let R be the TRS under consideration

a__f(b,_1,c) -> a__f(_1,a__c,_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 = b
a__c -> b is in R
let r'0 be the right-hand side of this rule
theta0 = {} is a mgu of l0|p0 and r'0

==> a__f(a__c,_1,c) -> a__f(_1,a__c,_1) is in EU_R^1
let l1 be the left-hand side of this rule
p1 = 2 is a position in l1
we have l1|p1 = c
a__c -> 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

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

Termination disproved by the backward process
proof stopped at iteration i=2, depth k=1
8 rule(s) generated