let R be the TRS under consideration

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

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

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

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

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

==> b(a(c(a(b(a(_1)))))) -> b(b(b(a(c(b(_1)))))) is in EU_R^5
let l5 be the left-hand side of this rule
p5 = 0.0.0.0.0 is a position in l5
we have l5|p5 = a(_1)
b(a(_2)) -> a(c(b(_2))) is in R
let r'5 be the right-hand side of this rule
theta5 = {_1/c(b(_2))} is a mgu of l5|p5 and r'5

==> b(a(c(a(b(b(a(_1))))))) -> b(b(b(a(c(b(c(b(_1)))))))) is in EU_R^6
let l6 be the left-hand side of this rule
p6 = 0.0.0 is a position in l6
we have l6|p6 = a(b(b(a(_1))))
b(c(_2)) -> a(b(b(_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(a(c(b(c(a(_1)))))) -> b(b(b(a(c(b(c(b(_1)))))))) is in EU_R^7
let l7 be the left-hand side of this rule
p7 = 0 is a position in l7
we have l7|p7 = a(c(b(c(a(_1)))))
b(a(_2)) -> a(c(b(_2))) is in R
let r'7 be the right-hand side of this rule
theta7 = {_2/c(a(_1))} is a mgu of l7|p7 and r'7

==> b(b(a(c(a(_1))))) -> b(b(b(a(c(b(c(b(_1)))))))) is in EU_R^8
let r8 be the right-hand side of this rule
p8 = 0.0.0.0.0 is a position in r8
we have r8|p8 = b(c(b(_1)))
b(c(_2)) -> a(b(b(_2))) is in R
let l'8 be the left-hand side of this rule
theta8 = {_2/b(_1)} is a mgu of r8|p8 and l'8

==> b(b(a(c(a(_1))))) -> b(b(b(a(c(a(b(b(b(_1))))))))) is in EU_R^9
let l be the left-hand side and r be the right-hand side of this rule
let p = 0
let theta = {}
let theta' = {_1/b(b(b(_1)))}
we have r|p = b(b(a(c(a(b(b(b(_1)))))))) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = b(b(a(c(a(_1))))) is non-terminating w.r.t. R

Termination disproved by the forward+backward process
proof stopped at iteration i=9, depth k=8
1765 rule(s) generated