YES
O(n^2)
TRS:
 {
   average(x, s(s(s(y)))) -> s(average(s(x), y)),
         average(s(x), y) -> average(x, s(y)),
  average(0(), s(s(0()))) -> s(0()),
     average(0(), s(0())) -> 0(),
        average(0(), 0()) -> 0()
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
     average(x, s(s(s(y)))) -> s(average(s(x), y)),
           average(s(x), y) -> average(x, s(y)),
    average(0(), s(s(0()))) -> s(0()),
       average(0(), s(0())) -> 0(),
          average(0(), 0()) -> 0()
   }
  Matrix Interpretation:
   Interpretation class: triangular
         [0]
   [0] = [0]
   
       [X1]    [1 0][X1]   [2]
   [s]([X0]) = [0 1][X0] + [1]
   
             [X3]  [X1]    [1 1][X3]   [1 0][X1]   [1]
   [average]([X2], [X0]) = [0 1][X2] + [0 1][X0] + [1]
   
   
   Qed