YES

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())

linear polynomial interpretations on N:

  average_A(x1,x2) = x1 + x2
  average#_A(x1,x2) = x1 + x2 + 3
  s_A(x1) = x1 + 1
  s#_A(x1) = x1
  0_A = 0
  0#_A = 2

precedence:

  average > s > 0