let R be the TRS under consideration

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

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

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

==> a(b(_1)) -> a(c(_1)) is in EU_R^3
let r3 be the right-hand side of this rule
p3 = 0 is a position in r3
we have r3|p3 = c(_1)
c(c(_2)) -> b(_2) is in R
let l'3 be the left-hand side of this rule
theta3 = {_1/c(_2)} is a mgu of r3|p3 and l'3

==> a(b(c(_1))) -> a(b(_1)) is in EU_R^4
let r4 be the right-hand side of this rule
p4 = 0 is a position in r4
we have r4|p4 = b(_1)
b(_2) -> a(_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

==> a(b(c(_1))) -> a(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 = _1
a(b(_2)) -> b(c(a(a(_2)))) is in R
let l'5 be the left-hand side of this rule
theta5 = {_1/a(b(_2))} is a mgu of r5|p5 and l'5

==> a(b(c(a(b(_1))))) -> a(a(b(c(a(a(_1)))))) is in EU_R^6
let r6 be the right-hand side of this rule
p6 = 0.0.0.0 is a position in r6
we have r6|p6 = a(a(_1))
a(_2) -> _2 is in R
let l'6 be the left-hand side of this rule
theta6 = {_2/a(_1)} is a mgu of r6|p6 and l'6

==> a(b(c(a(b(_1))))) -> a(a(b(c(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(_2) -> _2 is in R
let l'7 be the left-hand side of this rule
theta7 = {_1/_2} is a mgu of r7|p7 and l'7

==> a(b(c(a(b(_1))))) -> a(a(b(c(_1)))) is in EU_R^8
let r8 be the right-hand side of this rule
p8 = 0 is a position in r8
we have r8|p8 = a(b(c(_1)))
a(b(_2)) -> b(c(a(a(_2)))) is in R
let l'8 be the left-hand side of this rule
theta8 = {_2/c(_1)} is a mgu of r8|p8 and l'8

==> a(b(c(a(b(_1))))) -> a(b(c(a(a(c(_1)))))) is in EU_R^9
let r9 be the right-hand side of this rule
p9 = 0.0.0.0.0 is a position in r9
we have r9|p9 = c(_1)
c(c(_2)) -> b(_2) is in R
let l'9 be the left-hand side of this rule
theta9 = {_1/c(_2)} is a mgu of r9|p9 and l'9

==> a(b(c(a(b(c(_1)))))) -> a(b(c(a(a(b(_1)))))) is in EU_R^10
let r10 be the right-hand side of this rule
p10 = 0.0.0.0 is a position in r10
we have r10|p10 = a(b(_1))
a(b(_2)) -> b(c(a(a(_2)))) is in R
let l'10 be the left-hand side of this rule
theta10 = {_1/_2} is a mgu of r10|p10 and l'10

==> a(b(c(a(b(c(_1)))))) -> a(b(c(a(b(c(a(a(_1)))))))) is in EU_R^11
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(b(c(a(b(c(a(a(_1)))))))) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = a(b(c(a(b(c(_1)))))) is non-terminating w.r.t. R

Termination disproved by the forward process
proof stopped at iteration i=11, depth k=6
21728 rule(s) generated