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 = 1] app(app(app(fix,subst),_0),_1) -> app(app(app(fix,subst),_1),app(_0,_1))
Let l be the left-hand side and r be the right-hand side of this rule.
Let p = epsilon, theta1 = {} and theta2 = {_1->app(_0,_1), _0->_1}.
We have r|p = app(app(app(fix,subst),_1),app(_0,_1)) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = app(app(app(fix,subst),_0),_1) 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, 3 unfolded rules generated.
# Iteration 1: loop detected, 15 unfolded rules generated.
Here is the successful unfolding. Let IR be the TRS under analysis.
L0 = app^#(app(app(subst,_0),_1),_2) -> app^#(app(_0,_2),app(_1,_2)) is in U_IR^0.
Let p0 = [0].
We unfold the rule of L0 backwards at position p0
with the rule app(app(fix,_0),_1) -> app(app(_0,app(fix,_0)),_1).
==> L1 = app^#(app(app(fix,subst),_0),_1) -> app^#(app(app(fix,subst),_1),app(_0,_1)) is in U_IR^1.

** END proof description **

Proof stopped at iteration 1
Number of unfolded rules generated by this proof = 18
Number of unfolded rules generated by all the parallel proofs = 18