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 = [log^#(s(s(_0))) -> log^#(s(half(_0)))]
  TRS = {half(0) -> 0, half(s(s(_0))) -> s(half(_0)), log(s(0)) -> 0, log(s(s(_0))) -> s(log(s(half(_0))))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations...
      The constraints are satisfied by the polynomials:
      {half(_0):[_0], s(_0):[2 * _0], 0:[1], log(_0):[_0], log^#(_0):[_0]}
      for all instantiations of the variables with values greater than or equal to mu = 1.
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [half^#(s(s(_0))) -> half^#(_0)]
  TRS = {half(0) -> 0, half(s(s(_0))) -> s(half(_0)), log(s(0)) -> 0, log(s(s(_0))) -> s(log(s(half(_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 = 20