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 = [f^#(s(_0),s(_1),0) -> f^#(_0,_1,s(0)), f^#(s(_0),0,s(_1)) -> f^#(_0,s(0),_1), f^#(s(_0),s(_1),s(_2)) -> f^#(_0,_1,f(s(_0),s(_1),_2)), f^#(s(_0),s(_1),s(_2)) -> f^#(s(_0),s(_1),_2)]
  TRS = {f(_0,0,0) -> s(_0), f(0,_0,0) -> s(_0), f(0,0,_0) -> s(_0), f(s(0),_0,_1) -> f(0,s(_0),s(_1)), f(s(_0),s(_1),0) -> f(_0,_1,s(0)), f(s(_0),0,s(_1)) -> f(_0,s(0),_1), f(0,s(0),s(0)) -> s(s(0)), f(s(_0),s(_1),s(_2)) -> f(_0,_1,f(s(_0),s(_1),_2)), f(0,s(s(_0)),s(0)) -> f(0,_0,s(0)), f(0,s(0),s(s(_0))) -> f(0,s(0),_0), f(0,s(s(_0)),s(s(_1))) -> f(0,_0,f(0,s(s(_0)),s(_1)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      f > [s, 0], s > [0]
      and the argument filtering:
      {f:[0, 1, 2], s:[0], f^#:[0, 1, 2]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [f^#(0,s(s(_0)),s(s(_1))) -> f^#(0,_0,f(0,s(s(_0)),s(_1))), f^#(0,s(s(_0)),s(s(_1))) -> f^#(0,s(s(_0)),s(_1))]
  TRS = {f(_0,0,0) -> s(_0), f(0,_0,0) -> s(_0), f(0,0,_0) -> s(_0), f(s(0),_0,_1) -> f(0,s(_0),s(_1)), f(s(_0),s(_1),0) -> f(_0,_1,s(0)), f(s(_0),0,s(_1)) -> f(_0,s(0),_1), f(0,s(0),s(0)) -> s(s(0)), f(s(_0),s(_1),s(_2)) -> f(_0,_1,f(s(_0),s(_1),_2)), f(0,s(s(_0)),s(0)) -> f(0,_0,s(0)), f(0,s(0),s(s(_0))) -> f(0,s(0),_0), f(0,s(s(_0)),s(s(_1))) -> f(0,_0,f(0,s(s(_0)),s(_1)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      f > [s, 0], s > [0]
      and the argument filtering:
      {f:[0, 1, 2], s:[0], f^#:[0, 1, 2]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [f^#(0,s(0),s(s(_0))) -> f^#(0,s(0),_0)]
  TRS = {f(_0,0,0) -> s(_0), f(0,_0,0) -> s(_0), f(0,0,_0) -> s(_0), f(s(0),_0,_1) -> f(0,s(_0),s(_1)), f(s(_0),s(_1),0) -> f(_0,_1,s(0)), f(s(_0),0,s(_1)) -> f(_0,s(0),_1), f(0,s(0),s(0)) -> s(s(0)), f(s(_0),s(_1),s(_2)) -> f(_0,_1,f(s(_0),s(_1),_2)), f(0,s(s(_0)),s(0)) -> f(0,_0,s(0)), f(0,s(0),s(s(_0))) -> f(0,s(0),_0), f(0,s(s(_0)),s(s(_1))) -> f(0,_0,f(0,s(s(_0)),s(_1)))}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [f^#(0,s(s(_0)),s(0)) -> f^#(0,_0,s(0))]
  TRS = {f(_0,0,0) -> s(_0), f(0,_0,0) -> s(_0), f(0,0,_0) -> s(_0), f(s(0),_0,_1) -> f(0,s(_0),s(_1)), f(s(_0),s(_1),0) -> f(_0,_1,s(0)), f(s(_0),0,s(_1)) -> f(_0,s(0),_1), f(0,s(0),s(0)) -> s(s(0)), f(s(_0),s(_1),s(_2)) -> f(_0,_1,f(s(_0),s(_1),_2)), f(0,s(s(_0)),s(0)) -> f(0,_0,s(0)), f(0,s(0),s(s(_0))) -> f(0,s(0),_0), f(0,s(s(_0)),s(s(_1))) -> f(0,_0,f(0,s(s(_0)),s(_1)))}
    ## Trying with homeomorphic embeddings... Success!
  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 = 31006