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 = 2] ap(ap(ap(foldr,ap(f,foldr)),ap(ap(cons,foldr),nil)),ap(ap(cons,foldr),nil)) -> ap(ap(ap(foldr,ap(f,foldr)),ap(ap(cons,foldr),nil)),ap(ap(cons,foldr),nil))
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 = ap(ap(ap(foldr,ap(f,foldr)),ap(ap(cons,foldr),nil)),ap(ap(cons,foldr),nil)) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = ap(ap(ap(foldr,ap(f,foldr)),ap(ap(cons,foldr),nil)),ap(ap(cons,foldr),nil)) 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, 5 unfolded rules generated.
# Iteration 1: no loop detected, 39 unfolded rules generated.
# Iteration 2: loop detected, 126 unfolded rules generated.
Here is the successful unfolding. Let IR be the TRS under analysis.
L0 = ap^#(ap(ap(foldr,_0),_1),ap(ap(cons,_2),_3)) -> ap^#(ap(_0,_2),ap(ap(ap(foldr,_0),_1),_3)) is in U_IR^0.
Let p0 = [0].
We unfold the rule of L0 forwards at position p0
with the rule ap(ap(f,_0),_0) -> ap(ap(_0,ap(f,_0)),ap(ap(cons,_0),nil)).
==> L1 = ap^#(ap(ap(foldr,ap(f,foldr)),ap(ap(cons,foldr),nil)),ap(ap(cons,foldr),_0)) -> ap^#(ap(ap(foldr,ap(f,foldr)),ap(ap(cons,foldr),nil)),ap(ap(ap(foldr,ap(f,foldr)),ap(ap(cons,foldr),nil)),_0)) is in U_IR^1.
Let p1 = [1].
We unfold the rule of L1 forwards at position p1
with the rule ap(ap(ap(foldr,_0),_1),nil) -> _1.
==> L2 = ap^#(ap(ap(foldr,ap(f,foldr)),ap(ap(cons,foldr),nil)),ap(ap(cons,foldr),nil)) -> ap^#(ap(ap(foldr,ap(f,foldr)),ap(ap(cons,foldr),nil)),ap(ap(cons,foldr),nil)) is in U_IR^2.

** END proof description **

Proof stopped at iteration 2
Number of unfolded rules generated by this proof = 170
Number of unfolded rules generated by all the parallel proofs = 170