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^#(f(_0,_1),_2) -> f^#(_0,f(_1,_2)), f^#(f(_0,_1),_2) -> f^#(_1,_2), f^#(g(_0,_1),_2) -> f^#(_0,_2), f^#(g(_0,_1),_2) -> f^#(_1,_2)]
  TRS = {f(0,_0) -> _0, f(_0,0) -> _0, f(i(_0),_1) -> i(_0), f(f(_0,_1),_2) -> f(_0,f(_1,_2)), f(g(_0,_1),_2) -> g(f(_0,_2),f(_1,_2)), f(1,g(_0,_1)) -> _0, f(2,g(_0,_1)) -> _1}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Too many coefficients (14)! Aborting!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      f > [g]
      and the argument filtering:
      {f:[0, 1], g:[0, 1], i:[0], f^#:[0, 1]}
  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 = 14