YES

TRS:

  half(0()) -> 0()
  half(s(0())) -> 0()
  half(s(s(x))) -> s(half(x))
  lastbit(0()) -> 0()
  lastbit(s(0())) -> s(0())
  lastbit(s(s(x))) -> lastbit(x)
  conv(0()) -> cons(nil(),0())
  conv(s(x)) -> cons(conv(half(s(x))),lastbit(s(x)))

max/plus interpretations on N:

  half_A(x1) = max{13, -1 + x1}
  half#_A(x1) = max{14, -1}
  0_A = 11
  0#_A = 13
  s_A(x1) = max{21, 8 + x1}
  s#_A(x1) = max{0, 14}
  lastbit_A(x1) = max{21, -22 + x1}
  lastbit#_A(x1) = max{8, -7 + x1}
  conv_A(x1) = max{37, -6 + x1}
  conv#_A(x1) = max{18, 8 + x1}
  cons_A(x1,x2) = max{16, 16, 16 + x2}
  cons#_A(x1,x2) = max{17, 15, 19}
  nil_A = 1
  nil#_A = 12

precedence:

  conv > half > s > lastbit = cons = nil > 0