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] a__f(a__c,b,a__c) -> a__f(a__c,b,a__c)
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 = a__f(a__c,b,a__c) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = a__f(a__c,b,a__c) 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: no loop detected, 6 unfolded rules generated.
# Iteration 2: no loop detected, 25 unfolded rules generated.
# Iteration 3: no loop detected, 105 unfolded rules generated.
# Iteration 4: loop detected, 38 unfolded rules generated.
Here is the successful unfolding. Let IR be the TRS under analysis.
L0 = a__f^#(a,b,_0) -> a__f^#(_0,_0,mark(_0)) is in U_IR^0.
Let p0 = [0].
We unfold the rule of L0 backwards at position p0
with the rule a__c -> a.
==> L1 = a__f^#(a__c,b,a__c) -> a__f^#(a__c,a__c,mark(a__c)) is in U_IR^1.
Let p1 = [1].
We unfold the rule of L1 forwards at position p1
with the rule a__c -> b.
==> L2 = a__f^#(a__c,b,a__c) -> a__f^#(a__c,b,mark(a__c)) is in U_IR^2.
Let p2 = [2, 0].
We unfold the rule of L2 forwards at position p2
with the rule a__c -> c.
==> L3 = a__f^#(a__c,b,a__c) -> a__f^#(a__c,b,mark(c)) is in U_IR^3.
Let p3 = [2].
We unfold the rule of L3 forwards at position p3
with the rule mark(c) -> a__c.
==> L4 = a__f^#(a__c,b,a__c) -> a__f^#(a__c,b,a__c) is in U_IR^4.

** END proof description **

Proof stopped at iteration 4
Number of unfolded rules generated by this proof = 177
Number of unfolded rules generated by all the parallel proofs = 411