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 = [double^#(s(_0)) -> double^#(_0)]
  TRS = {double(0) -> 0, double(s(_0)) -> s(s(double(_0))), +(_0,0) -> _0, +(_0,s(_1)) -> s(+(_0,_1)), +(s(_0),_1) -> s(+(_0,_1)), double(_0) -> +(_0,_0)}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [+^#(_0,s(_1)) -> +^#(_0,_1), +^#(s(_0),_1) -> +^#(_0,_1)]
  TRS = {double(0) -> 0, double(s(_0)) -> s(s(double(_0))), +(_0,0) -> _0, +(_0,s(_1)) -> s(+(_0,_1)), +(s(_0),_1) -> s(+(_0,_1)), double(_0) -> +(_0,_0)}
    ## 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 = 0