NO

Prover = TRS(tech=GUIDED_UNF_TRIPLES, nb_unfoldings=unlimited, unfold_variables=false, max_nb_coefficients=12, max_nb_unfolded_rules=-1, strategy=LEFTMOST_NE)

** BEGIN proof argument **
The following rule was generated while unfolding the analyzed TRS:
[iteration = 3] f(_0,f(a,f(a,_1))) -> f(f(a,f(a,f(f(f(a,a),a),f(f(a,a),_1)))),_0)
Let l be the left-hand side and r be the right-hand side of this rule.
Let p = epsilon, theta1 = {_0->f(a,f(a,_2))} and theta2 = {_1->_2, _2->f(f(f(a,a),a),f(f(a,a),_1))}.
We have r|p = f(f(a,f(a,f(f(f(a,a),a),f(f(a,a),_1)))),_0) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = f(f(a,f(a,_2)),f(a,f(a,_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!

## Applying the DP framework...
## Round 1:
  ## DP problem: 
  Dependency pairs = [f^#(_0,f(a,_1)) -> f^#(a,f(f(f(a,a),_1),_0)), f^#(_0,f(a,_1)) -> f^#(f(f(a,a),_1),_0), f^#(_0,f(a,_1)) -> f^#(f(a,a),_1)]
  TRS = {f(_0,f(a,_1)) -> f(a,f(f(f(a,a),_1),_0))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders... Failed!
    ## Trying to prove nontermination by unfolding the dependency pairs with the rules of the TRS
      # max_depth=20, unfold_variables=false:
        # Iteration 0: nontermination not detected, 3 unfolded rules generated.
        # Iteration 1: nontermination not detected, 13 unfolded rules generated.
        # Iteration 2: nontermination not detected, 22 unfolded rules generated.
        # Iteration 3: nontermination detected, 38 unfolded rules generated.
        Here is the successful unfolding. Let IR be the TRS under analysis.
        L0 = f^#(_0,f(a,_1)) -> f^#(f(f(a,a),_1),_0) [trans] is in U_IR^0.
        We build a unit triple from L0.
        ==> L1 = f^#(_0,f(a,_1)) -> f^#(f(f(a,a),_1),_0) [unit] is in U_IR^1.
        Let p1 = [0].
        We unfold the rule of L1 forwards at position p1
        with the rule f(_0,f(a,_1)) -> f(a,f(f(f(a,a),_1),_0)).
        ==> L2 = f^#(_0,f(a,f(a,_1))) -> f^#(f(a,f(f(f(a,a),_1),f(a,a))),_0) [unit] is in U_IR^2.
        Let p2 = [0, 1].
        We unfold the rule of L2 forwards at position p2
        with the rule f(_0,f(a,_1)) -> f(a,f(f(f(a,a),_1),_0)).
        ==> L3 = f^#(_0,f(a,f(a,_1))) -> f^#(f(a,f(a,f(f(f(a,a),a),f(f(a,a),_1)))),_0) [unit] is in U_IR^3.
  This DP problem is infinite.

** END proof description **

Proof stopped at iteration 3
Number of unfolded rules generated by this proof = 76
Number of unfolded rules generated by all the parallel proofs = 318