let R be the TRS under consideration

f(g(_1),_2) -> f(_1,n__f(g(_1),activate(_2))) is in elim_R(R)
let r0 be the right-hand side of this rule
p0 = 1.1 is a position in r0
we have r0|p0 = activate(_2)
activate(n__f(_3,_4)) -> f(_3,_4) is in R
let l'0 be the left-hand side of this rule
theta0 = {_2/n__f(_3,_4)} is a mgu of r0|p0 and l'0

==> f(g(_1),n__f(_2,_3)) -> f(_1,n__f(g(_1),f(_2,_3))) is in EU_R^1
let l1 be the left-hand side of this rule
p1 = epsilon is a position in l1
we have l1|p1 = f(g(_1),n__f(_2,_3))
f(g(_4),_5) -> f(_4,n__f(g(_4),activate(_5))) is in R
let r'1 be the right-hand side of this rule
theta1 = {_2/g(g(_1)), _3/activate(_5), _4/g(_1)} is a mgu of l1|p1 and r'1

==> f(g(g(_1)),_2) -> f(_1,n__f(g(_1),f(g(g(_1)),activate(_2)))) is in EU_R^2
let l be the left-hand side and r be the right-hand side of this rule
let p = 1.1
let theta = {}
let theta' = {_1/_1, _2/activate(_2)}
we have r|p = f(g(g(_1)),activate(_2)) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = f(g(g(_1)),_2) is non-terminating w.r.t. R

Termination disproved by the forward+backward process
proof stopped at iteration i=2, depth k=3
23 rule(s) generated