MAYBE

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)
    Open
    
    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)
    Open
    
    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)
    Open