YES

Prover = TRS(tech=PATTERN_RULES, nb_unfoldings=unlimited, max_nb_unfolded_rules=200)

** BEGIN proof argument **
All the DP problems were proved finite.
As all the involved DP processors are sound,
the TRS under analysis terminates.
** 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 = [activate^#(n__h(_0)) -> activate^#(_0), activate^#(n__f(_0)) -> activate^#(_0)]
  TRS = {f(_0) -> g(n__h(n__f(_0))), h(_0) -> n__h(_0), f(_0) -> n__f(_0), activate(n__h(_0)) -> h(activate(_0)), activate(n__f(_0)) -> f(activate(_0)), activate(_0) -> _0}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.

** END proof description **

Proof stopped at iteration 0
Number of unfolded rules generated by this proof = 0
Number of unfolded rules generated by all the parallel proofs = 0