/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:
 half(0()) -> 0()
 half(s(0())) -> 0()
 half(s(s(x))) -> s(half(x))
 bits(0()) -> 0()
 bits(s(x)) -> s(bits(half(s(x))))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                [1 0 1]  
   [bits](x0) = [1 0 0]x0
                [1 0 1]  ,
   
             [1 0 0]  
   [s](x0) = [0 0 0]x0
             [0 0 1]  ,
   
                [1 0 0]  
   [half](x0) = [0 0 0]x0
                [0 0 1]  ,
   
         [0]
   [0] = [0]
         [1]
  orientation:
               [0]    [0]      
   half(0()) = [0] >= [0] = 0()
               [1]    [1]      
   
                  [0]    [0]      
   half(s(0())) = [0] >= [0] = 0()
                  [1]    [1]      
   
                   [1 0 0]     [1 0 0]              
   half(s(s(x))) = [0 0 0]x >= [0 0 0]x = s(half(x))
                   [0 0 1]     [0 0 1]              
   
               [1]    [0]      
   bits(0()) = [0] >= [0] = 0()
               [1]    [1]      
   
                [1 0 1]     [1 0 1]                       
   bits(s(x)) = [1 0 0]x >= [0 0 0]x = s(bits(half(s(x))))
                [1 0 1]     [1 0 1]                       
  problem:
   half(0()) -> 0()
   half(s(0())) -> 0()
   half(s(s(x))) -> s(half(x))
   bits(s(x)) -> s(bits(half(s(x))))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                 [1 0 0]  
    [bits](x0) = [0 0 0]x0
                 [0 0 0]  ,
    
              [1 1 0]  
    [s](x0) = [0 0 1]x0
              [0 1 0]  ,
    
                 [1 0 0]  
    [half](x0) = [0 1 1]x0
                 [0 1 1]  ,
    
          [0]
    [0] = [1]
          [0]
   orientation:
                [0]    [0]      
    half(0()) = [1] >= [1] = 0()
                [1]    [0]      
    
                   [1]    [0]      
    half(s(0())) = [1] >= [1] = 0()
                   [1]    [0]      
    
                    [1 1 1]     [1 1 1]              
    half(s(s(x))) = [0 1 1]x >= [0 1 1]x = s(half(x))
                    [0 1 1]     [0 1 1]              
    
                 [1 1 0]     [1 1 0]                       
    bits(s(x)) = [0 0 0]x >= [0 0 0]x = s(bits(half(s(x))))
                 [0 0 0]     [0 0 0]                       
   problem:
    half(0()) -> 0()
    half(s(s(x))) -> s(half(x))
    bits(s(x)) -> s(bits(half(s(x))))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                  [1 1 0]     [0]
     [bits](x0) = [1 0 1]x0 + [1]
                  [1 1 0]     [0],
     
               [1 0 0]     [1]
     [s](x0) = [1 0 0]x0 + [1]
               [1 0 0]     [0],
     
                  [1 0 0]  
     [half](x0) = [0 0 1]x0
                  [1 0 0]  ,
     
           [0]
     [0] = [0]
           [0]
    orientation:
                 [0]    [0]      
     half(0()) = [0] >= [0] = 0()
                 [0]    [0]      
     
                     [1 0 0]    [2]    [1 0 0]    [1]             
     half(s(s(x))) = [1 0 0]x + [1] >= [1 0 0]x + [1] = s(half(x))
                     [1 0 0]    [2]    [1 0 0]    [0]             
     
                  [2 0 0]    [2]    [2 0 0]    [2]                      
     bits(s(x)) = [2 0 0]x + [2] >= [2 0 0]x + [2] = s(bits(half(s(x))))
                  [2 0 0]    [2]    [2 0 0]    [1]                      
    problem:
     half(0()) -> 0()
     bits(s(x)) -> s(bits(half(s(x))))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                   [1 1 0]  
      [bits](x0) = [0 1 0]x0
                   [0 0 0]  ,
      
                [1 0 0]     [0]
      [s](x0) = [0 0 1]x0 + [1]
                [0 0 0]     [0],
      
                   [1 0 1]     [0]
      [half](x0) = [0 0 0]x0 + [0]
                   [0 0 0]     [1],
      
            [0]
      [0] = [0]
            [1]
     orientation:
                  [1]    [0]      
      half(0()) = [0] >= [0] = 0()
                  [1]    [1]      
      
                   [1 0 1]    [1]    [1 0 0]    [0]                      
      bits(s(x)) = [0 0 1]x + [1] >= [0 0 0]x + [1] = s(bits(half(s(x))))
                   [0 0 0]    [0]    [0 0 0]    [0]                      
     problem:
      
     Qed