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 = [s^#(f(_0,_1)) -> s^#(_1), s^#(f(_0,_1)) -> s^#(_0), s^#(g(_0,_1)) -> s^#(_0), s^#(g(_0,_1)) -> s^#(_1)]
  TRS = {s(a) -> a, s(s(_0)) -> _0, s(f(_0,_1)) -> f(s(_1),s(_0)), s(g(_0,_1)) -> g(s(_0),s(_1)), f(_0,a) -> _0, f(a,_0) -> _0, f(g(_0,_1),g(_2,_3)) -> g(f(_0,_2),f(_1,_3)), g(a,a) -> a}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [f^#(g(_0,_1),g(_2,_3)) -> f^#(_0,_2), f^#(g(_0,_1),g(_2,_3)) -> f^#(_1,_3)]
  TRS = {s(a) -> a, s(s(_0)) -> _0, s(f(_0,_1)) -> f(s(_1),s(_0)), s(g(_0,_1)) -> g(s(_0),s(_1)), f(_0,a) -> _0, f(a,_0) -> _0, f(g(_0,_1),g(_2,_3)) -> g(f(_0,_2),f(_1,_3)), g(a,a) -> a}
    ## 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