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 = [i^#(+(_0,_1)) -> i^#(_0), i^#(+(_0,_1)) -> i^#(_1)]
  TRS = {i(0) -> 0, +(0,_0) -> _0, +(_0,0) -> _0, i(i(_0)) -> _0, +(i(_0),_0) -> 0, +(_0,i(_0)) -> 0, i(+(_0,_1)) -> +(i(_0),i(_1)), +(_0,+(_1,_2)) -> +(+(_0,_1),_2), +(+(_0,i(_1)),_1) -> _0, +(+(_0,_1),i(_1)) -> _0}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [+^#(_0,+(_1,_2)) -> +^#(+(_0,_1),_2), +^#(_0,+(_1,_2)) -> +^#(_0,_1)]
  TRS = {i(0) -> 0, +(0,_0) -> _0, +(_0,0) -> _0, i(i(_0)) -> _0, +(i(_0),_0) -> 0, +(_0,i(_0)) -> 0, i(+(_0,_1)) -> +(i(_0),i(_1)), +(_0,+(_1,_2)) -> +(+(_0,_1),_2), +(+(_0,i(_1)),_1) -> _0, +(+(_0,_1),i(_1)) -> _0}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations...
      The constraints are satisfied by the polynomials:
      {i(_0):[_0], +(_0,_1):[_0 * _1], 0:[2], +^#(_0,_1):[_0]}
      for all instantiations of the variables with values greater than or equal to mu = 2.
  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 = 19