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 = [g^#(f(_0,_1),_2) -> g^#(_1,_2), g^#(h(_0,_1),_2) -> g^#(_0,f(_1,_2)), g^#(_0,h(_1,_2)) -> g^#(_0,_1)]
  TRS = {g(f(_0,_1),_2) -> f(_0,g(_1,_2)), g(h(_0,_1),_2) -> g(_0,f(_1,_2)), g(_0,h(_1,_2)) -> h(g(_0,_1),_2)}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Too many coefficients (13)! Aborting!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      g > [h, f]
      and the argument filtering:
      {g:[0, 1], h:[0, 1], f:[0, 1], g^#:[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 = 20