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)
 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))

Proof:
 DP Processor:
  DPs:
   half#(s(s(x))) -> half#(x)
   lastbit#(s(s(x))) -> lastbit#(x)
   conv#(x) -> conviter#(x,cons(0(),nil()))
   conviter#(x,l) -> zero#(x)
   conviter#(x,l) -> if#(zero(x),x,l)
   if#(false(),x,l) -> lastbit#(x)
   if#(false(),x,l) -> half#(x)
   if#(false(),x,l) -> conviter#(half(x),cons(lastbit(x),l))
  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))
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [if#](x0, x1, x2) = x0 + x1 + x2 + 0,
    
    [conviter#](x0, x1) = 1x0 + 2x1 + 2,
    
    [conv#](x0) = 14x0 + 7,
    
    [zero#](x0) = x0,
    
    [lastbit#](x0) = -3x0 + 0,
    
    [half#](x0) = -4x0 + 0,
    
    [if](x0, x1, x2) = 1x0 + 1x1 + 2x2 + 0,
    
    [conviter](x0, x1) = 2x0 + 3x1 + 3,
    
    [cons](x0, x1) = -8x0 + 0,
    
    [nil] = 0,
    
    [conv](x0) = 3x0 + 11,
    
    [false] = 3,
    
    [true] = 0,
    
    [zero](x0) = x0 + 1,
    
    [lastbit](x0) = x0 + 6,
    
    [s](x0) = 3x0 + 4,
    
    [half](x0) = -2x0 + 1,
    
    [0] = 0
   orientation:
    half#(s(s(x))) = 2x + 3 >= -4x + 0 = half#(x)
    
    lastbit#(s(s(x))) = 3x + 4 >= -3x + 0 = lastbit#(x)
    
    conv#(x) = 14x + 7 >= 1x + 2 = conviter#(x,cons(0(),nil()))
    
    conviter#(x,l) = 2l + 1x + 2 >= x = zero#(x)
    
    conviter#(x,l) = 2l + 1x + 2 >= l + x + 1 = if#(zero(x),x,l)
    
    if#(false(),x,l) = l + x + 3 >= -3x + 0 = lastbit#(x)
    
    if#(false(),x,l) = l + x + 3 >= -4x + 0 = half#(x)
    
    if#(false(),x,l) = l + x + 3 >= -1x + 2 = conviter#(half(x),cons(lastbit(x),l))
    
    half(0()) = 1 >= 0 = 0()
    
    half(s(0())) = 2 >= 0 = 0()
    
    half(s(s(x))) = 4x + 5 >= 1x + 4 = s(half(x))
    
    lastbit(0()) = 6 >= 0 = 0()
    
    lastbit(s(0())) = 6 >= 4 = s(0())
    
    lastbit(s(s(x))) = 6x + 7 >= x + 6 = lastbit(x)
    
    zero(0()) = 1 >= 0 = true()
    
    zero(s(x)) = 3x + 4 >= 3 = false()
    
    conv(x) = 3x + 11 >= 2x + 3 = conviter(x,cons(0(),nil()))
    
    conviter(x,l) = 3l + 2x + 3 >= 2l + 1x + 2 = if(zero(x),x,l)
    
    if(true(),x,l) = 2l + 1x + 1 >= l = l
    
    if(false(),x,l) = 2l + 1x + 4 >= x + 3 = conviter(half(x),cons(lastbit(x),l))
   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)
     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))
   Qed