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 = [a^#(a(_0)) -> b^#(b(_0)), b^#(b(a(_0))) -> a^#(b(b(_0))), b^#(b(a(_0))) -> b^#(b(_0)), b^#(b(a(_0))) -> b^#(_0), a^#(a(_0)) -> b^#(_0)]
  TRS = {a(a(_0)) -> b(b(_0)), b(b(a(_0))) -> a(b(b(_0)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations...
      The constraints are satisfied by the polynomials:
      {a(_0):[2 * _0], b(_0):[_0], b^#(_0):[_0], a^#(_0):[_0]}
      for all instantiations of the variables with values greater than or equal to mu = 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 = 33