/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: nonZero(0()) -> false()
    2: nonZero(s(x)) -> true()
    3: p(s(0())) -> 0()
    4: p(s(s(x))) -> s(p(s(x)))
    5: id_inc(x) -> x
    6: id_inc(x) -> s(x)
    7: random(x) -> rand(x,0())
    8: rand(x,y) -> if(nonZero(x),x,y)
    9: if(false(),x,y) -> y
    10: if(true(),x,y) -> rand(p(x),id_inc(y))
Number of strict rules: 10
Direct POLO(bPol) ... failed.
Uncurrying p
1: nonZero(0()) -> false()
2: nonZero(s(x)) -> true()
3: p^1_s(0()) -> 0()
4: p^1_s(s(x)) -> s(p^1_s(x))
5: id_inc(x) -> x
6: id_inc(x) -> s(x)
7: random(x) -> rand(x,0())
8: rand(x,y) -> if(nonZero(x),x,y)
9: if(false(),x,y) -> y
10: if(true(),x,y) -> rand(p(x),id_inc(y))
11: p(s(_1)) ->= p^1_s(_1)
Number of strict rules: 10
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #p(s(_1)) ->? #p^1_s(_1)
   #2: #random(x) -> #rand(x,0())
   #3: #if(true(),x,y) -> #rand(p(x),id_inc(y))
   #4: #if(true(),x,y) -> #p(x)
   #5: #if(true(),x,y) -> #id_inc(y)
   #6: #rand(x,y) -> #if(nonZero(x),x,y)
   #7: #rand(x,y) -> #nonZero(x)
   #8: #p^1_s(s(x)) -> #p^1_s(x)
Number of SCCs: 2, DPs: 3
  SCC { #8 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      #rand	w: 0
      nonZero	w: 0
      #p^1_s	w: x1
      false	w: 0
      p^1_s	w: 0
      #p 	w: 0
      true	w: 0
      #nonZero	w: 0
      rand	w: 0
      #id_inc	w: 0
      p 	w: 0
      0 	w: 0
      if	w: 0
      random	w: 0
      #random	w: 0
      id_inc	w: 0
      #if	w: 0
    USABLE RULES: { }
    Removed DPs: #8
Number of SCCs: 1, DPs: 2
  SCC { #3 #6 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
      s 	w: max(x1 + 6, 0)
      #rand	w: max(x1 + 4, 0)
      nonZero	w: max(x1 - 2, 0)
      #p^1_s	w: max(x1 - 1, 0)
      false	w: 0
      p^1_s	w: max(x1 + 1, 0)
      #p 	w: 0
      true	w: 2
      #nonZero	w: max(x1 - 1, 0)
      rand	w: max(x2 - 1, 0)
      #id_inc	w: max(x1 - 1, 0)
      p 	w: max(x1 - 5, 0)
      0 	w: 1
      if	w: max(x3 - 1, 0)
      random	w: max(x1 - 1, 0)
      #random	w: max(x1 - 1, 0)
      id_inc	w: 0
      #if	w: max(x1 + 3, x2 + 1, 0)
    USABLE RULES: { 1..4 11 }
    Removed DPs: #3 #6
Number of SCCs: 0, DPs: 0