YES

TRS:

  ack_in(0(),n) -> ack_out(s(n))
  ack_in(s(m),0()) -> u11(ack_in(m,s(0())))
  u11(ack_out(n)) -> ack_out(n)
  ack_in(s(m),s(n)) -> u21(ack_in(s(m),n),m)
  u21(ack_out(n),m) -> u22(ack_in(m,n))
  u22(ack_out(n)) -> ack_out(n)

max/plus interpretations on N:

  ack_in_A(x1,x2) = max{1, -2, x2}
  ack_in#_A(x1,x2) = max{7, 5 + x1, 4}
  0_A = 0
  0#_A = 8
  ack_out_A(x1) = max{0, 0}
  ack_out#_A(x1) = max{7, 1}
  s_A(x1) = max{0, 4 + x1}
  s#_A(x1) = max{0, 0}
  u11_A(x1) = max{0, -1}
  u11#_A(x1) = max{3, 0}
  u21_A(x1,x2) = max{4, 2, 3}
  u21#_A(x1,x2) = max{3, 9, 6 + x2}
  u22_A(x1) = max{4, 3}
  u22#_A(x1) = max{9, 2}

precedence:

  ack_in > 0 > s = u21 > u11 = u22 > ack_out