let R be the TRS under consideration

f(k(a),k(b),_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 = k(a)
u(d,c(_2),_3) -> k(_2) is in R
let r'0 be the right-hand side of this rule
theta0 = {_2/a} is a mgu of l0|p0 and r'0

==> f(u(d,c(a),_1),k(b),_2) -> f(_2,_2,_2) is in EU_R^1
let l1 be the left-hand side of this rule
p1 = 0.1 is a position in l1
we have l1|p1 = c(a)
h(d) -> 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

==> f(u(d,h(d),_1),k(b),_2) -> f(_2,_2,_2) 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 = k(b)
u(d,c(_3),_4) -> k(_3) is in R
let r'2 be the right-hand side of this rule
theta2 = {_3/b} is a mgu of l2|p2 and r'2

==> f(u(d,h(d),_1),u(d,c(b),_2),_3) -> f(_3,_3,_3) is in EU_R^3
let l3 be the left-hand side of this rule
p3 = 1.1 is a position in l3
we have l3|p3 = c(b)
h(d) -> c(b) is in R
let r'3 be the right-hand side of this rule
theta3 = {} is a mgu of l3|p3 and r'3

==> f(u(d,h(d),_1),u(d,h(d),_2),_3) -> f(_3,_3,_3) 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 = {_2/_1, _3/u(d,h(d),_1)}
let theta' = {}
we have r|p = f(_3,_3,_3) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = f(u(d,h(d),_1),u(d,h(d),_1),u(d,h(d),_1)) is non-terminating w.r.t. R

Termination disproved by the backward process
proof stopped at iteration i=4, depth k=3
105 rule(s) generated