/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: app(nil(),l) -> l
    10: app(cons(x,l1),l2) -> cons(x,app(l1,l2))
    11: sum(nil()) -> 0()
    12: sum(cons(x,l)) -> +(x,sum(l))
    13: sum(app(l1,l2)) -> +(sum(l1),sum(l2))
    14: prod(nil()) -> s(0())
    15: prod(cons(x,l)) -> *(x,prod(l))
    16: prod(app(l1,l2)) -> *(prod(l1),prod(l2))
Number of strict rules: 16
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
   #1: #sum(app(l1,l2)) -> #+(sum(l1),sum(l2))
   #2: #sum(app(l1,l2)) -> #sum(l1)
   #3: #sum(app(l1,l2)) -> #sum(l2)
   #4: #sum(cons(x,l)) -> #+(x,sum(l))
   #5: #sum(cons(x,l)) -> #sum(l)
   #6: #*(s(x),s(y)) -> #+(*(x,y),+(x,y))
   #7: #*(s(x),s(y)) -> #*(x,y)
   #8: #*(s(x),s(y)) -> #+(x,y)
   #9: #app(cons(x,l1),l2) -> #app(l1,l2)
   #10: #prod(app(l1,l2)) -> #*(prod(l1),prod(l2))
   #11: #prod(app(l1,l2)) -> #prod(l1)
   #12: #prod(app(l1,l2)) -> #prod(l2)
   #13: #+(s(x),s(y)) -> #+(x,y)
   #14: #*(*(x,y),z) -> #*(x,*(y,z))
   #15: #*(*(x,y),z) -> #*(y,z)
   #16: #prod(cons(x,l)) -> #*(x,prod(l))
   #17: #prod(cons(x,l)) -> #prod(l)
   #18: #+(+(x,y),z) -> #+(x,+(y,z))
   #19: #+(+(x,y),z) -> #+(y,z)
Number of SCCs: 5, DPs: 13
  SCC { #9 }
POLO(Sum)... succeeded.
      prod	w: 0
      s 	w: 0
      #prod	w: 0
      #* 	w: 0
      sum	w: 0
      0 	w: 0
      nil	w: 0
      #app	w: x1
      cons	w: x2 + 1
      + 	w: 0
      #sum	w: 0
      #+ 	w: 0
      * 	w: 0
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #9
Number of SCCs: 4, DPs: 12
  SCC { #11 #12 #17 }
POLO(Sum)... succeeded.
      prod	w: 0
      s 	w: 0
      #prod	w: x1
      #* 	w: 0
      sum	w: 0
      0 	w: 0
      nil	w: 0
      #app	w: 0
      cons	w: x2 + 1
      + 	w: 0
      #sum	w: 0
      #+ 	w: 0
      * 	w: 0
      app	w: x1 + x2 + 1
    USABLE RULES: { }
    Removed DPs: #11 #12 #17
Number of SCCs: 3, DPs: 9
  SCC { #2 #3 #5 }
POLO(Sum)... succeeded.
      prod	w: 0
      s 	w: 0
      #prod	w: 0
      #* 	w: 0
      sum	w: 0
      0 	w: 0
      nil	w: 0
      #app	w: 0
      cons	w: x2 + 1
      + 	w: 0
      #sum	w: x1
      #+ 	w: 0
      * 	w: 0
      app	w: x1 + x2 + 1
    USABLE RULES: { }
    Removed DPs: #2 #3 #5
Number of SCCs: 2, DPs: 6
  SCC { #7 #14 #15 }
POLO(Sum)... succeeded.
      prod	w: 0
      s 	w: x1 + 1
      #prod	w: 0
      #* 	w: x1
      sum	w: 0
      0 	w: 1
      nil	w: 0
      #app	w: 0
      cons	w: 1
      + 	w: x1 + 1
      #sum	w: 0
      #+ 	w: 0
      * 	w: x1 + x2 + 1
      app	w: 1
    USABLE RULES: { }
    Removed DPs: #7 #14 #15
Number of SCCs: 1, DPs: 3
  SCC { #13 #18 #19 }
POLO(Sum)... succeeded.
      prod	w: 0
      s 	w: x1 + 2
      #prod	w: 0
      #* 	w: 0
      sum	w: 0
      0 	w: 1
      nil	w: 0
      #app	w: 0
      cons	w: 1
      + 	w: x1 + x2 + 1
      #sum	w: 0
      #+ 	w: x1
      * 	w: x1 + x2 + 1
      app	w: 1
    USABLE RULES: { }
    Removed DPs: #13 #18 #19
Number of SCCs: 0, DPs: 0