let R be the TRS under consideration

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

==> f(n__a,n__b,n__b) -> f(b,b,n__b) 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 = b
b -> a is in R
let l'1 be the left-hand side of this rule
theta1 = {} is a mgu of r1|p1 and l'1

==> f(n__a,n__b,n__b) -> f(a,b,n__b) is in EU_R^2
let r2 be the right-hand side of this rule
p2 = 0 is a position in r2
we have r2|p2 = a
a -> n__a is in R
let l'2 be the left-hand side of this rule
theta2 = {} is a mgu of r2|p2 and l'2

==> f(n__a,n__b,n__b) -> f(n__a,b,n__b) is in EU_R^3
let r3 be the right-hand side of this rule
p3 = 1 is a position in r3
we have r3|p3 = b
b -> n__b is in R
let l'3 be the left-hand side of this rule
theta3 = {} is a mgu of r3|p3 and l'3

==> f(n__a,n__b,n__b) -> f(n__a,n__b,n__b) is in EU_R^4
let l be the left-hand side and r be the right-hand side of this rule
let p = epsilon
let theta = {}
let theta' = {}
we have r|p = f(n__a,n__b,n__b) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = f(n__a,n__b,n__b) is non-terminating w.r.t. R

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