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{3, x1, 1 + x2}
  ackin#_A(x1,x2) = max{3, x1, 1 + x2}
  s_A(x1) = max{5, 4 + x1}
  s#_A(x1) = max{5, 4 + x1}
  u21_A(x1,x2) = max{6, x1, 4 + x2}
  u21#_A(x1,x2) = max{6, x1, 4 + x2}
  ackout_A(x1) = max{2, 5 + x1}
  ackout#_A(x1) = max{2, 5 + x1}
  u22_A(x1) = max{6, 3 + x1}
  u22#_A(x1) = max{6, 3 + x1}

precedence:

  ackin = s = ackout > u21 > u22