/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:
 strict:
  a(b(b(x1))) -> c(b(a(x1)))
  a(a(c(x1))) -> b(c(a(x1)))
  a(a(b(x1))) -> a(c(b(x1)))
 weak:
  b(a(a(x1))) -> c(a(a(x1)))
  c(b(b(x1))) -> b(a(a(x1)))
  c(b(a(x1))) -> b(c(c(x1)))

Proof:
 String Reversal Processor:
  strict:
   b(b(a(x1))) -> a(b(c(x1)))
   c(a(a(x1))) -> a(c(b(x1)))
   b(a(a(x1))) -> b(c(a(x1)))
  weak:
   a(a(b(x1))) -> a(a(c(x1)))
   b(b(c(x1))) -> a(a(b(x1)))
   a(b(c(x1))) -> c(c(b(x1)))
  Arctic Interpretation Processor:
   dimension: 2
   interpretation:
              [0  1 ]  
    [a](x0) = [-& -&]x0,
    
              [0 1]  
    [b](x0) = [0 0]x0,
    
              [0  0 ]  
    [c](x0) = [-& -&]x0
   orientation:
                  [1 2]      [1  1 ]                
    b(b(a(x1))) = [0 1]x1 >= [-& -&]x1 = a(b(c(x1)))
    
                  [0  1 ]      [0  1 ]                
    c(a(a(x1))) = [-& -&]x1 >= [-& -&]x1 = a(c(b(x1)))
    
                  [0 1]      [0 1]                
    b(a(a(x1))) = [0 1]x1 >= [0 1]x1 = b(c(a(x1)))
    
                  [1  1 ]      [0  0 ]                
    a(a(b(x1))) = [-& -&]x1 >= [-& -&]x1 = a(a(c(x1)))
    
                  [1 1]      [1  1 ]                
    b(b(c(x1))) = [0 0]x1 >= [-& -&]x1 = a(a(b(x1)))
    
                  [1  1 ]      [0  1 ]                
    a(b(c(x1))) = [-& -&]x1 >= [-& -&]x1 = c(c(b(x1)))
   problem:
    strict:
     b(b(a(x1))) -> a(b(c(x1)))
     c(a(a(x1))) -> a(c(b(x1)))
     b(a(a(x1))) -> b(c(a(x1)))
    weak:
     b(b(c(x1))) -> a(a(b(x1)))
     a(b(c(x1))) -> c(c(b(x1)))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [a](x0) = 2x0 + 8,
     
     [b](x0) = 2x0,
     
     [c](x0) = 2x0 + 6
    orientation:
     b(b(a(x1))) = 8x1 + 32 >= 8x1 + 32 = a(b(c(x1)))
     
     c(a(a(x1))) = 8x1 + 54 >= 8x1 + 20 = a(c(b(x1)))
     
     b(a(a(x1))) = 8x1 + 48 >= 8x1 + 44 = b(c(a(x1)))
     
     b(b(c(x1))) = 8x1 + 24 >= 8x1 + 24 = a(a(b(x1)))
     
     a(b(c(x1))) = 8x1 + 32 >= 8x1 + 18 = c(c(b(x1)))
    problem:
     strict:
      b(b(a(x1))) -> a(b(c(x1)))
     weak:
      b(b(c(x1))) -> a(a(b(x1)))
    RT Transformation Processor:
     b(b(a(x1))) -> a(b(c(x1)))
     b(b(c(x1))) -> a(a(b(x1)))
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                 [1 0 0]     [0]
       [a](x0) = [0 1 0]x0 + [0]
                 [1 0 0]     [1],
       
                 [1 1 0]     [0]
       [b](x0) = [0 0 0]x0 + [1]
                 [1 1 0]     [0],
       
                 [1 1 0]  
       [c](x0) = [0 0 0]x0
                 [0 0 0]  
      orientation:
                     [1 1 0]     [1]    [1 1 0]     [0]              
       b(b(a(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(b(c(x1)))
                     [1 1 0]     [1]    [1 1 0]     [1]              
       
                     [1 1 0]     [1]    [1 1 0]     [0]              
       b(b(c(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(a(b(x1)))
                     [1 1 0]     [1]    [1 1 0]     [1]              
      problem:
       
      Qed