let R be the TRS under consideration

a(b(b(_1))) -> c(a(a(a(_1)))) is in elim_R(R)
let l0 be the left-hand side of this rule
p0 = 0.0 is a position in l0
we have l0|p0 = b(_1)
c(c(_2)) -> _2 is in R
let r'0 be the right-hand side of this rule
theta0 = {_2/b(_1)} is a mgu of l0|p0 and r'0

==> a(b(c(c(b(_1))))) -> c(a(a(a(_1)))) is in EU_R^1
let l1 be the left-hand side of this rule
p1 = 0 is a position in l1
we have l1|p1 = b(c(c(b(_1))))
a(_2) -> b(c(_2)) is in R
let r'1 be the right-hand side of this rule
theta1 = {_2/c(b(_1))} is a mgu of l1|p1 and r'1

==> a(a(c(b(_1)))) -> c(a(a(a(_1)))) is in EU_R^2
let l2 be the left-hand side of this rule
p2 = 0.0.0.0 is a position in l2
we have l2|p2 = _1
c(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

==> a(a(c(b(c(c(_1)))))) -> c(a(a(a(_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 = b(c(c(_1)))
a(_2) -> b(c(_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

==> a(a(c(a(c(_1))))) -> c(a(a(a(_1)))) is in EU_R^4
let l4 be the left-hand side of this rule
p4 = 0.0.0.0 is a position in l4
we have l4|p4 = c(_1)
a(b(b(_2))) -> c(a(a(a(_2)))) is in R
let r'4 be the right-hand side of this rule
theta4 = {_1/a(a(a(_2)))} is a mgu of l4|p4 and r'4

==> a(a(c(a(a(b(b(_1))))))) -> c(a(a(a(a(a(a(_1))))))) is in EU_R^5
let l5 be the left-hand side of this rule
p5 = 0.0.0.0.0.0 is a position in l5
we have l5|p5 = b(_1)
a(_2) -> b(c(_2)) is in R
let r'5 be the right-hand side of this rule
theta5 = {_1/c(_2)} is a mgu of l5|p5 and r'5

==> a(a(c(a(a(b(a(_1))))))) -> c(a(a(a(a(a(a(c(_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 = a(_1)
c(c(_2)) -> _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

==> a(a(c(a(a(b(c(c(a(_1))))))))) -> c(a(a(a(a(a(a(c(_1)))))))) is in EU_R^7
let l7 be the left-hand side of this rule
p7 = 0.0.0.0.0 is a position in l7
we have l7|p7 = b(c(c(a(_1))))
a(_2) -> b(c(_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

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

==> a(a(a(b(b(c(a(_1))))))) -> c(a(a(a(a(a(a(c(_1)))))))) is in EU_R^9
let l9 be the left-hand side of this rule
p9 = 0.0.0.0 is a position in l9
we have l9|p9 = b(c(a(_1)))
a(_2) -> b(c(_2)) is in R
let r'9 be the right-hand side of this rule
theta9 = {_2/a(_1)} is a mgu of l9|p9 and r'9

==> a(a(a(b(a(a(_1)))))) -> c(a(a(a(a(a(a(c(_1)))))))) is in EU_R^10
let l10 be the left-hand side of this rule
p10 = 0.0.0.0 is a position in l10
we have l10|p10 = a(a(_1))
c(c(_2)) -> _2 is in R
let r'10 be the right-hand side of this rule
theta10 = {_2/a(a(_1))} is a mgu of l10|p10 and r'10

==> a(a(a(b(c(c(a(a(_1)))))))) -> c(a(a(a(a(a(a(c(_1)))))))) is in EU_R^11
let l11 be the left-hand side of this rule
p11 = 0.0.0 is a position in l11
we have l11|p11 = b(c(c(a(a(_1)))))
a(_2) -> b(c(_2)) is in R
let r'11 be the right-hand side of this rule
theta11 = {_2/c(a(a(_1)))} is a mgu of l11|p11 and r'11

==> a(a(a(a(c(a(a(_1))))))) -> c(a(a(a(a(a(a(c(_1)))))))) is in EU_R^12
let l12 be the left-hand side of this rule
p12 = 0.0.0.0 is a position in l12
we have l12|p12 = c(a(a(_1)))
a(b(b(_2))) -> c(a(a(a(_2)))) is in R
let r'12 be the right-hand side of this rule
theta12 = {_1/a(_2)} is a mgu of l12|p12 and r'12

==> a(a(a(a(a(b(b(_1))))))) -> c(a(a(a(a(a(a(c(a(_1))))))))) is in EU_R^13
let l13 be the left-hand side of this rule
p13 = 0.0.0.0.0.0 is a position in l13
we have l13|p13 = b(_1)
c(c(_2)) -> _2 is in R
let r'13 be the right-hand side of this rule
theta13 = {_2/b(_1)} is a mgu of l13|p13 and r'13

==> a(a(a(a(a(b(c(c(b(_1))))))))) -> c(a(a(a(a(a(a(c(a(_1))))))))) is in EU_R^14
let l14 be the left-hand side of this rule
p14 = 0.0.0.0.0 is a position in l14
we have l14|p14 = b(c(c(b(_1))))
a(_2) -> b(c(_2)) is in R
let r'14 be the right-hand side of this rule
theta14 = {_2/c(b(_1))} is a mgu of l14|p14 and r'14

==> a(a(a(a(a(a(c(b(_1)))))))) -> c(a(a(a(a(a(a(c(a(_1))))))))) is in EU_R^15
let l15 be the left-hand side of this rule
p15 = 0.0.0.0.0.0.0 is a position in l15
we have l15|p15 = b(_1)
a(_2) -> b(c(_2)) is in R
let r'15 be the right-hand side of this rule
theta15 = {_1/c(_2)} is a mgu of l15|p15 and r'15

==> a(a(a(a(a(a(c(a(_1)))))))) -> c(a(a(a(a(a(a(c(a(c(_1)))))))))) is in EU_R^16
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(_1)}
we have r|p = a(a(a(a(a(a(c(a(c(_1))))))))) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = a(a(a(a(a(a(c(a(_1)))))))) is non-terminating w.r.t. R

Termination disproved by the backward process
proof stopped at iteration i=16, depth k=9
7170 rule(s) generated