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 = [mark^#(f(_0)) -> mark^#(_0), mark^#(g(_0)) -> mark^#(_0)]
  TRS = {a__f(f(a)) -> c(f(g(f(a)))), mark(f(_0)) -> a__f(mark(_0)), mark(a) -> a, mark(c(_0)) -> c(_0), mark(g(_0)) -> g(mark(_0)), a__f(_0) -> f(_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