YES
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()}
 DP:
  Strict:
   {average#(x, s(s(s(y)))) -> average#(s(x), y),
          average#(s(x), y) -> average#(x, s(y))}
  Weak:
  { 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()}
  EDG:
   {(average#(s(x), y) -> average#(x, s(y)), average#(s(x), y) -> average#(x, s(y)))
    (average#(s(x), y) -> average#(x, s(y)), average#(x, s(s(s(y)))) -> average#(s(x), y))
    (average#(x, s(s(s(y)))) -> average#(s(x), y), average#(x, s(s(s(y)))) -> average#(s(x), y))
    (average#(x, s(s(s(y)))) -> average#(s(x), y), average#(s(x), y) -> average#(x, s(y)))}
   SCCS:
    Scc:
     {average#(x, s(s(s(y)))) -> average#(s(x), y),
            average#(s(x), y) -> average#(x, s(y))}
    SCC:
     Strict:
      {average#(x, s(s(s(y)))) -> average#(s(x), y),
             average#(s(x), y) -> average#(x, s(y))}
     Weak:
     { 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()}
     POLY:
      Argument Filtering:
       pi(0) = [], pi(s) = [0], pi(average#) = [0,1], pi(average) = []
      Usable Rules:
       {}
      Interpretation:
       [average#](x0, x1) = x0 + x1,
       [s](x0) = x0 + 1
      Strict:
       {average#(s(x), y) -> average#(x, s(y))}
      Weak:
       { 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()}
      EDG:
       {(average#(s(x), y) -> average#(x, s(y)), average#(s(x), y) -> average#(x, s(y)))}
       SCCS:
        Scc:
         {average#(s(x), y) -> average#(x, s(y))}
        SCC:
         Strict:
          {average#(s(x), y) -> average#(x, s(y))}
         Weak:
         { 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()}
         SPSC:
          Simple Projection:
           pi(average#) = 0
          Strict:
           {}
          Qed