YES
Time: 0.007182
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:
  DP:
   {average#(x, s s s y) -> average#(s x, y),
        average#(s x, y) -> average#(x, s y)}
  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()}
  EDG:
   {(average#(x, s s s y) -> average#(s x, 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#(s x, y) -> average#(x, s y), average#(x, s s s y) -> average#(s x, y))
    (average#(s x, y) -> average#(x, s y), average#(s x, y) -> average#(x, s y))}
   SCCS (1):
    Scc:
     {average#(x, s s s y) -> average#(s x, y),
          average#(s x, y) -> average#(x, s y)}
    SCC (2):
     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:
      Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
      Interpretation:
       [average](x0, x1) = x0 + 1,
       
       [s](x0) = x0 + 1,
       
       [0] = 1,
       
       [average#](x0, x1) = x0 + x1 + 1
      Strict:
       average#(s x, y) -> average#(x, s y)
       2 + 1x + 1y >= 2 + 1x + 1y
       average#(x, s s s y) -> average#(s x, y)
       4 + 1x + 1y >= 2 + 1x + 1y
      Weak:
       
     EDG:
      {(average#(s x, y) -> average#(x, s y), average#(s x, y) -> average#(x, s y))}
      SCCS (1):
       Scc:
        {average#(s x, y) -> average#(x, s y)}
       SCC (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()}
        SPSC:
         Simple Projection:
          pi(average#) = 0
         Strict:
          {}
         Qed