let R be the TRS under consideration

ifappend(_1,_2,false) -> append(tl(_1),_2) is in elim_R(R)
let r0 be the right-hand side of this rule
p0 = 0 is a position in r0
we have r0|p0 = tl(_1)
tl(cons(_3,_4)) -> cons(_3,_4) is in R
let l'0 be the left-hand side of this rule
theta0 = {_1/cons(_3,_4)} is a mgu of r0|p0 and l'0

==> ifappend(cons(_1,_2),_3,false) -> append(cons(_1,_2),_3) is in EU_R^1
let r1 be the right-hand side of this rule
p1 = epsilon is a position in r1
we have r1|p1 = append(cons(_1,_2),_3)
append(_4,_5) -> ifappend(_4,_5,is_empty(_4)) is in R
let l'1 be the left-hand side of this rule
theta1 = {_3/_5, _4/cons(_1,_2)} is a mgu of r1|p1 and l'1

==> ifappend(cons(_1,_2),_3,false) -> ifappend(cons(_1,_2),_3,is_empty(cons(_1,_2))) is in EU_R^2
let r2 be the right-hand side of this rule
p2 = 2 is a position in r2
we have r2|p2 = is_empty(cons(_1,_2))
is_empty(cons(_4,_5)) -> false is in R
let l'2 be the left-hand side of this rule
theta2 = {_1/_4, _2/_5} is a mgu of r2|p2 and l'2

==> ifappend(cons(_1,_2),_3,false) -> ifappend(cons(_1,_2),_3,false) is in EU_R^3
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 = ifappend(cons(_1,_2),_3,false) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = ifappend(cons(_1,_2),_3,false) is non-terminating w.r.t. R

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