let R be the TRS under consideration

a(b(_1)) -> a(a(_1)) is in elim_R(R)
let r0 be the right-hand side of this rule
p0 = 0 is a position in r0
we have r0|p0 = a(_1)
a(b(_2)) -> b(b(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(b(b(_1))) -> a(b(b(a(a(_1))))) is in EU_R^1
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(b(b(a(a(_1))))) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = a(b(b(_1))) is non-terminating w.r.t. R

Termination disproved by the forward process
proof stopped at iteration i=1, depth k=4
2 rule(s) generated