/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 a(a(x1)) -> b(a(c(b(x1))))
 b(b(x1)) -> a(a(x1))
 c(a(x1)) -> x1

Proof:
 DP Processor:
  DPs:
   a#(a(x1)) -> b#(x1)
   a#(a(x1)) -> c#(b(x1))
   a#(a(x1)) -> a#(c(b(x1)))
   a#(a(x1)) -> b#(a(c(b(x1))))
   b#(b(x1)) -> a#(x1)
   b#(b(x1)) -> a#(a(x1))
  TRS:
   a(a(x1)) -> b(a(c(b(x1))))
   b(b(x1)) -> a(a(x1))
   c(a(x1)) -> x1
  TDG Processor:
   DPs:
    a#(a(x1)) -> b#(x1)
    a#(a(x1)) -> c#(b(x1))
    a#(a(x1)) -> a#(c(b(x1)))
    a#(a(x1)) -> b#(a(c(b(x1))))
    b#(b(x1)) -> a#(x1)
    b#(b(x1)) -> a#(a(x1))
   TRS:
    a(a(x1)) -> b(a(c(b(x1))))
    b(b(x1)) -> a(a(x1))
    c(a(x1)) -> x1
   graph:
    b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> b#(a(c(b(x1))))
    b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> a#(c(b(x1)))
    b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> c#(b(x1))
    b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> b#(x1)
    b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(c(b(x1))))
    b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(c(b(x1)))
    b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(b(x1))
    b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1)
    a#(a(x1)) -> b#(a(c(b(x1)))) -> b#(b(x1)) -> a#(a(x1))
    a#(a(x1)) -> b#(a(c(b(x1)))) -> b#(b(x1)) -> a#(x1)
    a#(a(x1)) -> b#(x1) -> b#(b(x1)) -> a#(a(x1))
    a#(a(x1)) -> b#(x1) -> b#(b(x1)) -> a#(x1)
    a#(a(x1)) -> a#(c(b(x1))) -> a#(a(x1)) -> b#(a(c(b(x1))))
    a#(a(x1)) -> a#(c(b(x1))) -> a#(a(x1)) -> a#(c(b(x1)))
    a#(a(x1)) -> a#(c(b(x1))) -> a#(a(x1)) -> c#(b(x1))
    a#(a(x1)) -> a#(c(b(x1))) -> a#(a(x1)) -> b#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 5
    #arcs: 16/36
    DPs:
     b#(b(x1)) -> a#(a(x1))
     a#(a(x1)) -> b#(x1)
     b#(b(x1)) -> a#(x1)
     a#(a(x1)) -> a#(c(b(x1)))
     a#(a(x1)) -> b#(a(c(b(x1))))
    TRS:
     a(a(x1)) -> b(a(c(b(x1))))
     b(b(x1)) -> a(a(x1))
     c(a(x1)) -> x1
    Arctic Interpretation Processor:
     dimension: 1
     usable rules:
      a(a(x1)) -> b(a(c(b(x1))))
      b(b(x1)) -> a(a(x1))
      c(a(x1)) -> x1
     interpretation:
      [b#](x0) = 8x0 + -16,
      
      [a#](x0) = 8x0 + 0,
      
      [c](x0) = -1x0 + 1,
      
      [b](x0) = 1x0 + 8,
      
      [a](x0) = 1x0 + 8
     orientation:
      b#(b(x1)) = 9x1 + 16 >= 9x1 + 16 = a#(a(x1))
      
      a#(a(x1)) = 9x1 + 16 >= 8x1 + -16 = b#(x1)
      
      b#(b(x1)) = 9x1 + 16 >= 8x1 + 0 = a#(x1)
      
      a#(a(x1)) = 9x1 + 16 >= 8x1 + 15 = a#(c(b(x1)))
      
      a#(a(x1)) = 9x1 + 16 >= 9x1 + 16 = b#(a(c(b(x1))))
      
      a(a(x1)) = 2x1 + 9 >= 2x1 + 9 = b(a(c(b(x1))))
      
      b(b(x1)) = 2x1 + 9 >= 2x1 + 9 = a(a(x1))
      
      c(a(x1)) = x1 + 7 >= x1 = x1
     problem:
      DPs:
       b#(b(x1)) -> a#(a(x1))
       a#(a(x1)) -> b#(a(c(b(x1))))
      TRS:
       a(a(x1)) -> b(a(c(b(x1))))
       b(b(x1)) -> a(a(x1))
       c(a(x1)) -> x1
     Restore Modifier:
      DPs:
       b#(b(x1)) -> a#(a(x1))
       a#(a(x1)) -> b#(a(c(b(x1))))
      TRS:
       a(a(x1)) -> b(a(c(b(x1))))
       b(b(x1)) -> a(a(x1))
       c(a(x1)) -> x1
      EDG Processor:
       DPs:
        b#(b(x1)) -> a#(a(x1))
        a#(a(x1)) -> b#(a(c(b(x1))))
       TRS:
        a(a(x1)) -> b(a(c(b(x1))))
        b(b(x1)) -> a(a(x1))
        c(a(x1)) -> x1
       graph:
        b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> b#(a(c(b(x1))))
        a#(a(x1)) -> b#(a(c(b(x1)))) -> b#(b(x1)) -> a#(a(x1))
       Arctic Interpretation Processor:
        dimension: 3
        usable rules:
         a(a(x1)) -> b(a(c(b(x1))))
         b(b(x1)) -> a(a(x1))
         c(a(x1)) -> x1
        interpretation:
         [b#](x0) = [-& 0  0 ]x0 + [0],
         
         [a#](x0) = [0 0 0]x0 + [0],
         
                   [-& 0  -&]     [0]
         [c](x0) = [-& 0  -&]x0 + [0]
                   [-& 0  -&]     [0],
         
                   [0  0  1 ]     [0]
         [b](x0) = [-& 0  0 ]x0 + [0]
                   [0  1  1 ]     [1],
         
                   [0  1  1 ]     [1]
         [a](x0) = [0  0  0 ]x0 + [0]
                   [0  0  -&]     [0]
        orientation:
         b#(b(x1)) = [0 1 1]x1 + [1] >= [0 1 1]x1 + [1] = a#(a(x1))
         
         a#(a(x1)) = [0 1 1]x1 + [1] >= [-& 0  0 ]x1 + [0] = b#(a(c(b(x1))))
         
                    [1 1 1]     [1]    [-& 1  1 ]     [1]                 
         a(a(x1)) = [0 1 1]x1 + [1] >= [-& 0  0 ]x1 + [0] = b(a(c(b(x1))))
                    [0 1 1]     [1]    [-& 1  1 ]     [1]                 
         
                    [1 2 2]     [2]    [1 1 1]     [1]           
         b(b(x1)) = [0 1 1]x1 + [1] >= [0 1 1]x1 + [1] = a(a(x1))
                    [1 2 2]     [2]    [0 1 1]     [1]           
         
                    [0 0 0]     [0]           
         c(a(x1)) = [0 0 0]x1 + [0] >= x1 = x1
                    [0 0 0]     [0]           
        problem:
         DPs:
          b#(b(x1)) -> a#(a(x1))
         TRS:
          a(a(x1)) -> b(a(c(b(x1))))
          b(b(x1)) -> a(a(x1))
          c(a(x1)) -> x1
        Restore Modifier:
         DPs:
          b#(b(x1)) -> a#(a(x1))
         TRS:
          a(a(x1)) -> b(a(c(b(x1))))
          b(b(x1)) -> a(a(x1))
          c(a(x1)) -> x1
         EDG Processor:
          DPs:
           b#(b(x1)) -> a#(a(x1))
          TRS:
           a(a(x1)) -> b(a(c(b(x1))))
           b(b(x1)) -> a(a(x1))
           c(a(x1)) -> x1
          graph:
           
          SCC Processor:
           #sccs: 0
           #rules: 0
           #arcs: 0/1