YES

Problem:
 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)))

Proof:
 DP Processor:
  DPs:
   half#(s(s(x))) -> half#(x)
   lastbit#(s(s(x))) -> lastbit#(x)
   conv#(s(x)) -> lastbit#(s(x))
   conv#(s(x)) -> half#(s(x))
   conv#(s(x)) -> conv#(half(s(x)))
  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)))
  Usable Rule Processor:
   DPs:
    half#(s(s(x))) -> half#(x)
    lastbit#(s(s(x))) -> lastbit#(x)
    conv#(s(x)) -> lastbit#(s(x))
    conv#(s(x)) -> half#(s(x))
    conv#(s(x)) -> conv#(half(s(x)))
   TRS:
    half(s(0())) -> 0()
    half(s(s(x))) -> s(half(x))
    half(0()) -> 0()
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     half(s(0())) -> 0()
     half(s(s(x))) -> s(half(x))
     half(0()) -> 0()
    interpretation:
     [conv#](x0) = 1x0 + -16,
     
     [lastbit#](x0) = x0 + -16,
     
     [half#](x0) = x0,
     
     [s](x0) = 2x0 + 5,
     
     [half](x0) = -1x0 + 3,
     
     [0] = 0
    orientation:
     half#(s(s(x))) = 4x + 7 >= x = half#(x)
     
     lastbit#(s(s(x))) = 4x + 7 >= x + -16 = lastbit#(x)
     
     conv#(s(x)) = 3x + 6 >= 2x + 5 = lastbit#(s(x))
     
     conv#(s(x)) = 3x + 6 >= 2x + 5 = half#(s(x))
     
     conv#(s(x)) = 3x + 6 >= 2x + 5 = conv#(half(s(x)))
     
     half(s(0())) = 4 >= 0 = 0()
     
     half(s(s(x))) = 3x + 6 >= 1x + 5 = s(half(x))
     
     half(0()) = 3 >= 0 = 0()
    problem:
     DPs:
      
     TRS:
      half(s(0())) -> 0()
      half(s(s(x))) -> s(half(x))
      half(0()) -> 0()
    Qed