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

Proof:
 String Reversal Processor:
  strict:
   a(c(b(x1))) -> d(d(x1))
   b(x1) -> c(c(x1))
   a(a(x1)) -> a(b(c(a(x1))))
  weak:
   b(a(x1)) -> d(x1)
   d(x1) -> b(a(x1))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 0 1]     [0]
    [d](x0) = [0 0 0]x0 + [2]
              [0 0 0]     [0],
    
              [1 0 0]     [0]
    [b](x0) = [0 0 1]x0 + [2]
              [0 0 0]     [0],
    
              [1 0 0]  
    [c](x0) = [0 0 0]x0
              [0 2 0]  ,
    
              [1 0 1]     [0]
    [a](x0) = [0 0 0]x0 + [2]
              [0 0 0]     [0]
   orientation:
                  [1 0 2]     [4]    [1 0 1]     [0]           
    a(c(b(x1))) = [0 0 0]x1 + [2] >= [0 0 0]x1 + [2] = d(d(x1))
                  [0 0 0]     [0]    [0 0 0]     [0]           
    
            [1 0 0]     [0]    [1 0 0]             
    b(x1) = [0 0 1]x1 + [2] >= [0 0 0]x1 = c(c(x1))
            [0 0 0]     [0]    [0 0 0]             
    
               [1 0 1]     [0]    [1 0 1]     [0]                 
    a(a(x1)) = [0 0 0]x1 + [2] >= [0 0 0]x1 + [2] = a(b(c(a(x1))))
               [0 0 0]     [0]    [0 0 0]     [0]                 
    
               [1 0 1]     [0]    [1 0 1]     [0]        
    b(a(x1)) = [0 0 0]x1 + [2] >= [0 0 0]x1 + [2] = d(x1)
               [0 0 0]     [0]    [0 0 0]     [0]        
    
            [1 0 1]     [0]    [1 0 1]     [0]           
    d(x1) = [0 0 0]x1 + [2] >= [0 0 0]x1 + [2] = b(a(x1))
            [0 0 0]     [0]    [0 0 0]     [0]           
   problem:
    strict:
     b(x1) -> c(c(x1))
     a(a(x1)) -> a(b(c(a(x1))))
    weak:
     b(a(x1)) -> d(x1)
     d(x1) -> b(a(x1))
   Arctic Interpretation Processor:
    dimension: 2
    interpretation:
               [6 7]  
     [d](x0) = [6 7]x0,
     
               [3  -&]  
     [b](x0) = [2  0 ]x0,
     
               [1  -&]  
     [c](x0) = [-& -&]x0,
     
               [3 4]  
     [a](x0) = [6 7]x0
    orientation:
             [3  -&]      [2  -&]             
     b(x1) = [2  0 ]x1 >= [-& -&]x1 = c(c(x1))
     
                [10 11]      [10 11]                   
     a(a(x1)) = [13 14]x1 >= [13 14]x1 = a(b(c(a(x1))))
     
                [6 7]      [6 7]          
     b(a(x1)) = [6 7]x1 >= [6 7]x1 = d(x1)
     
             [6 7]      [6 7]             
     d(x1) = [6 7]x1 >= [6 7]x1 = b(a(x1))
    problem:
     strict:
      a(a(x1)) -> a(b(c(a(x1))))
     weak:
      b(a(x1)) -> d(x1)
      d(x1) -> b(a(x1))
    Arctic Interpretation Processor:
     dimension: 2
     interpretation:
                [0 3]  
      [d](x0) = [1 7]x0,
      
                  
      [b](x0) = x0,
      
                [0  1 ]  
      [c](x0) = [0  -&]x0,
      
                [0 3]  
      [a](x0) = [1 7]x0
     orientation:
                 [4  10]      [3  8 ]                   
      a(a(x1)) = [8  14]x1 >= [7  10]x1 = a(b(c(a(x1))))
      
                 [0 3]      [0 3]          
      b(a(x1)) = [1 7]x1 >= [1 7]x1 = d(x1)
      
              [0 3]      [0 3]             
      d(x1) = [1 7]x1 >= [1 7]x1 = b(a(x1))
     problem:
      strict:
       
      weak:
       b(a(x1)) -> d(x1)
       d(x1) -> b(a(x1))
     Qed