YES
O(n^2)
TRS:
 {
      half(0()) -> 0(),
  half(s(s(x))) -> s(half(x)),
    log(s(0())) -> 0(),
   log(s(s(x))) -> s(log(s(half(x))))
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
        half(0()) -> 0(),
    half(s(s(x))) -> s(half(x)),
      log(s(0())) -> 0(),
     log(s(s(x))) -> s(log(s(half(x))))
   }
  Matrix Interpretation:
   Interpretation class: triangular
         [X1]    [1 2][X1]   [0]
   [log]([X0]) = [0 1][X0] + [0]
   
       [X1]    [1 0][X1]   [1]
   [s]([X0]) = [0 1][X0] + [2]
   
          [X1]    [1 0][X1]   [1]
   [half]([X0]) = [0 1][X0] + [0]
   
         [0]
   [0] = [0]
   
   
   Qed