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 = [ackin^#(s(_0),s(_1)) -> u21^#(ackin(s(_0),_1),_0), ackin^#(s(_0),s(_1)) -> ackin^#(s(_0),_1), u21^#(ackout(_0),_1) -> ackin^#(_1,_0)]
  TRS = {ackin(s(_0),s(_1)) -> u21(ackin(s(_0),_1),_0), u21(ackout(_0),_1) -> u22(ackin(_1,_0))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Too many coefficients (15)! Aborting!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      ackin > [u21], s > [ackin, u21], u21 > [ackin], ackout > [u22, ackin]
      and the argument filtering:
      {ackin:[1], u22:[0], s:[0], u21:[0], ackout:[0], ackin^#:[1], u21^#:[0]}
  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 = 15