YES
O(n^4)
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
         [X3]    [1 1 1 1][X3]   [1]
         [X2]    [0 1 0 0][X2]   [0]
   [log]([X1]) = [0 0 1 0][X1] + [0]
         [X0]    [0 0 0 1][X0]   [0]
   
       [X3]    [1 0 0 0][X3]   [0]
       [X2]    [0 1 1 0][X2]   [1]
   [s]([X1]) = [0 0 1 1][X1] + [1]
       [X0]    [0 0 0 0][X0]   [1]
   
          [X3]    [1 0 1 1][X3]   [0]
          [X2]    [0 1 0 0][X2]   [0]
   [half]([X1]) = [0 0 1 0][X1] + [0]
          [X0]    [0 0 0 1][X0]   [0]
   
         [0]
         [0]
   [0] = [0]
         [1]
   
   
   Qed