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^#(+(_0,s(0))) -> f^#(_0), f^#(+(_0,_1)) -> f^#(_0), f^#(+(_0,_1)) -> f^#(_1)]
  TRS = {f(0) -> s(0), f(s(0)) -> s(s(0)), f(s(0)) -> *(s(s(0)),f(0)), f(+(_0,s(0))) -> +(s(s(0)),f(_0)), f(+(_0,_1)) -> *(f(_0),f(_1))}
    ## 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