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)))
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [conv#](x0) = 1x0 + 2,
    
    [lastbit#](x0) = -3x0 + 0,
    
    [half#](x0) = x0,
    
    [cons](x0, x1) = x1,
    
    [nil] = 1,
    
    [conv](x0) = 3x0 + 0,
    
    [lastbit](x0) = 1x0 + 0,
    
    [s](x0) = 2x0 + 4,
    
    [half](x0) = -1x0 + 2,
    
    [0] = 0
   orientation:
    half#(s(s(x))) = 4x + 6 >= x = half#(x)
    
    lastbit#(s(s(x))) = 1x + 3 >= -3x + 0 = lastbit#(x)
    
    conv#(s(x)) = 3x + 5 >= -1x + 1 = lastbit#(s(x))
    
    conv#(s(x)) = 3x + 5 >= 2x + 4 = half#(s(x))
    
    conv#(s(x)) = 3x + 5 >= 2x + 4 = conv#(half(s(x)))
    
    half(0()) = 2 >= 0 = 0()
    
    half(s(0())) = 3 >= 0 = 0()
    
    half(s(s(x))) = 3x + 5 >= 1x + 4 = s(half(x))
    
    lastbit(0()) = 1 >= 0 = 0()
    
    lastbit(s(0())) = 5 >= 4 = s(0())
    
    lastbit(s(s(x))) = 5x + 7 >= 1x + 0 = lastbit(x)
    
    conv(0()) = 3 >= 0 = cons(nil(),0())
    
    conv(s(x)) = 5x + 7 >= 3x + 5 = cons(conv(half(s(x))),lastbit(s(x)))
   problem:
    DPs:
     
    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)))
   Qed