let R be the TRS under consideration

a(b(_1)) -> b(a(a(c(b(_1))))) is in elim_R(R)
let r0 be the right-hand side of this rule
p0 = 0.0.0.0 is a position in r0
we have r0|p0 = b(_1)
b(_2) -> 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(b(_1)) -> b(a(a(c(a(_1))))) is in EU_R^1
let r1 be the right-hand side of this rule
p1 = 0.0.0.0 is a position in r1
we have r1|p1 = a(_1)
a(_2) -> _2 is in R
let l'1 be the left-hand side of this rule
theta1 = {_1/_2} is a mgu of r1|p1 and l'1

==> a(b(_1)) -> b(a(a(c(_1)))) is in EU_R^2
let r2 be the right-hand side of this rule
p2 = 0.0.0.0 is a position in r2
we have r2|p2 = _1
a(_2) -> _2 is in R
let l'2 be the left-hand side of this rule
theta2 = {_1/a(_2)} is a mgu of r2|p2 and l'2

==> a(b(a(_1))) -> b(a(a(c(_1)))) is in EU_R^3
let r3 be the right-hand side of this rule
p3 = 0.0.0.0 is a position in r3
we have r3|p3 = _1
a(_2) -> _2 is in R
let l'3 be the left-hand side of this rule
theta3 = {_1/a(_2)} is a mgu of r3|p3 and l'3

==> a(b(a(a(_1)))) -> b(a(a(c(_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 = c(_1)
c(c(_2)) -> _2 is in R
let l'4 be the left-hand side of this rule
theta4 = {_1/c(_2)} is a mgu of r4|p4 and l'4

==> a(b(a(a(c(_1))))) -> b(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 = a(_1)
a(b(_2)) -> b(a(a(c(b(_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(b(a(a(c(b(_1)))))) -> b(a(b(a(a(c(b(_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 = 0
let theta = {}
let theta' = {}
we have r|p = a(b(a(a(c(b(_1)))))) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = a(b(a(a(c(b(_1)))))) is non-terminating w.r.t. R

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