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 = [f^#(g(_0),b) -> f^#(a,_0)]
  TRS = {a -> g(c), g(a) -> b, f(g(_0),b) -> f(a,_0)}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations...
      The constraints are satisfied by the polynomials:
      {a:[1], b:[1], c:[0], g(_0):[2 * _0], f(_0,_1):[_0 + _1], f^#(_0,_1):[_0 + _1 * _0]}
      for all instantiations of the variables with values greater than or equal to mu = 0.
  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 = 7