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