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)
  zero(0()) -> true()
  zero(s(x)) -> false()
  conv(x) -> conviter(x,cons(0(),nil()))
  conviter(x,l) -> if(zero(x),x,l)
  if(true(),x,l) -> l
  if(false(),x,l) -> conviter(half(x),cons(lastbit(x),l))

max/plus interpretations on N:

  half_A(x1) = max{3, -14 + x1}
  half#_A(x1) = max{25, 1}
  0_A = 3
  0#_A = 26
  s_A(x1) = max{16, 18 + x1}
  s#_A(x1) = max{23, 24}
  lastbit_A(x1) = max{2, 21}
  lastbit#_A(x1) = max{24, 24}
  zero_A(x1) = max{1, -1 + x1}
  zero#_A(x1) = max{13, 15}
  true_A = 2
  true#_A = 14
  false_A = 17
  false#_A = 14
  conv_A(x1) = max{0, 28}
  conv#_A(x1) = max{4, 27 + x1}
  conviter_A(x1,x2) = max{28, 1, 13 + x2}
  conviter#_A(x1,x2) = max{25, 16 + x1, 12 + x2}
  cons_A(x1,x2) = max{15, -10 + x1, -13}
  cons#_A(x1,x2) = max{3, 27, 27}
  nil_A = 1
  nil#_A = 0
  if_A(x1,x2,x3) = max{14, 28, 4, 1 + x3}
  if#_A(x1,x2,x3) = max{0, 10 + x1, 2 + x2, 24}

precedence:

  s = if > lastbit > 0 > half = conv > conviter = cons = nil > zero > true = false