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 = [.^#(.(_0,_1),_2) -> .^#(_0,.(_1,_2)), .^#(.(_0,_1),_2) -> .^#(_1,_2)]
  TRS = {.(.(_0,_1),_2) -> .(_0,.(_1,_2))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations...
      The constraints are satisfied by the polynomials:
      {.(_0,_1):[_0 * _1], .^#(_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 = 12