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 = [f^#(+(_0,_1),_2) -> f^#(_0,_2), f^#(+(_0,_1),_2) -> f^#(_1,_2)]
  TRS = {+(a,b) -> +(b,a), +(a,+(b,_0)) -> +(b,+(a,_0)), +(+(_0,_1),_2) -> +(_0,+(_1,_2)), f(a,_0) -> a, f(b,_0) -> b, f(+(_0,_1),_2) -> +(f(_0,_2),f(_1,_2))}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [+^#(+(_0,_1),_2) -> +^#(_0,+(_1,_2)), +^#(+(_0,_1),_2) -> +^#(_1,_2)]
  TRS = {+(a,b) -> +(b,a), +(a,+(b,_0)) -> +(b,+(a,_0)), +(+(_0,_1),_2) -> +(_0,+(_1,_2)), f(a,_0) -> a, f(b,_0) -> b, f(+(_0,_1),_2) -> +(f(_0,_2),f(_1,_2))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations...
      The constraints are satisfied by the polynomials:
      {+(_0,_1):[_0 + _1], a:[1], f(_0,_1):[_0 * _1], b:[1], +^#(_0,_1):[_0]}
      for all instantiations of the variables with values greater than or equal to mu = 1.
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [+^#(a,+(b,_0)) -> +^#(a,_0)]
  TRS = {+(a,b) -> +(b,a), +(a,+(b,_0)) -> +(b,+(a,_0)), +(+(_0,_1),_2) -> +(_0,+(_1,_2)), f(a,_0) -> a, f(b,_0) -> b, f(+(_0,_1),_2) -> +(f(_0,_2),f(_1,_2))}
    ## 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 = 695