/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: +(0(),y) -> y
    2: +(s(x),y) -> s(+(x,y))
    3: ++(nil(),ys) -> ys
    4: ++(:(x,xs),ys) -> :(x,++(xs,ys))
    5: sum(:(x,nil())) -> :(x,nil())
    6: sum(:(x,:(y,xs))) -> sum(:(+(x,y),xs))
    7: sum(++(xs,:(x,:(y,ys)))) -> sum(++(xs,sum(:(x,:(y,ys)))))
    8: -(x,0()) -> x
    9: -(0(),s(y)) -> 0()
    10: -(s(x),s(y)) -> -(x,y)
    11: quot(0(),s(y)) -> 0()
    12: quot(s(x),s(y)) -> s(quot(-(x,y),s(y)))
    13: length(nil()) -> 0()
    14: length(:(x,xs)) -> s(length(xs))
    15: hd(:(x,xs)) -> x
    16: avg(xs) -> quot(hd(sum(xs)),length(xs))
Number of strict rules: 16
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
   #1: #+(s(x),y) -> #+(x,y)
   #2: #sum(:(x,:(y,xs))) -> #sum(:(+(x,y),xs))
   #3: #sum(:(x,:(y,xs))) -> #+(x,y)
   #4: #quot(s(x),s(y)) -> #quot(-(x,y),s(y))
   #5: #quot(s(x),s(y)) -> #-(x,y)
   #6: #length(:(x,xs)) -> #length(xs)
   #7: #sum(++(xs,:(x,:(y,ys)))) -> #sum(++(xs,sum(:(x,:(y,ys)))))
   #8: #sum(++(xs,:(x,:(y,ys)))) -> #++(xs,sum(:(x,:(y,ys))))
   #9: #sum(++(xs,:(x,:(y,ys)))) -> #sum(:(x,:(y,ys)))
   #10: #-(s(x),s(y)) -> #-(x,y)
   #11: #avg(xs) -> #quot(hd(sum(xs)),length(xs))
   #12: #avg(xs) -> #hd(sum(xs))
   #13: #avg(xs) -> #sum(xs)
   #14: #avg(xs) -> #length(xs)
   #15: #++(:(x,xs),ys) -> #++(xs,ys)
Number of SCCs: 7, DPs: 7
  SCC { #6 }
POLO(Sum)... succeeded.
      hd	w: 0
      s 	w: 0
      ++	w: 0
      sum	w: 0
      #avg	w: 0
      0 	w: 0
      quot	w: 0
      : 	w: x2 + 1
      #++	w: 0
      nil	w: 0
      - 	w: 0
      avg	w: 0
      #hd	w: 0
      #- 	w: 0
      #quot	w: 0
      + 	w: 0
      #sum	w: 0
      length	w: 0
      #length	w: x1
      #+ 	w: 0
    USABLE RULES: { }
    Removed DPs: #6
Number of SCCs: 6, DPs: 6
  SCC { #1 }
POLO(Sum)... succeeded.
      hd	w: 0
      s 	w: x1 + 1
      ++	w: 0
      sum	w: 0
      #avg	w: 0
      0 	w: 0
      quot	w: 0
      : 	w: 1
      #++	w: 0
      nil	w: 0
      - 	w: 0
      avg	w: 0
      #hd	w: 0
      #- 	w: 0
      #quot	w: 0
      + 	w: 0
      #sum	w: 0
      length	w: 0
      #length	w: 0
      #+ 	w: x1
    USABLE RULES: { }
    Removed DPs: #1
Number of SCCs: 5, DPs: 5
  SCC { #10 }
POLO(Sum)... succeeded.
      hd	w: 0
      s 	w: x1 + 1
      ++	w: 0
      sum	w: 0
      #avg	w: 0
      0 	w: 0
      quot	w: 0
      : 	w: 1
      #++	w: 0
      nil	w: 0
      - 	w: 0
      avg	w: 0
      #hd	w: 0
      #- 	w: x2
      #quot	w: 0
      + 	w: 0
      #sum	w: 0
      length	w: 0
      #length	w: 0
      #+ 	w: 0
    USABLE RULES: { }
    Removed DPs: #10
Number of SCCs: 4, DPs: 4
  SCC { #15 }
POLO(Sum)... succeeded.
      hd	w: 0
      s 	w: 1
      ++	w: 0
      sum	w: 0
      #avg	w: 0
      0 	w: 0
      quot	w: 0
      : 	w: x2 + 1
      #++	w: x1
      nil	w: 0
      - 	w: 0
      avg	w: 0
      #hd	w: 0
      #- 	w: 0
      #quot	w: 0
      + 	w: 0
      #sum	w: 0
      length	w: 0
      #length	w: 0
      #+ 	w: 0
    USABLE RULES: { }
    Removed DPs: #15
Number of SCCs: 3, DPs: 3
  SCC { #4 }
POLO(Sum)... succeeded.
      hd	w: 0
      s 	w: x1 + 2
      ++	w: 0
      sum	w: 0
      #avg	w: 0
      0 	w: 1
      quot	w: 0
      : 	w: 1
      #++	w: 0
      nil	w: 0
      - 	w: x1 + 1
      avg	w: 0
      #hd	w: 0
      #- 	w: 0
      #quot	w: x1
      + 	w: 0
      #sum	w: 0
      length	w: 0
      #length	w: 0
      #+ 	w: 0
    USABLE RULES: { 8..10 }
    Removed DPs: #4
Number of SCCs: 2, DPs: 2
  SCC { #2 }
POLO(Sum)... succeeded.
      hd	w: 0
      s 	w: x1 + 2
      ++	w: 0
      sum	w: 0
      #avg	w: 0
      0 	w: 1
      quot	w: 0
      : 	w: x1 + x2 + 2
      #++	w: 0
      nil	w: 0
      - 	w: x1 + 1
      avg	w: 0
      #hd	w: 0
      #- 	w: 0
      #quot	w: x1
      + 	w: x1 + x2 + 1
      #sum	w: x1
      length	w: 0
      #length	w: 0
      #+ 	w: 0
    USABLE RULES: { 1 2 8..10 }
    Removed DPs: #2
Number of SCCs: 1, DPs: 1
  SCC { #7 }
POLO(Sum)... succeeded.
      hd	w: 0
      s 	w: x1 + 2
      ++	w: x1 + x2 + 1
      sum	w: 3
      #avg	w: 0
      0 	w: 1
      quot	w: 0
      : 	w: x2 + 2
      #++	w: 0
      nil	w: 1
      - 	w: x1 + 1
      avg	w: 0
      #hd	w: 0
      #- 	w: 0
      #quot	w: x1
      + 	w: x1 + x2 + 1
      #sum	w: x1
      length	w: 0
      #length	w: 0
      #+ 	w: 0
    USABLE RULES: { 1..6 8..10 }
    Removed DPs: #7
Number of SCCs: 0, DPs: 0