/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:
 strict:
  b(c(a(x1))) -> d(d(x1))
  b(x1) -> c(c(x1))
  a(a(x1)) -> 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(x1)
  weak:
   b(a(x1)) -> d(x1)
   d(x1) -> b(a(x1))
  Matrix Interpretation Processor: dim=5
   
   interpretation:
              [1 0 0 0 1]     [0]
              [0 0 0 0 0]     [0]
    [d](x0) = [0 0 1 0 1]x0 + [1]
              [0 0 0 0 0]     [1]
              [0 0 0 0 0]     [0],
    
              [1 0 0 0 0]     [0]
              [0 0 0 0 0]     [0]
    [b](x0) = [0 0 1 0 1]x0 + [1]
              [0 0 0 0 0]     [1]
              [0 0 0 0 0]     [0],
    
              [1 0 0 0 0]  
              [0 0 1 0 0]  
    [c](x0) = [0 0 0 0 0]x0
              [0 0 0 0 0]  
              [0 0 1 1 0]  ,
    
              [1 0 0 0 1]     [0]
              [0 1 0 0 0]     [0]
    [a](x0) = [0 0 1 0 1]x0 + [0]
              [0 0 0 0 0]     [1]
              [0 0 0 0 0]     [0]
   orientation:
                  [1 0 1 0 1]     [2]    [1 0 0 0 1]     [0]           
                  [0 0 1 0 1]     [1]    [0 0 0 0 0]     [0]           
    a(c(b(x1))) = [0 0 1 0 1]x1 + [2] >= [0 0 1 0 1]x1 + [2] = d(d(x1))
                  [0 0 0 0 0]     [1]    [0 0 0 0 0]     [1]           
                  [0 0 0 0 0]     [0]    [0 0 0 0 0]     [0]           
    
            [1 0 0 0 0]     [0]    [1 0 0 0 0]             
            [0 0 0 0 0]     [0]    [0 0 0 0 0]             
    b(x1) = [0 0 1 0 1]x1 + [1] >= [0 0 0 0 0]x1 = c(c(x1))
            [0 0 0 0 0]     [1]    [0 0 0 0 0]             
            [0 0 0 0 0]     [0]    [0 0 0 0 0]             
    
               [1 0 0 0 1]     [0]    [1 0 0 0 1]     [0]        
               [0 1 0 0 0]     [0]    [0 1 0 0 0]     [0]        
    a(a(x1)) = [0 0 1 0 1]x1 + [0] >= [0 0 1 0 1]x1 + [0] = a(x1)
               [0 0 0 0 0]     [1]    [0 0 0 0 0]     [1]        
               [0 0 0 0 0]     [0]    [0 0 0 0 0]     [0]        
    
               [1 0 0 0 1]     [0]    [1 0 0 0 1]     [0]        
               [0 0 0 0 0]     [0]    [0 0 0 0 0]     [0]        
    b(a(x1)) = [0 0 1 0 1]x1 + [1] >= [0 0 1 0 1]x1 + [1] = d(x1)
               [0 0 0 0 0]     [1]    [0 0 0 0 0]     [1]        
               [0 0 0 0 0]     [0]    [0 0 0 0 0]     [0]        
    
            [1 0 0 0 1]     [0]    [1 0 0 0 1]     [0]           
            [0 0 0 0 0]     [0]    [0 0 0 0 0]     [0]           
    d(x1) = [0 0 1 0 1]x1 + [1] >= [0 0 1 0 1]x1 + [1] = b(a(x1))
            [0 0 0 0 0]     [1]    [0 0 0 0 0]     [1]           
            [0 0 0 0 0]     [0]    [0 0 0 0 0]     [0]           
   problem:
    strict:
     b(x1) -> c(c(x1))
     a(a(x1)) -> a(x1)
    weak:
     b(a(x1)) -> d(x1)
     d(x1) -> b(a(x1))
   Arctic Interpretation Processor:
    dimension: 2
    interpretation:
               [5 5]  
     [d](x0) = [6 5]x0,
     
               [5 2]  
     [b](x0) = [4 4]x0,
     
               [1 0]  
     [c](x0) = [2 2]x0,
     
               [0 0]  
     [a](x0) = [2 1]x0
    orientation:
             [5 2]      [2 2]             
     b(x1) = [4 4]x1 >= [4 4]x1 = c(c(x1))
     
                [2 1]      [0 0]          
     a(a(x1)) = [3 2]x1 >= [2 1]x1 = a(x1)
     
                [5 5]      [5 5]          
     b(a(x1)) = [6 5]x1 >= [6 5]x1 = d(x1)
     
             [5 5]      [5 5]             
     d(x1) = [6 5]x1 >= [6 5]x1 = b(a(x1))
    problem:
     strict:
      b(x1) -> c(c(x1))
     weak:
      b(a(x1)) -> d(x1)
      d(x1) -> b(a(x1))
    String Reversal Processor:
     strict:
      b(x1) -> c(c(x1))
     weak:
      a(b(x1)) -> d(x1)
      d(x1) -> a(b(x1))
     Arctic Interpretation Processor:
      dimension: 2
      interpretation:
                 [7 5]  
       [d](x0) = [4 2]x0,
       
                 [3 2]  
       [b](x0) = [4 2]x0,
       
                 [0 0]  
       [c](x0) = [0 0]x0,
       
                 [0  3 ]  
       [a](x0) = [-& 0 ]x0
      orientation:
               [3 2]      [0 0]             
       b(x1) = [4 2]x1 >= [0 0]x1 = c(c(x1))
       
                  [7 5]      [7 5]          
       a(b(x1)) = [4 2]x1 >= [4 2]x1 = d(x1)
       
               [7 5]      [7 5]             
       d(x1) = [4 2]x1 >= [4 2]x1 = a(b(x1))
      problem:
       strict:
        
       weak:
        a(b(x1)) -> d(x1)
        d(x1) -> a(b(x1))
      Qed