let R be the TRS under consideration

f(s(_1)) -> f(g(_1,_1)) is in elim_R(R)
let r0 be the right-hand side of this rule
p0 = 0.1 is a position in r0
we have r0|p0 = _1
0 -> 1 is in R
let l'0 be the left-hand side of this rule
theta0 = {_1/0} is a mgu of r0|p0 and l'0

==> f(s(0)) -> f(g(0,1)) 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 = g(0,1)
g(0,1) -> s(0) 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(s(0)) -> f(s(0)) is in EU_R^2
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(s(0)) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = f(s(0)) is non-terminating w.r.t. R

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