let R be the TRS under consideration

a(b(_1)) -> a(c(b(b(a(a(_1)))))) is in elim_R(R)
let r0 be the right-hand side of this rule
p0 = 0.0 is a position in r0
we have r0|p0 = b(b(a(a(_1))))
b(_2) -> _2 is in R
let l'0 be the left-hand side of this rule
theta0 = {_2/b(a(a(_1)))} is a mgu of r0|p0 and l'0

==> a(b(_1)) -> a(c(b(a(a(_1))))) is in EU_R^1
let r1 be the right-hand side of this rule
p1 = 0.0 is a position in r1
we have r1|p1 = b(a(a(_1)))
b(_2) -> _2 is in R
let l'1 be the left-hand side of this rule
theta1 = {_2/a(a(_1))} is a mgu of r1|p1 and l'1

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

==> a(b(_1)) -> a(c(a(_1))) is in EU_R^3
let l3 be the left-hand side of this rule
p3 = 0 is a position in l3
we have l3|p3 = b(_1)
c(c(_2)) -> _2 is in R
let r'3 be the right-hand side of this rule
theta3 = {_2/b(_1)} is a mgu of l3|p3 and r'3

==> a(c(c(b(_1)))) -> a(c(a(_1))) is in EU_R^4
let l4 be the left-hand side of this rule
p4 = 0.0 is a position in l4
we have l4|p4 = c(b(_1))
a(_2) -> _2 is in R
let r'4 be the right-hand side of this rule
theta4 = {_2/c(b(_1))} is a mgu of l4|p4 and r'4

==> a(c(a(c(b(_1))))) -> a(c(a(_1))) is in EU_R^5
let r5 be the right-hand side of this rule
p5 = 0.0 is a position in r5
we have r5|p5 = a(_1)
a(b(_2)) -> a(c(b(b(a(a(_2)))))) is in R
let l'5 be the left-hand side of this rule
theta5 = {_1/b(_2)} is a mgu of r5|p5 and l'5

==> a(c(a(c(b(b(_1)))))) -> a(c(a(c(b(b(a(a(_1)))))))) is in EU_R^6
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(a(_1))}
we have r|p = a(c(a(c(b(b(a(a(_1)))))))) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = a(c(a(c(b(b(_1)))))) is non-terminating w.r.t. R

Termination disproved by the forward+backward process
proof stopped at iteration i=6, depth k=6
2756 rule(s) generated