/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES
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 POLO(bPol) ... failed.
Uncurrying ... 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
  SCC { #8 }
POLO(Sum)... succeeded.
      zero	w: 0
      s 	w: x1 + 1
      bitIter	w: 0
      false	w: 0
      #half	w: 0
      #inc	w: x1
      #p 	w: 0
      inc	w: 0
      true	w: 0
      half	w: 0
      p 	w: 0
      0 	w: 0
      if	w: 0
      #bits	w: 0
      #bitIter	w: 0
      #if	w: 0
      #zero	w: 0
      bits	w: 0
    USABLE RULES: { }
    Removed DPs: #8
Number of SCCs: 2, DPs: 3
  SCC { #9 }
POLO(Sum)... succeeded.
      zero	w: 0
      s 	w: x1 + 1
      bitIter	w: 0
      false	w: 0
      #half	w: x1
      #inc	w: 0
      #p 	w: 0
      inc	w: 0
      true	w: 0
      half	w: 0
      p 	w: 0
      0 	w: 0
      if	w: 0
      #bits	w: 0
      #bitIter	w: 0
      #if	w: 0
      #zero	w: 0
      bits	w: 0
    USABLE RULES: { }
    Removed DPs: #9
Number of SCCs: 1, DPs: 2
  SCC { #1 #3 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
      zero	w: max(x1 - 2, 0)
      s 	w: max(x1 + 4, 0)
      bitIter	w: max(x1 - 1, 0)
      false	w: 2
      #half	w: 0
      #inc	w: 0
      #p 	w: 0
      inc	w: 3
      true	w: 0
      half	w: max(x1 - 3, 0)
      p 	w: max(x1 - 1, 0)
      0 	w: 0
      if	w: 0
      #bits	w: 0
      #bitIter	w: max(x1 + 2, 0)
      #if	w: max(x1 + 1, x2 + 1, 0)
      #zero	w: 0
      bits	w: 0
    USABLE RULES: { 1..3 6 7 }
    Removed DPs: #1 #3
Number of SCCs: 0, DPs: 0