let R be the TRS under consideration

a__f(a,b,_1) -> a__f(mark(_1),_1,mark(_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 = a
mark(a) -> a 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(mark(a),b,_1) -> a__f(mark(_1),_1,mark(_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 = a
a__c -> a 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(mark(a__c),b,_1) -> a__f(mark(_1),_1,mark(_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 = b
a__c -> b is in R
let r'2 be the right-hand side of this rule
theta2 = {} is a mgu of l2|p2 and r'2

==> a__f(mark(a__c),a__c,_1) -> a__f(mark(_1),_1,mark(_1)) is in EU_R^3
let l3 be the left-hand side of this rule
p3 = 2 is a position in l3
we have l3|p3 = _1
mark(c) -> a__c is in R
let r'3 be the right-hand side of this rule
theta3 = {_1/a__c} is a mgu of l3|p3 and r'3

==> a__f(mark(a__c),a__c,mark(c)) -> a__f(mark(a__c),a__c,mark(a__c)) is in EU_R^4
let l4 be the left-hand side of this rule
p4 = 2.0 is a position in l4
we have l4|p4 = c
a__c -> c is in R
let r'4 be the right-hand side of this rule
theta4 = {} is a mgu of l4|p4 and r'4

==> a__f(mark(a__c),a__c,mark(a__c)) -> a__f(mark(a__c),a__c,mark(a__c)) is in EU_R^5
let l be the left-hand side and r be the right-hand side of this rule
let p = epsilon
let theta = {}
let theta' = {}
we have r|p = a__f(mark(a__c),a__c,mark(a__c)) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = a__f(mark(a__c),a__c,mark(a__c)) is non-terminating w.r.t. R

Termination disproved by the backward process
proof stopped at iteration i=5, depth k=2
314 rule(s) generated