/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: isEmpty(cons(x,xs)) -> false()
    2: isEmpty(nil()) -> true()
    3: isZero(0()) -> true()
    4: isZero(s(x)) -> false()
    5: head(cons(x,xs)) -> x
    6: tail(cons(x,xs)) -> xs
    7: tail(nil()) -> nil()
    8: p(s(s(x))) -> s(p(s(x)))
    9: p(s(0())) -> 0()
    10: p(0()) -> 0()
    11: inc(s(x)) -> s(inc(x))
    12: inc(0()) -> s(0())
    13: sumList(xs,y) -> if(isEmpty(xs),isZero(head(xs)),y,tail(xs),cons(p(head(xs)),tail(xs)),inc(y))
    14: if(true(),b,y,xs,ys,x) -> y
    15: if(false(),true(),y,xs,ys,x) -> sumList(xs,y)
    16: if(false(),false(),y,xs,ys,x) -> sumList(ys,x)
    17: sum(xs) -> sumList(xs,0())
Number of strict rules: 17
Direct POLO(bPol) ... failed.
Uncurrying p
1: isEmpty(cons(x,xs)) -> false()
2: isEmpty(nil()) -> true()
3: isZero(0()) -> true()
4: isZero(s(x)) -> false()
5: head(cons(x,xs)) -> x
6: tail(cons(x,xs)) -> xs
7: tail(nil()) -> nil()
8: p^1_s(s(x)) -> s(p^1_s(x))
9: p^1_s(0()) -> 0()
10: p^1_0() -> 0()
11: inc(s(x)) -> s(inc(x))
12: inc(0()) -> s(0())
13: sumList(xs,y) -> if(isEmpty(xs),isZero(head(xs)),y,tail(xs),cons(p(head(xs)),tail(xs)),inc(y))
14: if(true(),b,y,xs,ys,x) -> y
15: if(false(),true(),y,xs,ys,x) -> sumList(xs,y)
16: if(false(),false(),y,xs,ys,x) -> sumList(ys,x)
17: sum(xs) -> sumList(xs,0())
18: p(0()) ->= p^1_0()
19: p(s(_1)) ->= p^1_s(_1)
Number of strict rules: 17
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #sumList(xs,y) -> #if(isEmpty(xs),isZero(head(xs)),y,tail(xs),cons(p(head(xs)),tail(xs)),inc(y))
   #2: #sumList(xs,y) -> #isEmpty(xs)
   #3: #sumList(xs,y) -> #isZero(head(xs))
   #4: #sumList(xs,y) -> #head(xs)
   #5: #sumList(xs,y) -> #tail(xs)
   #6: #sumList(xs,y) -> #p(head(xs))
   #7: #sumList(xs,y) -> #head(xs)
   #8: #sumList(xs,y) -> #tail(xs)
   #9: #sumList(xs,y) -> #inc(y)
   #10: #inc(s(x)) -> #inc(x)
   #11: #sum(xs) -> #sumList(xs,0())
   #12: #p(s(_1)) ->? #p^1_s(_1)
   #13: #if(false(),false(),y,xs,ys,x) -> #sumList(ys,x)
   #14: #p^1_s(s(x)) -> #p^1_s(x)
   #15: #if(false(),true(),y,xs,ys,x) -> #sumList(xs,y)
   #16: #p(0()) ->? #p^1_0()
Number of SCCs: 3, DPs: 5
  SCC { #14 }
POLO(Sum)... succeeded.
      sumList	w: 0
      s 	w: x1 + 1
      #p^1_0	w: 0
      #isZero	w: 0
      #sumList	w: 0
      #p^1_s	w: x1
      #isEmpty	w: 0
      p^1_0	w: 0
      false	w: 0
      #head	w: 0
      isEmpty	w: 0
      p^1_s	w: 0
      #inc	w: 0
      #p 	w: 0
      inc	w: 0
      true	w: 0
      sum	w: 0
      p 	w: 0
      tail	w: 0
      0 	w: 0
      if	w: 0
      nil	w: 0
      #tail	w: 0
      head	w: 0
      cons	w: 0
      #if	w: 0
      isZero	w: 0
      #sum	w: 0
    USABLE RULES: { }
    Removed DPs: #14
Number of SCCs: 2, DPs: 4
  SCC { #10 }
POLO(Sum)... succeeded.
      sumList	w: 0
      s 	w: x1 + 1
      #p^1_0	w: 0
      #isZero	w: 0
      #sumList	w: 0
      #p^1_s	w: 0
      #isEmpty	w: 0
      p^1_0	w: 0
      false	w: 0
      #head	w: 0
      isEmpty	w: 0
      p^1_s	w: 0
      #inc	w: x1
      #p 	w: 0
      inc	w: 0
      true	w: 0
      sum	w: 0
      p 	w: 0
      tail	w: 0
      0 	w: 0
      if	w: 0
      nil	w: 0
      #tail	w: 0
      head	w: 0
      cons	w: 0
      #if	w: 0
      isZero	w: 0
      #sum	w: 0
    USABLE RULES: { }
    Removed DPs: #10
Number of SCCs: 1, DPs: 3
  SCC { #1 #13 #15 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
      sumList	w: 0
      s 	w: 4
      #p^1_0	w: 0
      #isZero	w: max(x1 - 1, 0)
      #sumList	w: max(x1 - 6, 0)
      #p^1_s	w: 0
      #isEmpty	w: max(x1 - 1, 0)
      p^1_0	w: 4
      false	w: 2
      #head	w: 0
      isEmpty	w: 1
      p^1_s	w: 4
      #inc	w: 0
      #p 	w: 0
      inc	w: max(x1, 0)
      true	w: 2
      sum	w: 0
      p 	w: max(x1, 0)
      tail	w: max(x1 - 6, 0)
      0 	w: 4
      if	w: max(x6 - 1, 0)
      nil	w: 0
      #tail	w: 0
      head	w: max(x1 - 4, 0)
      cons	w: max(x1 + 4, x2 + 6, 0)
      #if	w: max(x2 - 1, x4, x5 - 6, 0)
      isZero	w: max(x1 - 2, 0)
      #sum	w: 0
    USABLE RULES: { 3..12 18 19 }
    Removed DPs: #15
Number of SCCs: 1, DPs: 2
  SCC { #1 #13 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
      sumList	w: 0
      s 	w: max(x1 + 5, 0)
      #p^1_0	w: 0
      #isZero	w: max(x1 - 1, 0)
      #sumList	w: max(x1 - 2, 0)
      #p^1_s	w: 0
      #isEmpty	w: max(x1 - 1, 0)
      p^1_0	w: 0
      false	w: 6
      #head	w: 0
      isEmpty	w: 0
      p^1_s	w: max(x1 + 1, 0)
      #inc	w: 0
      #p 	w: 0
      inc	w: max(x1 - 1, 0)
      true	w: 1
      sum	w: 0
      p 	w: max(x1 - 4, 0)
      tail	w: 0
      0 	w: 0
      if	w: max(x6 - 1, 0)
      nil	w: 1
      #tail	w: 0
      head	w: max(x1 + 1, 0)
      cons	w: max(x1 - 1, 0)
      #if	w: max(x2 - 5, x5, 0)
      isZero	w: max(x1 + 1, 0)
      #sum	w: 0
    USABLE RULES: { 3..5 8..10 18 19 }
    Removed DPs: #13
Number of SCCs: 0, DPs: 0