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


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YES
Input TRS:
    1: lt(0(),s(x)) -> true()
    2: lt(x,0()) -> false()
    3: lt(s(x),s(y)) -> lt(x,y)
    4: logarithm(x) -> ifa(lt(0(),x),x)
    5: ifa(true(),x) -> help(x,1())
    6: ifa(false(),x) -> logZeroError()
    7: help(x,y) -> ifb(lt(y,x),x,y)
    8: ifb(true(),x,y) -> help(half(x),s(y))
    9: ifb(false(),x,y) -> y
    10: half(0()) -> 0()
    11: half(s(0())) -> 0()
    12: half(s(s(x))) -> s(half(x))
Number of strict rules: 12
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
   #1: #half(s(s(x))) -> #half(x)
   #2: #help(x,y) -> #ifb(lt(y,x),x,y)
   #3: #help(x,y) -> #lt(y,x)
   #4: #ifa(true(),x) -> #help(x,1())
   #5: #lt(s(x),s(y)) -> #lt(x,y)
   #6: #ifb(true(),x,y) -> #help(half(x),s(y))
   #7: #ifb(true(),x,y) -> #half(x)
   #8: #logarithm(x) -> #ifa(lt(0(),x),x)
   #9: #logarithm(x) -> #lt(0(),x)
Number of SCCs: 3, DPs: 4
  SCC { #1 }
POLO(Sum)... succeeded.
      1 	w: 0
      ifa	w: 0
      s 	w: x1 + 1
      #lt	w: 0
      #help	w: 0
      #ifb	w: 0
      false	w: 0
      logZeroError	w: 0
      #half	w: x1
      true	w: 0
      half	w: 0
      0 	w: 0
      #ifa	w: 0
      logarithm	w: 0
      #logarithm	w: 0
      help	w: 0
      ifb	w: 0
      lt	w: 0
    USABLE RULES: { }
    Removed DPs: #1
Number of SCCs: 2, DPs: 3
  SCC { #5 }
POLO(Sum)... succeeded.
      1 	w: 0
      ifa	w: 0
      s 	w: x1 + 1
      #lt	w: x2
      #help	w: 0
      #ifb	w: 0
      false	w: 0
      logZeroError	w: 0
      #half	w: 0
      true	w: 0
      half	w: 0
      0 	w: 0
      #ifa	w: 0
      logarithm	w: 0
      #logarithm	w: 0
      help	w: 0
      ifb	w: 0
      lt	w: 0
    USABLE RULES: { }
    Removed DPs: #5
Number of SCCs: 1, DPs: 2
  SCC { #2 #6 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
      1 	w: 0
      ifa	w: max(x2 - 1, 0)
      s 	w: max(x1 + 3, 0)
      #lt	w: 0
      #help	w: max(x1 + 3, 0)
      #ifb	w: max(x1 + 1, x2 + 2, 0)
      false	w: 1
      logZeroError	w: 0
      #half	w: 0
      true	w: 3
      half	w: max(x1 - 2, 0)
      0 	w: 0
      #ifa	w: 0
      logarithm	w: max(x1 - 1, 0)
      #logarithm	w: 0
      help	w: 0
      ifb	w: max(x2 - 1, 0)
      lt	w: max(x2 + 1, 0)
    USABLE RULES: { 1..3 10..12 }
    Removed DPs: #2 #6
Number of SCCs: 0, DPs: 0