YES

Problem:
 half(0()) -> 0()
 half(s(0())) -> 0()
 half(s(s(x))) -> s(half(x))
 inc(0()) -> 0()
 inc(s(x)) -> s(inc(x))
 zero(0()) -> true()
 zero(s(x)) -> false()
 p(0()) -> 0()
 p(s(x)) -> x
 bits(x) -> bitIter(x,0())
 bitIter(x,y) -> if(zero(x),x,inc(y))
 if(true(),x,y) -> p(y)
 if(false(),x,y) -> bitIter(half(x),y)

Proof:
 DP Processor:
  DPs:
   half#(s(s(x))) -> half#(x)
   inc#(s(x)) -> inc#(x)
   bits#(x) -> bitIter#(x,0())
   bitIter#(x,y) -> inc#(y)
   bitIter#(x,y) -> zero#(x)
   bitIter#(x,y) -> if#(zero(x),x,inc(y))
   if#(true(),x,y) -> p#(y)
   if#(false(),x,y) -> half#(x)
   if#(false(),x,y) -> bitIter#(half(x),y)
  TRS:
   half(0()) -> 0()
   half(s(0())) -> 0()
   half(s(s(x))) -> s(half(x))
   inc(0()) -> 0()
   inc(s(x)) -> s(inc(x))
   zero(0()) -> true()
   zero(s(x)) -> false()
   p(0()) -> 0()
   p(s(x)) -> x
   bits(x) -> bitIter(x,0())
   bitIter(x,y) -> if(zero(x),x,inc(y))
   if(true(),x,y) -> p(y)
   if(false(),x,y) -> bitIter(half(x),y)
  TDG Processor:
   DPs:
    half#(s(s(x))) -> half#(x)
    inc#(s(x)) -> inc#(x)
    bits#(x) -> bitIter#(x,0())
    bitIter#(x,y) -> inc#(y)
    bitIter#(x,y) -> zero#(x)
    bitIter#(x,y) -> if#(zero(x),x,inc(y))
    if#(true(),x,y) -> p#(y)
    if#(false(),x,y) -> half#(x)
    if#(false(),x,y) -> bitIter#(half(x),y)
   TRS:
    half(0()) -> 0()
    half(s(0())) -> 0()
    half(s(s(x))) -> s(half(x))
    inc(0()) -> 0()
    inc(s(x)) -> s(inc(x))
    zero(0()) -> true()
    zero(s(x)) -> false()
    p(0()) -> 0()
    p(s(x)) -> x
    bits(x) -> bitIter(x,0())
    bitIter(x,y) -> if(zero(x),x,inc(y))
    if(true(),x,y) -> p(y)
    if(false(),x,y) -> bitIter(half(x),y)
   graph:
    if#(false(),x,y) -> bitIter#(half(x),y) ->
    bitIter#(x,y) -> if#(zero(x),x,inc(y))
    if#(false(),x,y) -> bitIter#(half(x),y) ->
    bitIter#(x,y) -> zero#(x)
    if#(false(),x,y) -> bitIter#(half(x),y) -> bitIter#(x,y) -> inc#(y)
    if#(false(),x,y) -> half#(x) ->
    half#(s(s(x))) -> half#(x)
    bitIter#(x,y) -> if#(zero(x),x,inc(y)) ->
    if#(false(),x,y) -> bitIter#(half(x),y)
    bitIter#(x,y) -> if#(zero(x),x,inc(y)) ->
    if#(false(),x,y) -> half#(x)
    bitIter#(x,y) -> if#(zero(x),x,inc(y)) -> if#(true(),x,y) -> p#(y)
    bitIter#(x,y) -> inc#(y) -> inc#(s(x)) -> inc#(x)
    bits#(x) -> bitIter#(x,0()) ->
    bitIter#(x,y) -> if#(zero(x),x,inc(y))
    bits#(x) -> bitIter#(x,0()) -> bitIter#(x,y) -> zero#(x)
    bits#(x) -> bitIter#(x,0()) -> bitIter#(x,y) -> inc#(y)
    inc#(s(x)) -> inc#(x) -> inc#(s(x)) -> inc#(x)
    half#(s(s(x))) -> half#(x) -> half#(s(s(x))) -> half#(x)
   SCC Processor:
    #sccs: 3
    #rules: 4
    #arcs: 13/81
    DPs:
     if#(false(),x,y) -> bitIter#(half(x),y)
     bitIter#(x,y) -> if#(zero(x),x,inc(y))
    TRS:
     half(0()) -> 0()
     half(s(0())) -> 0()
     half(s(s(x))) -> s(half(x))
     inc(0()) -> 0()
     inc(s(x)) -> s(inc(x))
     zero(0()) -> true()
     zero(s(x)) -> false()
     p(0()) -> 0()
     p(s(x)) -> x
     bits(x) -> bitIter(x,0())
     bitIter(x,y) -> if(zero(x),x,inc(y))
     if(true(),x,y) -> p(y)
     if(false(),x,y) -> bitIter(half(x),y)
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [if#](x0, x1, x2) = 3/2x0 + 3/2x1 + 2x2,
      
      [bitIter#](x0, x1) = 3x0 + 2x1 + 1/2,
      
      [if](x0, x1, x2) = x1 + 1/2x2 + 7/2,
      
      [bitIter](x0, x1) = x0 + 1/2x1 + 7/2,
      
      [bits](x0) = 2x0 + 7/2,
      
      [p](x0) = 1/2x0 + 2,
      
      [false] = 3,
      
      [true] = 0,
      
      [zero](x0) = x0,
      
      [inc](x0) = x0,
      
      [s](x0) = 2x0 + 3,
      
      [half](x0) = 1/2x0,
      
      [0] = 0
     orientation:
      if#(false(),x,y) = 3/2x + 2y + 9/2 >= 3/2x + 2y + 1/2 = bitIter#(half(x),y)
      
      bitIter#(x,y) = 3x + 2y + 1/2 >= 3x + 2y = if#(zero(x),x,inc(y))
      
      half(0()) = 0 >= 0 = 0()
      
      half(s(0())) = 3/2 >= 0 = 0()
      
      half(s(s(x))) = 2x + 9/2 >= x + 3 = s(half(x))
      
      inc(0()) = 0 >= 0 = 0()
      
      inc(s(x)) = 2x + 3 >= 2x + 3 = s(inc(x))
      
      zero(0()) = 0 >= 0 = true()
      
      zero(s(x)) = 2x + 3 >= 3 = false()
      
      p(0()) = 2 >= 0 = 0()
      
      p(s(x)) = x + 7/2 >= x = x
      
      bits(x) = 2x + 7/2 >= x + 7/2 = bitIter(x,0())
      
      bitIter(x,y) = x + 1/2y + 7/2 >= x + 1/2y + 7/2 = if(zero(x),x,inc(y))
      
      if(true(),x,y) = x + 1/2y + 7/2 >= 1/2y + 2 = p(y)
      
      if(false(),x,y) = x + 1/2y + 7/2 >= 1/2x + 1/2y + 7/2 = bitIter(half(x),y)
     problem:
      DPs:
       
      TRS:
       half(0()) -> 0()
       half(s(0())) -> 0()
       half(s(s(x))) -> s(half(x))
       inc(0()) -> 0()
       inc(s(x)) -> s(inc(x))
       zero(0()) -> true()
       zero(s(x)) -> false()
       p(0()) -> 0()
       p(s(x)) -> x
       bits(x) -> bitIter(x,0())
       bitIter(x,y) -> if(zero(x),x,inc(y))
       if(true(),x,y) -> p(y)
       if(false(),x,y) -> bitIter(half(x),y)
     Qed
    
    DPs:
     half#(s(s(x))) -> half#(x)
    TRS:
     half(0()) -> 0()
     half(s(0())) -> 0()
     half(s(s(x))) -> s(half(x))
     inc(0()) -> 0()
     inc(s(x)) -> s(inc(x))
     zero(0()) -> true()
     zero(s(x)) -> false()
     p(0()) -> 0()
     p(s(x)) -> x
     bits(x) -> bitIter(x,0())
     bitIter(x,y) -> if(zero(x),x,inc(y))
     if(true(),x,y) -> p(y)
     if(false(),x,y) -> bitIter(half(x),y)
    KBO Processor:
     argument filtering:
      pi(0) = []
      pi(half) = 0
      pi(s) = [0]
      pi(inc) = 0
      pi(zero) = []
      pi(true) = []
      pi(false) = []
      pi(p) = 0
      pi(bits) = []
      pi(bitIter) = 1
      pi(if) = 2
      pi(half#) = 0
     weight function:
      w0 = 1
      w(half#) = w(if) = w(bitIter) = w(bits) = w(p) = w(false) = w(true) = w(
      zero) = w(inc) = w(s) = w(0) = 1
      w(half) = 0
     precedence:
      inc > zero > bits > half# ~ if ~ bitIter ~ p ~ false ~ true ~ s ~ half ~ 0
     problem:
      DPs:
       
      TRS:
       half(0()) -> 0()
       half(s(0())) -> 0()
       half(s(s(x))) -> s(half(x))
       inc(0()) -> 0()
       inc(s(x)) -> s(inc(x))
       zero(0()) -> true()
       zero(s(x)) -> false()
       p(0()) -> 0()
       p(s(x)) -> x
       bits(x) -> bitIter(x,0())
       bitIter(x,y) -> if(zero(x),x,inc(y))
       if(true(),x,y) -> p(y)
       if(false(),x,y) -> bitIter(half(x),y)
     Qed
    
    DPs:
     inc#(s(x)) -> inc#(x)
    TRS:
     half(0()) -> 0()
     half(s(0())) -> 0()
     half(s(s(x))) -> s(half(x))
     inc(0()) -> 0()
     inc(s(x)) -> s(inc(x))
     zero(0()) -> true()
     zero(s(x)) -> false()
     p(0()) -> 0()
     p(s(x)) -> x
     bits(x) -> bitIter(x,0())
     bitIter(x,y) -> if(zero(x),x,inc(y))
     if(true(),x,y) -> p(y)
     if(false(),x,y) -> bitIter(half(x),y)
    KBO Processor:
     argument filtering:
      pi(0) = []
      pi(half) = [0]
      pi(s) = [0]
      pi(inc) = 0
      pi(zero) = 0
      pi(true) = []
      pi(false) = []
      pi(p) = 0
      pi(bits) = []
      pi(bitIter) = 1
      pi(if) = 2
      pi(inc#) = 0
     weight function:
      w0 = 1
      w(inc#) = w(if) = w(bitIter) = w(bits) = w(p) = w(false) = w(true) = w(
      zero) = w(inc) = w(s) = w(half) = w(0) = 1
     precedence:
      bitIter > inc# ~ s ~ half > bits > 0 > if ~ p ~ false ~ true ~ zero ~ inc
     problem:
      DPs:
       
      TRS:
       half(0()) -> 0()
       half(s(0())) -> 0()
       half(s(s(x))) -> s(half(x))
       inc(0()) -> 0()
       inc(s(x)) -> s(inc(x))
       zero(0()) -> true()
       zero(s(x)) -> false()
       p(0()) -> 0()
       p(s(x)) -> x
       bits(x) -> bitIter(x,0())
       bitIter(x,y) -> if(zero(x),x,inc(y))
       if(true(),x,y) -> p(y)
       if(false(),x,y) -> bitIter(half(x),y)
     Qed