let R be the TRS under consideration

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

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

==> a(a(b(b(_1)))) -> a(a(_1)) is in EU_R^3
let r3 be the right-hand side of this rule
p3 = 0 is a position in r3
we have r3|p3 = a(_1)
a(c(_2)) -> a(a(_2)) is in R
let l'3 be the left-hand side of this rule
theta3 = {_1/c(_2)} is a mgu of r3|p3 and l'3

==> a(a(b(b(c(_1))))) -> a(a(a(_1))) is in EU_R^4
let r4 be the right-hand side of this rule
p4 = 0.0 is a position in r4
we have r4|p4 = a(_1)
a(a(b(_2))) -> b(b(c(a(c(_2))))) is in R
let l'4 be the left-hand side of this rule
theta4 = {_1/a(b(_2))} is a mgu of r4|p4 and l'4

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

==> a(a(b(b(c(a(b(_1))))))) -> a(c(b(c(a(c(_1)))))) is in EU_R^6
let r6 be the right-hand side of this rule
p6 = epsilon is a position in r6
we have r6|p6 = a(c(b(c(a(c(_1))))))
a(c(_2)) -> a(a(_2)) is in R
let l'6 be the left-hand side of this rule
theta6 = {_2/b(c(a(c(_1))))} is a mgu of r6|p6 and l'6

==> a(a(b(b(c(a(b(_1))))))) -> a(a(b(c(a(c(_1)))))) is in EU_R^7
let r7 be the right-hand side of this rule
p7 = epsilon is a position in r7
we have r7|p7 = a(a(b(c(a(c(_1))))))
a(a(b(_2))) -> b(b(c(a(c(_2))))) is in R
let l'7 be the left-hand side of this rule
theta7 = {_2/c(a(c(_1)))} is a mgu of r7|p7 and l'7

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

==> a(a(b(b(c(a(b(_1))))))) -> a(a(c(a(c(_1))))) is in EU_R^9
let r9 be the right-hand side of this rule
p9 = 0 is a position in r9
we have r9|p9 = a(c(a(c(_1))))
a(c(_2)) -> a(a(_2)) is in R
let l'9 be the left-hand side of this rule
theta9 = {_2/a(c(_1))} is a mgu of r9|p9 and l'9

==> a(a(b(b(c(a(b(_1))))))) -> a(a(a(a(c(_1))))) is in EU_R^10
let r10 be the right-hand side of this rule
p10 = 0.0.0 is a position in r10
we have r10|p10 = a(c(_1))
a(c(_2)) -> a(a(_2)) is in R
let l'10 be the left-hand side of this rule
theta10 = {_1/_2} is a mgu of r10|p10 and l'10

==> a(a(b(b(c(a(b(_1))))))) -> a(a(a(a(a(_1))))) is in EU_R^11
let l11 be the left-hand side of this rule
p11 = 0.0.0.0.0.0 is a position in l11
we have l11|p11 = b(_1)
a(a(b(_2))) -> b(b(c(a(c(_2))))) is in R
let r'11 be the right-hand side of this rule
theta11 = {_1/b(c(a(c(_2))))} is a mgu of l11|p11 and r'11

==> a(a(b(b(c(a(a(a(b(_1))))))))) -> a(a(a(a(a(b(c(a(c(_1))))))))) is in EU_R^12
let r12 be the right-hand side of this rule
p12 = 0.0.0.0.0.0.0 is a position in r12
we have r12|p12 = a(c(_1))
a(c(_2)) -> a(a(_2)) is in R
let l'12 be the left-hand side of this rule
theta12 = {_1/_2} is a mgu of r12|p12 and l'12

==> a(a(b(b(c(a(a(a(b(_1))))))))) -> a(a(a(a(a(b(c(a(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 = a(a(b(_1)))
a(c(_2)) -> a(a(_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(b(b(c(a(a(c(b(_1))))))))) -> a(a(a(a(a(b(c(a(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 = a(a(c(b(_1))))
a(c(_2)) -> a(a(_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(b(b(c(a(c(c(b(_1))))))))) -> a(a(a(a(a(b(c(a(a(_1))))))))) is in EU_R^15
let l15 be the left-hand side of this rule
p15 = 0.0 is a position in l15
we have l15|p15 = b(b(c(a(c(c(b(_1)))))))
a(a(b(_2))) -> b(b(c(a(c(_2))))) is in R
let r'15 be the right-hand side of this rule
theta15 = {_2/c(b(_1))} is a mgu of l15|p15 and r'15

==> a(a(a(a(b(c(b(_1))))))) -> a(a(a(a(a(b(c(a(a(_1))))))))) is in EU_R^16
let r16 be the right-hand side of this rule
p16 = 0.0.0.0.0.0.0 is a position in r16
we have r16|p16 = a(a(_1))
a(a(b(_2))) -> b(b(c(a(c(_2))))) is in R
let l'16 be the left-hand side of this rule
theta16 = {_1/b(_2)} is a mgu of r16|p16 and l'16

==> a(a(a(a(b(c(b(b(_1)))))))) -> a(a(a(a(a(b(c(b(b(c(a(c(_1)))))))))))) is in EU_R^17
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(c(_1)))}
we have r|p = a(a(a(a(b(c(b(b(c(a(c(_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=17, depth k=9
4276 rule(s) generated