let R be the TRS under consideration

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

Termination disproved by the backward process
proof stopped at iteration i=0, depth k=0
1 rule(s) generated