YES

Problem:
 average(s(x),y) -> average(x,s(y))
 average(x,s(s(s(y)))) -> s(average(s(x),y))
 average(0(),0()) -> 0()
 average(0(),s(0())) -> 0()
 average(0(),s(s(0()))) -> s(0())

Proof:
 DP Processor:
  DPs:
   average#(s(x),y) -> average#(x,s(y))
   average#(x,s(s(s(y)))) -> average#(s(x),y)
  TRS:
   average(s(x),y) -> average(x,s(y))
   average(x,s(s(s(y)))) -> s(average(s(x),y))
   average(0(),0()) -> 0()
   average(0(),s(0())) -> 0()
   average(0(),s(s(0()))) -> s(0())
  KBO Processor:
   argument filtering:
    pi(s) = [0]
    pi(average) = [0,1]
    pi(0) = []
    pi(average#) = [0,1]
   weight function:
    w0 = 1
    w(0) = w(s) = 1
    w(average#) = w(average) = 0
   precedence:
    average# ~ 0 ~ average ~ s
   problem:
    DPs:
     
    TRS:
     average(s(x),y) -> average(x,s(y))
     average(x,s(s(s(y)))) -> s(average(s(x),y))
     average(0(),0()) -> 0()
     average(0(),s(0())) -> 0()
     average(0(),s(s(0()))) -> s(0())
   Qed