/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:
 c(c(c(b(x)))) -> a(1(),b(c(x)))
 b(c(b(c(x)))) -> a(0(),a(1(),x))
 a(0(),x) -> c(c(x))
 a(1(),x) -> c(b(x))

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
         [1]
   [0] = [0],
   
                 [3 0]     [2 1]     [1]
   [a](x0, x1) = [1 0]x0 + [1 1]x1 + [1],
   
         [0]
   [1] = [0],
   
             [1 1]     [1]
   [c](x0) = [1 0]x0 + [1],
   
             [1 1]  
   [b](x0) = [1 0]x0
  orientation:
                   [5 3]    [6]    [5 3]    [6]                 
   c(c(c(b(x)))) = [3 2]x + [4] >= [3 2]x + [4] = a(1(),b(c(x)))
   
                   [5 3]    [7]    [5 3]    [7]                  
   b(c(b(c(x)))) = [3 2]x + [4] >= [3 2]x + [4] = a(0(),a(1(),x))
   
              [2 1]    [4]    [2 1]    [3]          
   a(0(),x) = [1 1]x + [2] >= [1 1]x + [2] = c(c(x))
   
              [2 1]    [1]    [2 1]    [1]          
   a(1(),x) = [1 1]x + [1] >= [1 1]x + [1] = c(b(x))
  problem:
   c(c(c(b(x)))) -> a(1(),b(c(x)))
   b(c(b(c(x)))) -> a(0(),a(1(),x))
   a(1(),x) -> c(b(x))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
          [0]
    [0] = [0]
          [0],
    
                  [1 0 0]     [1 0 1]  
    [a](x0, x1) = [0 0 1]x0 + [0 0 0]x1
                  [0 0 0]     [0 1 0]  ,
    
          [0]
    [1] = [0]
          [1],
    
              [1 0 1]     [0]
    [c](x0) = [0 0 0]x0 + [1]
              [0 1 0]     [0],
    
                
    [b](x0) = x0
                
   orientation:
                    [1 1 1]    [1]    [1 1 1]    [0]                 
    c(c(c(b(x)))) = [0 0 0]x + [1] >= [0 0 0]x + [1] = a(1(),b(c(x)))
                    [0 0 0]    [1]    [0 0 0]    [1]                 
    
                    [1 1 1]    [0]    [1 1 1]    [0]                  
    b(c(b(c(x)))) = [0 0 0]x + [1] >= [0 0 0]x + [0] = a(0(),a(1(),x))
                    [0 0 0]    [1]    [0 0 0]    [1]                  
    
               [1 0 1]    [0]    [1 0 1]    [0]          
    a(1(),x) = [0 0 0]x + [1] >= [0 0 0]x + [1] = c(b(x))
               [0 1 0]    [0]    [0 1 0]    [0]          
   problem:
    b(c(b(c(x)))) -> a(0(),a(1(),x))
    a(1(),x) -> c(b(x))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
           [0]
     [0] = [0]
           [0],
     
                   [1 0 0]     [1 0 1]  
     [a](x0, x1) = [0 1 0]x0 + [1 0 0]x1
                   [0 0 0]     [0 1 0]  ,
     
           [0]
     [1] = [1]
           [0],
     
                    [0]
     [c](x0) = x0 + [1]
                    [0],
     
               [1 0 1]  
     [b](x0) = [1 0 0]x0
               [0 1 0]  
    orientation:
                     [1 1 1]    [1]    [1 1 1]    [0]                  
     b(c(b(c(x)))) = [1 0 1]x + [0] >= [1 0 1]x + [0] = a(0(),a(1(),x))
                     [1 0 0]    [1]    [1 0 0]    [1]                  
     
                [1 0 1]    [0]    [1 0 1]    [0]          
     a(1(),x) = [1 0 0]x + [1] >= [1 0 0]x + [1] = c(b(x))
                [0 1 0]    [0]    [0 1 0]    [0]          
    problem:
     a(1(),x) -> c(b(x))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                    [1 0 1]     [1 1 0]  
      [a](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                    [0 0 0]     [0 0 0]  ,
      
            [0]
      [1] = [0]
            [1],
      
                [1 0 1]  
      [c](x0) = [0 0 0]x0
                [0 0 0]  ,
      
                [1 0 0]  
      [b](x0) = [0 0 0]x0
                [0 1 0]  
     orientation:
                 [1 1 0]    [1]    [1 1 0]           
      a(1(),x) = [0 0 0]x + [0] >= [0 0 0]x = c(b(x))
                 [0 0 0]    [0]    [0 0 0]           
     problem:
      
     Qed