Input TRS:
    1: half(0()) -> 0()
    2: half(s(0())) -> 0()
    3: half(s(s(x))) -> s(half(x))
    4: inc(0()) -> 0()
    5: inc(s(x)) -> s(inc(x))
    6: zero(0()) -> true()
    7: zero(s(x)) -> false()
    8: p(0()) -> 0()
    9: p(s(x)) -> x
    10: bits(x) -> bitIter(x,0())
    11: bitIter(x,y) -> if(zero(x),x,inc(y))
    12: if(true(),x,y) -> p(y)
    13: if(false(),x,y) -> bitIter(half(x),y)
Number of strict rules: 13
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #if(false(),x,y) -> #bitIter(half(x),y)
   #2: #if(false(),x,y) -> #half(x)
   #3: #bitIter(x,y) -> #if(zero(x),x,inc(y))
   #4: #bitIter(x,y) -> #zero(x)
   #5: #bitIter(x,y) -> #inc(y)
   #6: #if(true(),x,y) -> #p(y)
   #7: #bits(x) -> #bitIter(x,0())
   #8: #inc(s(x)) -> #inc(x)
   #9: #half(s(s(x))) -> #half(x)
Number of SCCs: 3, DPs: 4, edges: 4
	SCC { #8 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
  zero(x1)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
bitIter(x1,x2)	weight: 0
 false()	weight: 0
#half(x1)	weight: 0
 #inc(x1)	weight: x1
   #p(x1)	weight: 0
   inc(x1)	weight: 0
  true()	weight: 0
  half(x1)	weight: 0
     p(x1)	weight: 0
     0()	weight: 0
    if(x1,x2,x3)	weight: 0
#bits(x1)	weight: 0
#bitIter(x1,x2)	weight: 0
  #if(x1,x2,x3)	weight: 0
#zero(x1)	weight: 0
  bits(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #8
Number of SCCs: 2, DPs: 3, edges: 3
	SCC { #9 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
  zero(x1)	weight: 0
     s(x1)	weight: (/ 1 4) + x1
bitIter(x1,x2)	weight: 0
 false()	weight: 0
#half(x1)	weight: x1
 #inc(x1)	weight: 0
   #p(x1)	weight: 0
   inc(x1)	weight: 0
  true()	weight: 0
  half(x1)	weight: 0
     p(x1)	weight: 0
     0()	weight: 0
    if(x1,x2,x3)	weight: 0
#bits(x1)	weight: 0
#bitIter(x1,x2)	weight: 0
  #if(x1,x2,x3)	weight: 0
#zero(x1)	weight: 0
  bits(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #9
Number of SCCs: 1, DPs: 2, edges: 2
	SCC { #1 #3 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... succeeded.
  zero(x1)	weight: max{0, (- (/ 1 2)) + x1}
     s(x1)	weight: max{0, (/ 3 4) + x1}
bitIter(x1,x2)	weight: 0
 false()	weight: (/ 1 4)
#half(x1)	weight: 0
 #inc(x1)	weight: 0
   #p(x1)	weight: 0
   inc(x1)	weight: (max (- (/ 1 4)) 0)
  true()	weight: 0
  half(x1)	weight: max{0, (- (/ 1 4)) + x1}
     p(x1)	weight: 0
     0()	weight: 0
    if(x1,x2,x3)	weight: 0
#bits(x1)	weight: 0
#bitIter(x1,x2)	weight: max{0, (- (/ 1 4)) + x1}
  #if(x1,x2,x3)	weight: max{0, x1, (- (/ 1 4)) + x2}
#zero(x1)	weight: 0
  bits(x1)	weight: 0
    Usable rules: { 1..3 6 7 }
    Removed DPs: #1
Number of SCCs: 0, DPs: 0, edges: 0
YES