YES
O(n^5)
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
         [1]
         [0]
   [0] = [1]
         [0]
         [0]
   
       [X4]    [1 0 0 0 0][X4]   [0]
       [X3]    [0 0 0 0 0][X3]   [0]
   [s]([X2]) = [0 0 1 0 0][X2] + [1]
       [X1]    [0 0 0 0 0][X1]   [0]
       [X0]    [0 0 0 0 1][X0]   [1]
   
             [X9]  [X4]    [1 0 1 0 1][X9]   [1 0 0 0 1][X4]   [0]
             [X8]  [X3]    [0 0 0 0 0][X8]   [0 0 0 0 0][X3]   [0]
   [average]([X7], [X2]) = [0 0 0 0 1][X7] + [0 0 0 0 1][X2] + [1]
             [X6]  [X1]    [0 0 0 0 0][X6]   [0 0 0 0 0][X1]   [0]
             [X5]  [X0]    [0 0 0 0 1][X5]   [0 0 0 0 1][X0]   [0]
   
   
   Qed