let R be the TRS under consideration

f(_1,g(_1),_2) -> f(_2,_2,_2) is in elim_R(R)
let l0 be the left-hand side of this rule
p0 = 0 is a position in l0
we have l0|p0 = _1
g(b) -> c is in R
let r'0 be the right-hand side of this rule
theta0 = {_1/c} is a mgu of l0|p0 and r'0

==> f(g(b),g(c),_1) -> f(_1,_1,_1) is in EU_R^1
let l1 be the left-hand side of this rule
p1 = 1.0 is a position in l1
we have l1|p1 = c
b -> c is in R
let r'1 be the right-hand side of this rule
theta1 = {} is a mgu of l1|p1 and r'1

==> f(g(b),g(b),_1) -> f(_1,_1,_1) 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 = {_1/g(b)}
let theta' = {}
we have r|p = f(_1,_1,_1) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = f(g(b),g(b),g(b)) is non-terminating w.r.t. R

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