let R be the TRS under consideration

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

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

==> c(c(a(_1))) -> 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 = _1
c(_2) -> _2 is in R
let r'2 be the right-hand side of this rule
theta2 = {_1/_2} is a mgu of l2|p2 and r'2

==> c(c(a(c(_1)))) -> b(_1) is in EU_R^3
let l3 be the left-hand side of this rule
p3 = 0.0.0 is a position in l3
we have l3|p3 = c(_1)
c(_2) -> _2 is in R
let r'3 be the right-hand side of this rule
theta3 = {_2/c(_1)} is a mgu of l3|p3 and r'3

==> c(c(a(c(c(_1))))) -> b(_1) is in EU_R^4
let l4 be the left-hand side of this rule
p4 = 0.0.0 is a position in l4
we have l4|p4 = c(c(_1))
b(a(c(_2))) -> c(c(a(b(a(_2))))) is in R
let r'4 be the right-hand side of this rule
theta4 = {_1/a(b(a(_2)))} is a mgu of l4|p4 and r'4

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

==> b(a(c(c(_1)))) -> b(a(b(a(_1)))) is in EU_R^6
let l6 be the left-hand side of this rule
p6 = 0.0.0.0 is a position in l6
we have l6|p6 = _1
a(_2) -> _2 is in R
let r'6 be the right-hand side of this rule
theta6 = {_1/_2} is a mgu of l6|p6 and r'6

==> b(a(c(c(a(_1))))) -> b(a(b(a(_1)))) is in EU_R^7
let l7 be the left-hand side of this rule
p7 = 0.0 is a position in l7
we have l7|p7 = c(c(a(_1)))
b(a(c(_2))) -> c(c(a(b(a(_2))))) is in R
let r'7 be the right-hand side of this rule
theta7 = {_1/b(a(_2))} is a mgu of l7|p7 and r'7

==> b(a(b(a(c(_1))))) -> b(a(b(a(b(a(_1)))))) is in EU_R^8
let l8 be the left-hand side of this rule
p8 = 0.0.0.0 is a position in l8
we have l8|p8 = c(_1)
b(a(c(_2))) -> c(c(a(b(a(_2))))) is in R
let r'8 be the right-hand side of this rule
theta8 = {_1/c(a(b(a(_2))))} is a mgu of l8|p8 and r'8

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

Termination disproved by the backward process
proof stopped at iteration i=9, depth k=6
1504 rule(s) generated