let R be the TRS under consideration

a__f(_1,g(_1),_2) -> a__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
a__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

==> a__f(a__g(b),g(c),_1) -> a__f(_1,_1,_1) 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 = b
a__b -> b is in R
let r'1 be the right-hand side of this rule
theta1 = {} is a mgu of l1|p1 and r'1

==> a__f(a__g(a__b),g(c),_1) -> a__f(_1,_1,_1) is in EU_R^2
let l2 be the left-hand side of this rule
p2 = 1 is a position in l2
we have l2|p2 = g(c)
a__g(_2) -> g(_2) is in R
let r'2 be the right-hand side of this rule
theta2 = {_2/c} is a mgu of l2|p2 and r'2

==> a__f(a__g(a__b),a__g(c),_1) -> a__f(_1,_1,_1) is in EU_R^3
let l3 be the left-hand side of this rule
p3 = 1.0 is a position in l3
we have l3|p3 = c
a__b -> c is in R
let r'3 be the right-hand side of this rule
theta3 = {} is a mgu of l3|p3 and r'3

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

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