let R be the TRS under consideration

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

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

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

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

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

==> a(a(b(b(c(a(b(_1))))))) -> a(a(c(a(a(_1))))) is in EU_R^5
let r5 be the right-hand side of this rule
p5 = 0 is a position in r5
we have r5|p5 = a(c(a(a(_1))))
a(c(_2)) -> a(a(_2)) is in R
let l'5 be the left-hand side of this rule
theta5 = {_2/a(a(_1))} is a mgu of r5|p5 and l'5

==> a(a(b(b(c(a(b(_1))))))) -> a(a(a(a(a(_1))))) is in EU_R^6
let l6 be the left-hand side of this rule
p6 = 0.0.0.0.0.0 is a position in l6
we have l6|p6 = b(_1)
a(a(b(_2))) -> b(b(c(a(a(_2))))) is in R
let r'6 be the right-hand side of this rule
theta6 = {_1/b(c(a(a(_2))))} is a mgu of l6|p6 and r'6

==> a(a(b(b(c(a(a(a(b(_1))))))))) -> a(a(a(a(a(b(c(a(a(_1))))))))) is in EU_R^7
let l7 be the left-hand side of this rule
p7 = 0.0.0.0.0.0 is a position in l7
we have l7|p7 = a(a(b(_1)))
a(c(_2)) -> a(a(_2)) is in R
let r'7 be the right-hand side of this rule
theta7 = {_2/b(_1)} is a mgu of l7|p7 and r'7

==> a(a(b(b(c(a(a(c(b(_1))))))))) -> a(a(a(a(a(b(c(a(a(_1))))))))) is in EU_R^8
let l8 be the left-hand side of this rule
p8 = 0.0 is a position in l8
we have l8|p8 = b(b(c(a(a(c(b(_1)))))))
a(a(b(_2))) -> b(b(c(a(a(_2))))) is in R
let r'8 be the right-hand side of this rule
theta8 = {_2/c(b(_1))} is a mgu of l8|p8 and r'8

==> a(a(a(a(b(c(b(_1))))))) -> a(a(a(a(a(b(c(a(a(_1))))))))) is in EU_R^9
let r9 be the right-hand side of this rule
p9 = 0.0.0.0.0.0.0 is a position in r9
we have r9|p9 = a(a(_1))
a(a(b(_2))) -> b(b(c(a(a(_2))))) is in R
let l'9 be the left-hand side of this rule
theta9 = {_1/b(_2)} is a mgu of r9|p9 and l'9

==> a(a(a(a(b(c(b(b(_1)))))))) -> a(a(a(a(a(b(c(b(b(c(a(a(_1)))))))))))) is in EU_R^10
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/c(a(a(_1)))}
we have r|p = a(a(a(a(b(c(b(b(c(a(a(_1))))))))))) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = a(a(a(a(b(c(b(b(_1)))))))) is non-terminating w.r.t. R

Termination disproved by the forward+backward process
proof stopped at iteration i=10, depth k=9
1569 rule(s) generated