YES

TRS:

  half(0()) -> 0()
  half(s(0())) -> 0()
  half(s(s(x))) -> s(half(x))
  bits(0()) -> 0()
  bits(s(x)) -> s(bits(half(s(x))))

max/plus interpretations on N:

  half_A(x1) = max{8, -5 + x1}
  half#_A(x1) = max{12, -2 + x1}
  0_A = 3
  0#_A = 5
  s_A(x1) = max{13, 5 + x1}
  s#_A(x1) = max{12, 1 + x1}
  bits_A(x1) = max{2, 1 + x1}
  bits#_A(x1) = max{0, -1 + x1}

precedence:

  bits > half > s > 0