let R be the TRS under consideration

f(0) -> f(s(0)) 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 = f(s(0))
f(s(0)) -> f(p(s(0))) is in R
let l'0 be the left-hand side of this rule
theta0 = {} is a mgu of r0|p0 and l'0

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

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