/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: p(0()) -> 0()
    2: p(s(x)) -> x
    3: le(0(),y) -> true()
    4: le(s(x),0()) -> false()
    5: le(s(x),s(y)) -> le(x,y)
    6: minus(x,y) -> if(le(x,y),x,y)
    7: if(true(),x,y) -> 0()
    8: if(false(),x,y) -> s(minus(p(x),y))
Number of strict rules: 8
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
   #1: #minus(x,y) -> #if(le(x,y),x,y)
   #2: #minus(x,y) -> #le(x,y)
   #3: #le(s(x),s(y)) -> #le(x,y)
   #4: #if(false(),x,y) -> #minus(p(x),y)
   #5: #if(false(),x,y) -> #p(x)
Number of SCCs: 2, DPs: 3
  SCC { #3 }
POLO(Sum)... succeeded.
      le	w: 0
      s 	w: x1 + 1
      #le	w: x1 + x2
      minus	w: 0
      false	w: 0
      #p 	w: 0
      true	w: 0
      p 	w: 0
      0 	w: 0
      if	w: 0
      #minus	w: 0
      #if	w: 0
    USABLE RULES: { }
    Removed DPs: #3
Number of SCCs: 1, DPs: 2
  SCC { #1 #4 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
      le	w: max(x1 + 1, 0)
      s 	w: max(x1 + 2, 0)
      #le	w: 0
      minus	w: max(x2 - 1, 0)
      false	w: 3
      #p 	w: max(x1 - 1, 0)
      true	w: 1
      p 	w: max(x1 - 1, 0)
      0 	w: 0
      if	w: 0
      #minus	w: max(x1, 0)
      #if	w: max(x1 - 2, x2, 0)
    USABLE RULES: { 1..5 }
    Removed DPs: #4
Number of SCCs: 0, DPs: 0