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 = 2] activate(n__f(g(g(_0)),_1)) -> f(_0,n__f(g(_0),activate(n__f(g(g(_0)),activate(_1)))))
Let l be the left-hand side and r be the right-hand side of this rule.
Let p = [1, 1], theta1 = {} and theta2 = {_1->activate(_1)}.
We have r|p = activate(n__f(g(g(_0)),activate(_1))) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = activate(n__f(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!

## 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: loop detected, 4 unfolded rules generated.
Here is the successful unfolding. Let IR be the TRS under analysis.
L0 = f^#(g(_0),_1) -> f^#(_0,n__f(g(_0),activate(_1))) is in U_IR^0.
Let p0 = epsilon.
We unfold the rule of L0 forwards at position p0
with the dependency pair f^#(g(_0),_1) -> f^#(_0,n__f(g(_0),activate(_1))).
==> L1 = f^#(g(g(_0)),_1) -> f^#(_0,n__f(g(_0),activate(n__f(g(g(_0)),activate(_1))))) is in U_IR^1.
Let p1 = epsilon.
We unfold the rule of L1 backwards at position p1
with the dependency pair activate^#(n__f(_0,_1)) -> f^#(_0,_1).
==> L2 = activate^#(n__f(g(g(_0)),_1)) -> f^#(_0,n__f(g(_0),activate(n__f(g(g(_0)),activate(_1))))) is in U_IR^2.

** END proof description **

Proof stopped at iteration 2
Number of unfolded rules generated by this proof = 13
Number of unfolded rules generated by all the parallel proofs = 13