YES

TRS:

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

max/plus interpretations on N:

  ackin_A(x1,x2) = max{4, 1, -1}
  ackin#_A(x1,x2) = max{4, 3, 2}
  s_A(x1) = max{3, 4}
  s#_A(x1) = max{0, 1}
  u21_A(x1,x2) = max{2, -2, -1}
  u21#_A(x1,x2) = max{1, x1, 4}
  ackout_A(x1) = max{5, 5 + x1}
  ackout#_A(x1) = max{0, 0}
  u22_A(x1) = max{2, -1}
  u22#_A(x1) = max{2, -2 + x1}

precedence:

  ackin = ackout > s = u21 > u22