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


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YES

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

Proof:
 String Reversal Processor:
  b(a(a(x1))) -> a(a(a(b(x1))))
  a(b(a(b(x1)))) -> b(b(a(x1)))
  DP Processor:
   DPs:
    b#(a(a(x1))) -> b#(x1)
    b#(a(a(x1))) -> a#(b(x1))
    b#(a(a(x1))) -> a#(a(b(x1)))
    b#(a(a(x1))) -> a#(a(a(b(x1))))
    a#(b(a(b(x1)))) -> a#(x1)
    a#(b(a(b(x1)))) -> b#(a(x1))
    a#(b(a(b(x1)))) -> b#(b(a(x1)))
   TRS:
    b(a(a(x1))) -> a(a(a(b(x1))))
    a(b(a(b(x1)))) -> b(b(a(x1)))
   TDG Processor:
    DPs:
     b#(a(a(x1))) -> b#(x1)
     b#(a(a(x1))) -> a#(b(x1))
     b#(a(a(x1))) -> a#(a(b(x1)))
     b#(a(a(x1))) -> a#(a(a(b(x1))))
     a#(b(a(b(x1)))) -> a#(x1)
     a#(b(a(b(x1)))) -> b#(a(x1))
     a#(b(a(b(x1)))) -> b#(b(a(x1)))
    TRS:
     b(a(a(x1))) -> a(a(a(b(x1))))
     a(b(a(b(x1)))) -> b(b(a(x1)))
    graph:
     a#(b(a(b(x1)))) -> a#(x1) -> a#(b(a(b(x1)))) -> b#(b(a(x1)))
     a#(b(a(b(x1)))) -> a#(x1) -> a#(b(a(b(x1)))) -> b#(a(x1))
     a#(b(a(b(x1)))) -> a#(x1) -> a#(b(a(b(x1)))) -> a#(x1)
     a#(b(a(b(x1)))) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(a(a(b(x1))))
     a#(b(a(b(x1)))) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(a(b(x1)))
     a#(b(a(b(x1)))) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(x1))
     a#(b(a(b(x1)))) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(x1)
     a#(b(a(b(x1)))) -> b#(b(a(x1))) ->
     b#(a(a(x1))) -> a#(a(a(b(x1))))
     a#(b(a(b(x1)))) -> b#(b(a(x1))) -> b#(a(a(x1))) -> a#(a(b(x1)))
     a#(b(a(b(x1)))) -> b#(b(a(x1))) -> b#(a(a(x1))) -> a#(b(x1))
     a#(b(a(b(x1)))) -> b#(b(a(x1))) -> b#(a(a(x1))) -> b#(x1)
     b#(a(a(x1))) -> a#(a(a(b(x1)))) ->
     a#(b(a(b(x1)))) -> b#(b(a(x1)))
     b#(a(a(x1))) -> a#(a(a(b(x1)))) -> a#(b(a(b(x1)))) -> b#(a(x1))
     b#(a(a(x1))) -> a#(a(a(b(x1)))) -> a#(b(a(b(x1)))) -> a#(x1)
     b#(a(a(x1))) -> a#(a(b(x1))) -> a#(b(a(b(x1)))) -> b#(b(a(x1)))
     b#(a(a(x1))) -> a#(a(b(x1))) -> a#(b(a(b(x1)))) -> b#(a(x1))
     b#(a(a(x1))) -> a#(a(b(x1))) -> a#(b(a(b(x1)))) -> a#(x1)
     b#(a(a(x1))) -> a#(b(x1)) -> a#(b(a(b(x1)))) -> b#(b(a(x1)))
     b#(a(a(x1))) -> a#(b(x1)) -> a#(b(a(b(x1)))) -> b#(a(x1))
     b#(a(a(x1))) -> a#(b(x1)) -> a#(b(a(b(x1)))) -> a#(x1)
     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(a(b(x1))))
     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(b(x1)))
     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(b(x1))
     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(x1)
    Arctic Interpretation Processor:
     dimension: 1
     usable rules:
      b(a(a(x1))) -> a(a(a(b(x1))))
      a(b(a(b(x1)))) -> b(b(a(x1)))
     interpretation:
      [a#](x0) = x0,
      
      [b#](x0) = 8x0,
      
      [a](x0) = x0,
      
      [b](x0) = 8x0
     orientation:
      b#(a(a(x1))) = 8x1 >= 8x1 = b#(x1)
      
      b#(a(a(x1))) = 8x1 >= 8x1 = a#(b(x1))
      
      b#(a(a(x1))) = 8x1 >= 8x1 = a#(a(b(x1)))
      
      b#(a(a(x1))) = 8x1 >= 8x1 = a#(a(a(b(x1))))
      
      a#(b(a(b(x1)))) = 16x1 >= x1 = a#(x1)
      
      a#(b(a(b(x1)))) = 16x1 >= 8x1 = b#(a(x1))
      
      a#(b(a(b(x1)))) = 16x1 >= 16x1 = b#(b(a(x1)))
      
      b(a(a(x1))) = 8x1 >= 8x1 = a(a(a(b(x1))))
      
      a(b(a(b(x1)))) = 16x1 >= 16x1 = b(b(a(x1)))
     problem:
      DPs:
       b#(a(a(x1))) -> b#(x1)
       b#(a(a(x1))) -> a#(b(x1))
       b#(a(a(x1))) -> a#(a(b(x1)))
       b#(a(a(x1))) -> a#(a(a(b(x1))))
       a#(b(a(b(x1)))) -> b#(b(a(x1)))
      TRS:
       b(a(a(x1))) -> a(a(a(b(x1))))
       a(b(a(b(x1)))) -> b(b(a(x1)))
     Restore Modifier:
      DPs:
       b#(a(a(x1))) -> b#(x1)
       b#(a(a(x1))) -> a#(b(x1))
       b#(a(a(x1))) -> a#(a(b(x1)))
       b#(a(a(x1))) -> a#(a(a(b(x1))))
       a#(b(a(b(x1)))) -> b#(b(a(x1)))
      TRS:
       b(a(a(x1))) -> a(a(a(b(x1))))
       a(b(a(b(x1)))) -> b(b(a(x1)))
      EDG Processor:
       DPs:
        b#(a(a(x1))) -> b#(x1)
        b#(a(a(x1))) -> a#(b(x1))
        b#(a(a(x1))) -> a#(a(b(x1)))
        b#(a(a(x1))) -> a#(a(a(b(x1))))
        a#(b(a(b(x1)))) -> b#(b(a(x1)))
       TRS:
        b(a(a(x1))) -> a(a(a(b(x1))))
        a(b(a(b(x1)))) -> b(b(a(x1)))
       graph:
        a#(b(a(b(x1)))) -> b#(b(a(x1))) -> b#(a(a(x1))) -> b#(x1)
        a#(b(a(b(x1)))) -> b#(b(a(x1))) -> b#(a(a(x1))) -> a#(b(x1))
        a#(b(a(b(x1)))) -> b#(b(a(x1))) ->
        b#(a(a(x1))) -> a#(a(b(x1)))
        a#(b(a(b(x1)))) -> b#(b(a(x1))) ->
        b#(a(a(x1))) -> a#(a(a(b(x1))))
        b#(a(a(x1))) -> a#(a(a(b(x1)))) ->
        a#(b(a(b(x1)))) -> b#(b(a(x1)))
        b#(a(a(x1))) -> a#(a(b(x1))) -> a#(b(a(b(x1)))) -> b#(b(a(x1)))
        b#(a(a(x1))) -> a#(b(x1)) -> a#(b(a(b(x1)))) -> b#(b(a(x1)))
        b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(x1)
        b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(b(x1))
        b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(b(x1)))
        b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(a(b(x1))))
       Matrix Interpretation Processor: dim=1
        
        usable rules:
         b(a(a(x1))) -> a(a(a(b(x1))))
         a(b(a(b(x1)))) -> b(b(a(x1)))
        interpretation:
         [a#](x0) = 2x0 + 13/2,
         
         [b#](x0) = 3x0 + 1,
         
         [a](x0) = x0 + 4,
         
         [b](x0) = 3/2x0 + 1
        orientation:
         b#(a(a(x1))) = 3x1 + 25 >= 3x1 + 1 = b#(x1)
         
         b#(a(a(x1))) = 3x1 + 25 >= 3x1 + 17/2 = a#(b(x1))
         
         b#(a(a(x1))) = 3x1 + 25 >= 3x1 + 33/2 = a#(a(b(x1)))
         
         b#(a(a(x1))) = 3x1 + 25 >= 3x1 + 49/2 = a#(a(a(b(x1))))
         
         a#(b(a(b(x1)))) = 9/2x1 + 47/2 >= 9/2x1 + 22 = b#(b(a(x1)))
         
         b(a(a(x1))) = 3/2x1 + 13 >= 3/2x1 + 13 = a(a(a(b(x1))))
         
         a(b(a(b(x1)))) = 9/4x1 + 25/2 >= 9/4x1 + 23/2 = b(b(a(x1)))
        problem:
         DPs:
          
         TRS:
          b(a(a(x1))) -> a(a(a(b(x1))))
          a(b(a(b(x1)))) -> b(b(a(x1)))
        Qed