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