YES

TRS:

  ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
  u21(ackout(X),Y) -> u22(ackin(Y,X))

linear polynomial interpretations on N:

  ackin_A(x1,x2) = 1
  ackin#_A(x1,x2) = x1
  s_A(x1) = x1 + 2
  s#_A(x1) = 0
  u21_A(x1,x2) = x1
  u21#_A(x1,x2) = x2 + 1
  ackout_A(x1) = x1 + 1
  ackout#_A(x1) = 0
  u22_A(x1) = 0
  u22#_A(x1) = 0

precedence:

  u21 = ackout = u22 > ackin > s