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 = [average^#(s(_0),_1) -> average^#(_0,s(_1)), average^#(_0,s(s(s(_1)))) -> average^#(s(_0),_1)]
  TRS = {average(s(_0),_1) -> average(_0,s(_1)), average(_0,s(s(s(_1)))) -> s(average(s(_0),_1)), average(0,0) -> 0, average(0,s(0)) -> 0, average(0,s(s(0))) -> s(0)}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations...
      The constraints are satisfied by the polynomials:
      {average(_0,_1):[_0 * _1], 0:[1], s(_0):[2 * _0], average^#(_0,_1):[_0 + _0 * _1]}
      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 = 10