YES

Prover = TRS(tech=GUIDED_UNF_TRIPLES, nb_unfoldings=unlimited, unfold_variables=false, max_nb_coefficients=12, max_nb_unfolded_rules=-1, strategy=LEFTMOST_NE)

** 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 = [g^#(s(_0),_1) -> g^#(_0,+(_1,s(_0))), g^#(s(_0),_1) -> g^#(_0,s(+(_1,_0)))]
  TRS = {f(0) -> 1, f(s(_0)) -> g(_0,s(_0)), g(0,_0) -> _0, g(s(_0),_1) -> g(_0,+(_1,s(_0))), +(_0,0) -> _0, +(_0,s(_1)) -> s(+(_0,_1)), g(s(_0),_1) -> g(_0,s(+(_1,_0)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Too many coefficients (15)! Aborting!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      f > [g, s, +], g > [s, +], + > [s], 0 > [1]
      and the argument filtering:
      {f:[0], s:[0], g:[0, 1], +:[0, 1], g^#:[0, 1]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [+^#(_0,s(_1)) -> +^#(_0,_1)]
  TRS = {f(0) -> 1, f(s(_0)) -> g(_0,s(_0)), g(0,_0) -> _0, g(s(_0),_1) -> g(_0,+(_1,s(_0))), +(_0,0) -> _0, +(_0,s(_1)) -> s(+(_0,_1)), g(s(_0),_1) -> g(_0,s(+(_1,_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 = 16