is in EU_R^5
let l5 be the left-hand side of this rule
p5 = 0.0.0 is a position in l5
we have l5|p5 = a(_1)
b(a(a(_2))) -> a(_2) is in R
let r'5 be the right-hand side of this rule
theta5 = {_1/_2} is a mgu of l5|p5 and r'5

==> b(b(a(b(a(a(_1)))))) -> b(b(b(b(a(_1))))) is in EU_R^6
let l6 be the left-hand side of this rule
p6 = 0.0 is a position in l6
we have l6|p6 = a(b(a(a(_1))))
b(b(_2)) -> a(b(a(_2))) is in R
let r'6 be the right-hand side of this rule
theta6 = {_2/a(_1)} is a mgu of l6|p6 and r'6

==> b(b(b(b(a(_1))))) -> b(b(b(b(a(_1))))) is in EU_R^7
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 = b(b(b(b(a(_1))))) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = b(b(b(b(a(_1))))) is non-terminating w.r.t. R

Termination disproved by the backward process
proof stopped at iteration i=7, depth k=6
101 rule(s) generated