YES

TRS:

  ack(0(),y) -> s(y)
  ack(s(x),0()) -> ack(x,s(0()))
  ack(s(x),s(y)) -> ack(x,ack(s(x),y))

linear polynomial interpretations on N:

  ack_A(x1,x2) = 1
  ack#_A(x1,x2) = 2
  0_A = 1
  0#_A = 0
  s_A(x1) = 1
  s#_A(x1) = 1

precedence:

  s > 0 > ack