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 = [-^#(s(_0),s(_1)) -> -^#(_0,_1)]
  TRS = {double(0) -> 0, double(s(_0)) -> s(s(double(_0))), half(0) -> 0, half(s(0)) -> 0, half(s(s(_0))) -> s(half(_0)), -(_0,0) -> _0, -(s(_0),s(_1)) -> -(_0,_1), if(0,_0,_1) -> _0, if(s(_0),_1,_2) -> _2, half(double(_0)) -> _0}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [half^#(s(s(_0))) -> half^#(_0)]
  TRS = {double(0) -> 0, double(s(_0)) -> s(s(double(_0))), half(0) -> 0, half(s(0)) -> 0, half(s(s(_0))) -> s(half(_0)), -(_0,0) -> _0, -(s(_0),s(_1)) -> -(_0,_1), if(0,_0,_1) -> _0, if(s(_0),_1,_2) -> _2, half(double(_0)) -> _0}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [double^#(s(_0)) -> double^#(_0)]
  TRS = {double(0) -> 0, double(s(_0)) -> s(s(double(_0))), half(0) -> 0, half(s(0)) -> 0, half(s(s(_0))) -> s(half(_0)), -(_0,0) -> _0, -(s(_0),s(_1)) -> -(_0,_1), if(0,_0,_1) -> _0, if(s(_0),_1,_2) -> _2, half(double(_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