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


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


YES
Input TRS:
    1: log(s(x1)) -> s(log(half(s(x1))))
    2: half(0(x1)) -> 0(s(s(half(x1))))
    3: half(s(0(x1))) -> 0(x1)
    4: half(s(s(x1))) -> s(half(p(s(s(x1)))))
    5: half(half(s(s(s(s(x1)))))) -> s(s(half(half(x1))))
    6: p(s(s(s(x1)))) -> s(p(s(s(x1))))
    7: s(s(p(s(x1)))) -> s(s(x1))
    8: 0(x1) -> x1
Number of strict rules: 8
Direct POLO(bPol) ... removes: 8
      s 	w: x1
      half	w: x1
      p 	w: x1
      log	w: x1 + 1
      0 	w: x1 + 1
Number of strict rules: 7
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
   #1: #half(0(x1)) -> #s(s(half(x1)))
   #2: #half(0(x1)) -> #s(half(x1))
   #3: #half(0(x1)) -> #half(x1)
   #4: #p(s(s(s(x1)))) -> #s(p(s(s(x1))))
   #5: #p(s(s(s(x1)))) -> #p(s(s(x1)))
   #6: #s(s(p(s(x1)))) -> #s(s(x1))
   #7: #half(half(s(s(s(s(x1)))))) -> #s(s(half(half(x1))))
   #8: #half(half(s(s(s(s(x1)))))) -> #s(half(half(x1)))
   #9: #half(half(s(s(s(s(x1)))))) -> #half(half(x1))
   #10: #half(half(s(s(s(s(x1)))))) -> #half(x1)
   #11: #log(s(x1)) -> #s(log(half(s(x1))))
   #12: #log(s(x1)) -> #log(half(s(x1)))
   #13: #log(s(x1)) -> #half(s(x1))
   #14: #half(s(s(x1))) -> #s(half(p(s(s(x1)))))
   #15: #half(s(s(x1))) -> #half(p(s(s(x1))))
   #16: #half(s(s(x1))) -> #p(s(s(x1)))
Number of SCCs: 5, DPs: 7
  SCC { #12 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
      s 	w: max(x1 + 3, 0)
      #log	w: max(x1 - 2, 0)
      #half	w: max(x1 - 1, 0)
      #p 	w: 0
      half	w: max(x1 - 2, 0)
      p 	w: max(x1 - 3, 0)
      log	w: max(x1 - 1, 0)
      0 	w: max(x1 - 1, 0)
      #s 	w: 0
    USABLE RULES: { 3 4 6 7 }
    Removed DPs: #12
Number of SCCs: 4, DPs: 6
  SCC { #6 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      #log	w: 0
      #half	w: 0
      #p 	w: 0
      half	w: 1
      p 	w: x1
      log	w: 0
      0 	w: x1 + 2
      #s 	w: x1
    USABLE RULES: { 7 }
    Removed DPs: #6
Number of SCCs: 3, DPs: 5
  SCC { #15 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
      s 	w: max(x1 + 3, 0)
      #log	w: max(x1 - 2, 0)
      #half	w: max(x1 + 4, 0)
      #p 	w: 0
      half	w: max(x1 - 2, 0)
      p 	w: max(x1 - 3, 0)
      log	w: max(x1 - 1, 0)
      0 	w: max(x1 - 1, 0)
      #s 	w: 0
    USABLE RULES: { 3 4 6 7 }
    Removed DPs: #15
Number of SCCs: 2, DPs: 4
  SCC { #5 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      #log	w: 0
      #half	w: 0
      #p 	w: x1
      half	w: 1
      p 	w: x1
      log	w: 0
      0 	w: x1 + 2
      #s 	w: 0
    USABLE RULES: { 6 7 }
    Removed DPs: #5
Number of SCCs: 1, DPs: 3
  SCC { #3 #9 #10 }
POLO(Sum)... succeeded.
      s 	w: x1
      #log	w: 0
      #half	w: x1
      #p 	w: x1
      half	w: x1 + 1
      p 	w: x1
      log	w: 0
      0 	w: x1 + 2
      #s 	w: 0
    USABLE RULES: { 2..7 }
    Removed DPs: #3 #10
Number of SCCs: 1, DPs: 1
  SCC { #9 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
      s 	w: max(x1 + 5, 0)
      #log	w: max(x1 - 2, 0)
      #half	w: max(x1 - 1, 0)
      #p 	w: 0
      half	w: max(x1 - 3, 0)
      p 	w: max(x1 - 5, 0)
      log	w: max(x1 - 1, 0)
      0 	w: 0
      #s 	w: 0
    USABLE RULES: { 2..7 }
    Removed DPs: #9
Number of SCCs: 0, DPs: 0