NO

Prover = TRS(tech=GUIDED_UNF, nb_unfoldings=unlimited, unfold_variables=true, strategy=LEFTMOST_NE)

** BEGIN proof argument **
The following rule was generated while unfolding the analyzed TRS:
[iteration = 4] ifappend(cons(_0,_1),_2,false) -> ifappend(cons(_0,_1),_2,false)
Let l be the left-hand side and r be the right-hand side of this rule.
Let p = epsilon, theta1 = {} and theta2 = {}.
We have r|p = ifappend(cons(_0,_1),_2,false) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = ifappend(cons(_0,_1),_2,false) loops w.r.t. the analyzed TRS.
** END proof argument **

** BEGIN proof description **
## Searching for a generalized rewrite rule
(a rule whose right-hand side contains a variable
that does not occur in the left-hand side)...
No generalized rewrite rule found!

## Searching for a loop by unfolding (unfolding of variable subterms: ON)...
# Iteration 0: no loop detected, 1 unfolded rule generated.
# Iteration 1: no loop detected, 1 unfolded rule generated.
# Iteration 2: no loop detected, 2 unfolded rules generated.
# Iteration 3: no loop detected, 8 unfolded rules generated.
# Iteration 4: loop detected, 1 unfolded rule generated.
Here is the successful unfolding. Let IR be the TRS under analysis.
L0 = [ifappend^#(_0,_1,false) -> append^#(tl(_0),_1), append^#(_2,_3) -> ifappend^#(_2,_3,is_empty(_2))] is in U_IR^0.
We merge the first and the second rule of L0.
==> L1 = ifappend^#(_0,_1,false) -> ifappend^#(tl(_0),_1,is_empty(tl(_0))) is in U_IR^1.
Let p1 = [0].
We unfold the rule of L1 forwards at position p1
with the rule tl(cons(_0,_1)) -> cons(_0,_1).
==> L2 = ifappend^#(cons(_0,_1),_2,false) -> ifappend^#(cons(_0,_1),_2,is_empty(tl(cons(_0,_1)))) is in U_IR^2.
Let p2 = [2, 0].
We unfold the rule of L2 forwards at position p2
with the rule tl(cons(_0,_1)) -> cons(_0,_1).
==> L3 = ifappend^#(cons(_0,_1),_2,false) -> ifappend^#(cons(_0,_1),_2,is_empty(cons(_0,_1))) is in U_IR^3.
Let p3 = [2].
We unfold the rule of L3 forwards at position p3
with the rule is_empty(cons(_0,_1)) -> false.
==> L4 = ifappend^#(cons(_0,_1),_2,false) -> ifappend^#(cons(_0,_1),_2,false) is in U_IR^4.

** END proof description **

Proof stopped at iteration 4
Number of unfolded rules generated by this proof = 13
Number of unfolded rules generated by all the parallel proofs = 13