let R be the TRS under consideration

h(_1) -> g(_1,_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 = g(_1,_1)
g(a,_2) -> f(b,activate(_2)) is in R
let l'0 be the left-hand side of this rule
theta0 = {_1/a, _2/a} is a mgu of r0|p0 and l'0

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

==> h(a) -> f(b,a) is in EU_R^2
let r2 be the right-hand side of this rule
p2 = 1 is a position in r2
we have r2|p2 = a
a -> b is in R
let l'2 be the left-hand side of this rule
theta2 = {} is a mgu of r2|p2 and l'2

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

==> h(a) -> h(a) 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 = h(a) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = h(a) is non-terminating w.r.t. R

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