/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: +(x,0()) -> x
    2: +(0(),x) -> x
    3: +(s(x),s(y)) -> s(s(+(x,y)))
    4: +(+(x,y),z) -> +(x,+(y,z))
    5: *(x,0()) -> 0()
    6: *(0(),x) -> 0()
    7: *(s(x),s(y)) -> s(+(*(x,y),+(x,y)))
    8: *(*(x,y),z) -> *(x,*(y,z))
    9: sum(nil()) -> 0()
    10: sum(cons(x,l)) -> +(x,sum(l))
    11: prod(nil()) -> s(0())
    12: prod(cons(x,l)) -> *(x,prod(l))
Number of strict rules: 12
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
   #1: #prod(cons(x,l)) -> #*(x,prod(l))
   #2: #prod(cons(x,l)) -> #prod(l)
   #3: #*(s(x),s(y)) -> #+(*(x,y),+(x,y))
   #4: #*(s(x),s(y)) -> #*(x,y)
   #5: #*(s(x),s(y)) -> #+(x,y)
   #6: #sum(cons(x,l)) -> #+(x,sum(l))
   #7: #sum(cons(x,l)) -> #sum(l)
   #8: #+(s(x),s(y)) -> #+(x,y)
   #9: #*(*(x,y),z) -> #*(x,*(y,z))
   #10: #*(*(x,y),z) -> #*(y,z)
   #11: #+(+(x,y),z) -> #+(x,+(y,z))
   #12: #+(+(x,y),z) -> #+(y,z)
Number of SCCs: 4, DPs: 8
  SCC { #7 }
POLO(Sum)... succeeded.
      prod	w: 0
      s 	w: 0
      #prod	w: 0
      #* 	w: 0
      sum	w: 0
      0 	w: 0
      nil	w: 0
      cons	w: x2 + 1
      + 	w: 0
      #sum	w: x1
      #+ 	w: 0
      * 	w: 0
    USABLE RULES: { }
    Removed DPs: #7
Number of SCCs: 3, DPs: 7
  SCC { #2 }
POLO(Sum)... succeeded.
      prod	w: 0
      s 	w: 0
      #prod	w: x1
      #* 	w: 0
      sum	w: 0
      0 	w: 0
      nil	w: 0
      cons	w: x2 + 1
      + 	w: 0
      #sum	w: 0
      #+ 	w: 0
      * 	w: 0
    USABLE RULES: { }
    Removed DPs: #2
Number of SCCs: 2, DPs: 6
  SCC { #4 #9 #10 }
POLO(Sum)... succeeded.
      prod	w: 0
      s 	w: x1 + 1
      #prod	w: 0
      #* 	w: x1
      sum	w: 0
      0 	w: 1
      nil	w: 0
      cons	w: 1
      + 	w: x1 + x2 + 1
      #sum	w: 0
      #+ 	w: 0
      * 	w: x1 + x2 + 1
    USABLE RULES: { }
    Removed DPs: #4 #9 #10
Number of SCCs: 1, DPs: 3
  SCC { #8 #11 #12 }
POLO(Sum)... succeeded.
      prod	w: 0
      s 	w: x1 + 1
      #prod	w: 0
      #* 	w: 0
      sum	w: 0
      0 	w: 1
      nil	w: 0
      cons	w: 1
      + 	w: x1 + x2 + 1
      #sum	w: 0
      #+ 	w: x1
      * 	w: x1 + x2 + 1
    USABLE RULES: { 1..4 }
    Removed DPs: #8 #11 #12
Number of SCCs: 0, DPs: 0