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 = 7] f(c,n__g(c),n__g(b)) -> f(c,n__g(c),n__g(b))
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 = f(c,n__g(c),n__g(b)) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = f(c,n__g(c),n__g(b)) 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,n__g(_0),_1) -> f^#(activate(_1),activate(_1),activate(_1))]
  TRS = {f(_0,n__g(_0),_1) -> f(activate(_1),activate(_1),activate(_1)), g(b) -> c, b -> c, g(_0) -> n__g(_0), activate(n__g(_0)) -> g(activate(_0)), activate(_0) -> _0}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Too many coefficients (17)! Aborting!
    ## Trying with lexicographic path orders... Failed!
    ## Trying to prove nontermination by unfolding the dependency pairs with the rules of the TRS
      # max_depth=2, unfold_variables=false:
        # Iteration 0: nontermination not detected, 1 unfolded rule generated.
        # Iteration 1: nontermination not detected, 1 unfolded rule generated.
        # Iteration 2: nontermination not detected, 2 unfolded rules generated.
        # Iteration 3: nontermination not detected, 2 unfolded rules generated.
        # Iteration 4: nontermination not detected, 2 unfolded rules generated.
        # Iteration 5: nontermination not detected, 0 unfolded rule generated.
        Nontermination not detected!
      # max_depth=2, unfold_variables=true:
        # Iteration 0: nontermination not detected, 1 unfolded rule generated.
        # Iteration 1: nontermination not detected, 1 unfolded rule generated.
        # Iteration 2: nontermination not detected, 2 unfolded rules generated.
        # Iteration 3: nontermination not detected, 2 unfolded rules generated.
        # Iteration 4: nontermination not detected, 1 unfolded rule generated.
        # Iteration 5: nontermination not detected, 1 unfolded rule generated.
        # Iteration 6: nontermination not detected, 3 unfolded rules generated.
        # Iteration 7: nontermination not detected, 0 unfolded rule generated.
        Nontermination not detected!
      # max_depth=3, unfold_variables=false:
        # Iteration 0: nontermination not detected, 1 unfolded rule generated.
        # Iteration 1: nontermination not detected, 1 unfolded rule generated.
        # Iteration 2: nontermination not detected, 4 unfolded rules generated.
        # Iteration 3: nontermination not detected, 8 unfolded rules generated.
        # Iteration 4: nontermination not detected, 16 unfolded rules generated.
        # Iteration 5: nontermination not detected, 19 unfolded rules generated.
        # Iteration 6: nontermination not detected, 31 unfolded rules generated.
        # Iteration 7: nontermination detected, 23 unfolded rules generated.
        Here is the successful unfolding. Let IR be the TRS under analysis.
        L0 = f^#(_0,n__g(_0),_1) -> f^#(activate(_1),activate(_1),activate(_1)) [trans] is in U_IR^0.
        We build a unit triple from L0.
        ==> L1 = f^#(_0,n__g(_0),_1) -> f^#(activate(_1),activate(_1),activate(_1)) [unit] is in U_IR^1.
        Let p1 = [0].
        We unfold the rule of L1 forwards at position p1
        with the rule activate(n__g(_0)) -> g(activate(_0)).
        ==> L2 = f^#(_0,n__g(_0),n__g(_1)) -> f^#(g(activate(_1)),activate(n__g(_1)),activate(n__g(_1))) [unit] is in U_IR^2.
        Let p2 = [0, 0].
        We unfold the rule of L2 forwards at position p2
        with the rule activate(_0) -> _0.
        ==> L3 = f^#(_0,n__g(_0),n__g(_1)) -> f^#(g(_1),activate(n__g(_1)),activate(n__g(_1))) [unit] is in U_IR^3.
        Let p3 = [0].
        We unfold the rule of L3 forwards at position p3
        with the rule g(b) -> c.
        ==> L4 = f^#(c,n__g(c),n__g(b)) -> f^#(c,activate(n__g(b)),activate(n__g(b))) [unit] is in U_IR^4.
        Let p4 = [1].
        We unfold the rule of L4 forwards at position p4
        with the rule activate(_0) -> _0.
        ==> L5 = f^#(c,n__g(c),n__g(b)) -> f^#(c,n__g(b),activate(n__g(b))) [unit] is in U_IR^5.
        Let p5 = [1, 0].
        We unfold the rule of L5 forwards at position p5
        with the rule b -> c.
        ==> L6 = f^#(c,n__g(c),n__g(b)) -> f^#(c,n__g(c),activate(n__g(b))) [unit] is in U_IR^6.
        Let p6 = [2].
        We unfold the rule of L6 forwards at position p6
        with the rule activate(_0) -> _0.
        ==> L7 = f^#(c,n__g(c),n__g(b)) -> f^#(c,n__g(c),n__g(b)) [unit] is in U_IR^7.
  This DP problem is infinite.

** END proof description **

Proof stopped at iteration 7
Number of unfolded rules generated by this proof = 122
Number of unfolded rules generated by all the parallel proofs = 609