/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [b](x0) = x0 + 2,
   
   [a](x0) = x0
  orientation:
   a(b(a(a(x1)))) = x1 + 2 >= x1 = a(a(a(a(x1))))
   
   b(a(b(a(x1)))) = x1 + 4 >= x1 + 4 = a(a(b(b(x1))))
   
   b(a(a(b(x1)))) = x1 + 4 >= x1 + 4 = b(a(b(a(x1))))
  problem:
   b(a(b(a(x1)))) -> a(a(b(b(x1))))
   b(a(a(b(x1)))) -> b(a(b(a(x1))))
  DP Processor:
   DPs:
    b#(a(b(a(x1)))) -> b#(x1)
    b#(a(b(a(x1)))) -> b#(b(x1))
    b#(a(a(b(x1)))) -> b#(a(x1))
    b#(a(a(b(x1)))) -> b#(a(b(a(x1))))
   TRS:
    b(a(b(a(x1)))) -> a(a(b(b(x1))))
    b(a(a(b(x1)))) -> b(a(b(a(x1))))
   KBO Processor:
    argument filtering:
     pi(a) = 0
     pi(b) = [0]
     pi(b#) = 0
    usable rules:
     b(a(b(a(x1)))) -> a(a(b(b(x1))))
     b(a(a(b(x1)))) -> b(a(b(a(x1))))
    weight function:
     w0 = 1
     w(b) = w(a) = 1
     w(b#) = 0
    precedence:
     b > a > b#
    problem:
     DPs:
      b#(a(b(a(x1)))) -> b#(b(x1))
      b#(a(a(b(x1)))) -> b#(a(b(a(x1))))
     TRS:
      b(a(b(a(x1)))) -> a(a(b(b(x1))))
      b(a(a(b(x1)))) -> b(a(b(a(x1))))
    Restore Modifier:
     DPs:
      b#(a(b(a(x1)))) -> b#(b(x1))
      b#(a(a(b(x1)))) -> b#(a(b(a(x1))))
     TRS:
      b(a(b(a(x1)))) -> a(a(b(b(x1))))
      b(a(a(b(x1)))) -> b(a(b(a(x1))))
     Arctic Interpretation Processor:
      dimension: 1
      usable rules:
       b(a(b(a(x1)))) -> a(a(b(b(x1))))
       b(a(a(b(x1)))) -> b(a(b(a(x1))))
      interpretation:
       [b](x0) = x0,
       
       [a](x0) = 1x0,
       
       [b#](x0) = x0
      orientation:
       b#(a(b(a(x1)))) = 2x1 >= x1 = b#(b(x1))
       
       b#(a(a(b(x1)))) = 2x1 >= 2x1 = b#(a(b(a(x1))))
       
       b(a(b(a(x1)))) = 2x1 >= 2x1 = a(a(b(b(x1))))
       
       b(a(a(b(x1)))) = 2x1 >= 2x1 = b(a(b(a(x1))))
      problem:
       DPs:
        b#(a(a(b(x1)))) -> b#(a(b(a(x1))))
       TRS:
        b(a(b(a(x1)))) -> a(a(b(b(x1))))
        b(a(a(b(x1)))) -> b(a(b(a(x1))))
      Restore Modifier:
       DPs:
        b#(a(a(b(x1)))) -> b#(a(b(a(x1))))
       TRS:
        b(a(b(a(x1)))) -> a(a(b(b(x1))))
        b(a(a(b(x1)))) -> b(a(b(a(x1))))
       Matrix Interpretation Processor: dim=4
        
        interpretation:
                   [0]
                   [0]
         [b](x0) = [1]
                   [0],
         
                   [0 0 0 0]  
                   [0 0 0 0]  
         [a](x0) = [0 0 0 1]x0
                   [0 0 1 0]  ,
         
         [b#](x0) = [0 0 1 0]x0
        orientation:
         b#(a(a(b(x1)))) = [1] >= [0] = b#(a(b(a(x1))))
         
                          [0]    [0]                 
                          [0]    [0]                 
         b(a(b(a(x1)))) = [1] >= [1] = a(a(b(b(x1))))
                          [0]    [0]                 
         
                          [0]    [0]                 
                          [0]    [0]                 
         b(a(a(b(x1)))) = [1] >= [1] = b(a(b(a(x1))))
                          [0]    [0]                 
        problem:
         DPs:
          
         TRS:
          b(a(b(a(x1)))) -> a(a(b(b(x1))))
          b(a(a(b(x1)))) -> b(a(b(a(x1))))
        Qed