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 = 4] activate(n__f(n__g(g(_0)),_1)) -> activate(n__f(n__g(g(_0)),activate(_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->activate(_1)}.
We have r|p = activate(n__f(n__g(g(_0)),activate(_1))) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = activate(n__f(n__g(g(_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!

## Applying the DP framework...
## Round 1:
  ## DP problem: 
  Dependency pairs = [f^#(g(_0),_1) -> f^#(_0,n__f(n__g(_0),activate(_1))), activate^#(n__f(_0,_1)) -> f^#(activate(_0),_1), activate^#(n__f(_0,_1)) -> activate^#(_0), activate^#(n__g(_0)) -> activate^#(_0), f^#(g(_0),_1) -> activate^#(_1)]
  TRS = {f(g(_0),_1) -> f(_0,n__f(n__g(_0),activate(_1))), f(_0,_1) -> n__f(_0,_1), g(_0) -> n__g(_0), activate(n__f(_0,_1)) -> f(activate(_0),_1), activate(n__g(_0)) -> g(activate(_0)), activate(_0) -> _0}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Too many coefficients (15)! Aborting!
    ## Trying with lexicographic path orders... Failed!
    ## Trying to prove nontermination by unfolding the dependency pairs with the rules of the TRS
      # max_depth=3, unfold_variables=false:
        # Iteration 0: nontermination not detected, 5 unfolded rules generated.
        # Iteration 1: nontermination not detected, 18 unfolded rules generated.
        # Iteration 2: nontermination not detected, 29 unfolded rules generated.
        # Iteration 3: nontermination not detected, 32 unfolded rules generated.
        # Iteration 4: nontermination detected, 10 unfolded rules generated.
        Here is the successful unfolding. Let IR be the TRS under analysis.
        L0 = activate^#(n__f(_0,_1)) -> f^#(activate(_0),_1) [trans] is in U_IR^0.
        D = f^#(g(_0),_1) -> f^#(_0,n__f(n__g(_0),activate(_1))) is a dependency pair of IR.
        We build a composed triple from L0 and D.
        ==> L1 = [activate^#(n__f(_0,_1)) -> f^#(activate(_0),_1), f^#(g(_2),_3) -> f^#(_2,n__f(n__g(_2),activate(_3)))] [comp] is in U_IR^1.
        Let p1 = [0].
        We unfold the first rule of L1 forwards at position p1
        with the rule activate(n__g(_0)) -> g(activate(_0)).
        ==> L2 = [activate^#(n__f(n__g(_0),_1)) -> f^#(g(activate(_0)),_1), f^#(g(_2),_3) -> f^#(_2,n__f(n__g(_2),activate(_3)))] [comp] is in U_IR^2.
        Let p2 = [0, 0].
        We unfold the first rule of L2 forwards at position p2
        with the rule activate(_0) -> _0.
        ==> L3 = activate^#(n__f(n__g(_0),_1)) -> f^#(_0,n__f(n__g(_0),activate(_1))) [trans] is in U_IR^3.
        D = f^#(g(_0),_1) -> activate^#(_1) is a dependency pair of IR.
        We build a composed triple from L3 and D.
        ==> L4 = activate^#(n__f(n__g(g(_0)),_1)) -> activate^#(n__f(n__g(g(_0)),activate(_1))) [trans] is in U_IR^4.
  This DP problem is infinite.

** END proof description **

Proof stopped at iteration 4
Number of unfolded rules generated by this proof = 94
Number of unfolded rules generated by all the parallel proofs = 573