let R be the TRS under consideration

f(0,1,_1) -> f(_1,_1,_1) 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 = 0
g(_2,_2,_3) -> _3 is in R
let r'0 be the right-hand side of this rule
theta0 = {_3/0} is a mgu of l0|p0 and r'0

==> f(g(_1,_1,0),1,_2) -> f(_2,_2,_2) is in EU_R^1
let l1 be the left-hand side of this rule
p1 = 0.0 is a position in l1
we have l1|p1 = _1
1 -> 2 is in R
let r'1 be the right-hand side of this rule
theta1 = {_1/2} is a mgu of l1|p1 and r'1

==> f(g(1,2,0),1,_1) -> f(_1,_1,_1) is in EU_R^2
let l2 be the left-hand side of this rule
p2 = 0.1 is a position in l2
we have l2|p2 = 2
0 -> 2 is in R
let r'2 be the right-hand side of this rule
theta2 = {} is a mgu of l2|p2 and r'2

==> f(g(1,0,0),1,_1) -> f(_1,_1,_1) is in EU_R^3
let l3 be the left-hand side of this rule
p3 = 1 is a position in l3
we have l3|p3 = 1
g(_2,_3,_3) -> _2 is in R
let r'3 be the right-hand side of this rule
theta3 = {_2/1} is a mgu of l3|p3 and r'3

==> f(g(1,0,0),g(1,_1,_1),_2) -> f(_2,_2,_2) 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 = {_1/0, _2/g(1,0,0)}
let theta' = {}
we have r|p = f(_2,_2,_2) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = f(g(1,0,0),g(1,0,0),g(1,0,0)) is non-terminating w.r.t. R

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