/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:
 half(0()) -> 0()
 half(s(0())) -> 0()
 half(s(s(x))) -> s(half(x))
 lastbit(0()) -> 0()
 lastbit(s(0())) -> s(0())
 lastbit(s(s(x))) -> lastbit(x)
 conv(0()) -> cons(nil(),0())
 conv(s(x)) -> cons(conv(half(s(x))),lastbit(s(x)))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                    [1 0 0]     [1 0 0]  
   [cons](x0, x1) = [0 0 1]x0 + [0 0 0]x1
                    [0 0 0]     [0 0 0]  ,
   
           [0]
   [nil] = [0]
           [0],
   
                [1 0 1]  
   [conv](x0) = [1 0 0]x0
                [1 0 0]  ,
   
                   [1 0 0]     [0]
   [lastbit](x0) = [1 0 0]x0 + [1]
                   [1 1 0]     [1],
   
             [1 0 0]  
   [s](x0) = [0 0 1]x0
             [1 1 1]  ,
   
                [1 0 0]  
   [half](x0) = [0 0 1]x0
                [0 1 0]  ,
   
         [0]
   [0] = [1]
         [1]
  orientation:
               [0]    [0]      
   half(0()) = [1] >= [1] = 0()
               [1]    [1]      
   
                  [0]    [0]      
   half(s(0())) = [2] >= [1] = 0()
                  [1]    [1]      
   
                   [1 0 0]     [1 0 0]              
   half(s(s(x))) = [2 1 2]x >= [0 1 0]x = s(half(x))
                   [1 1 1]     [1 1 1]              
   
                  [0]    [0]      
   lastbit(0()) = [1] >= [1] = 0()
                  [2]    [1]      
   
                     [0]    [0]         
   lastbit(s(0())) = [1] >= [1] = s(0())
                     [2]    [2]         
   
                      [1 0 0]    [0]    [1 0 0]    [0]             
   lastbit(s(s(x))) = [1 0 0]x + [1] >= [1 0 0]x + [1] = lastbit(x)
                      [2 1 1]    [1]    [1 1 0]    [1]             
   
               [1]    [0]                  
   conv(0()) = [0] >= [0] = cons(nil(),0())
               [0]    [0]                  
   
                [2 1 1]     [2 0 1]                                        
   conv(s(x)) = [1 0 0]x >= [1 0 0]x = cons(conv(half(s(x))),lastbit(s(x)))
                [1 0 0]     [0 0 0]                                        
  problem:
   half(0()) -> 0()
   half(s(0())) -> 0()
   half(s(s(x))) -> s(half(x))
   lastbit(0()) -> 0()
   lastbit(s(0())) -> s(0())
   lastbit(s(s(x))) -> lastbit(x)
   conv(s(x)) -> cons(conv(half(s(x))),lastbit(s(x)))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                     [1 0 0]     [1 0 0]  
    [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                     [0 0 1]     [1 0 0]  ,
    
                 [1 1 0]     [1]
    [conv](x0) = [0 0 0]x0 + [1]
                 [1 1 0]     [0],
    
                    [1 0 0]  
    [lastbit](x0) = [1 0 0]x0
                    [0 1 0]  ,
    
              [1 0 0]     [1]
    [s](x0) = [1 1 1]x0 + [1]
              [0 1 1]     [0],
    
                 [1 0 0]  
    [half](x0) = [0 0 1]x0
                 [0 1 0]  ,
    
          [1]
    [0] = [0]
          [0]
   orientation:
                [1]    [1]      
    half(0()) = [0] >= [0] = 0()
                [0]    [0]      
    
                   [2]    [1]      
    half(s(0())) = [0] >= [0] = 0()
                   [2]    [0]      
    
                    [1 0 0]    [2]    [1 0 0]    [1]             
    half(s(s(x))) = [1 2 2]x + [1] >= [1 1 1]x + [1] = s(half(x))
                    [2 2 2]    [3]    [0 1 1]    [0]             
    
                   [1]    [1]      
    lastbit(0()) = [1] >= [0] = 0()
                   [0]    [0]      
    
                      [2]    [2]         
    lastbit(s(0())) = [2] >= [2] = s(0())
                      [2]    [0]         
    
                       [1 0 0]    [2]    [1 0 0]              
    lastbit(s(s(x))) = [1 0 0]x + [2] >= [1 0 0]x = lastbit(x)
                       [2 2 2]    [3]    [0 1 0]              
    
                 [2 1 1]    [3]    [2 1 1]    [3]                                       
    conv(s(x)) = [0 0 0]x + [1] >= [0 0 0]x + [0] = cons(conv(half(s(x))),lastbit(s(x)))
                 [2 1 1]    [2]    [2 1 1]    [2]                                       
   problem:
    half(0()) -> 0()
    lastbit(0()) -> 0()
    lastbit(s(0())) -> s(0())
    conv(s(x)) -> cons(conv(half(s(x))),lastbit(s(x)))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                      [1 0 0]     [1 0 0]  
     [cons](x0, x1) = [1 1 0]x0 + [0 0 0]x1
                      [0 0 0]     [0 0 0]  ,
     
                  [1 1 0]     [0]
     [conv](x0) = [0 1 0]x0 + [1]
                  [1 1 0]     [1],
     
                     [1 0 1]  
     [lastbit](x0) = [0 0 0]x0
                     [0 0 1]  ,
     
               [1 0 0]  
     [s](x0) = [1 1 0]x0
               [0 0 0]  ,
     
                  [1 0 0]     [0]
     [half](x0) = [0 0 0]x0 + [0]
                  [1 0 0]     [1],
     
           [0]
     [0] = [0]
           [1]
    orientation:
                 [0]    [0]      
     half(0()) = [0] >= [0] = 0()
                 [1]    [1]      
     
                    [1]    [0]      
     lastbit(0()) = [0] >= [0] = 0()
                    [1]    [1]      
     
                       [0]    [0]         
     lastbit(s(0())) = [0] >= [0] = s(0())
                       [0]    [0]         
     
                  [2 1 0]    [0]    [2 0 0]    [0]                                       
     conv(s(x)) = [1 1 0]x + [1] >= [1 0 0]x + [1] = cons(conv(half(s(x))),lastbit(s(x)))
                  [2 1 0]    [1]    [0 0 0]    [0]                                       
    problem:
     half(0()) -> 0()
     lastbit(s(0())) -> s(0())
     conv(s(x)) -> cons(conv(half(s(x))),lastbit(s(x)))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                       [1 0 0]     [1 0 0]  
      [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                       [0 0 0]     [0 1 0]  ,
      
                   [1 1 1]     [0]
      [conv](x0) = [0 1 0]x0 + [1]
                   [0 1 1]     [0],
      
                      [1 0 0]     [0]
      [lastbit](x0) = [0 0 1]x0 + [1]
                      [0 0 1]     [0],
      
                [1 0 0]     [0]
      [s](x0) = [0 0 0]x0 + [1]
                [1 0 0]     [1],
      
                   [1 1 0]     [1]
      [half](x0) = [0 0 0]x0 + [0]
                   [0 0 0]     [0],
      
            [1]
      [0] = [0]
            [0]
     orientation:
                  [2]    [1]      
      half(0()) = [0] >= [0] = 0()
                  [0]    [0]      
      
                        [1]    [1]         
      lastbit(s(0())) = [3] >= [1] = s(0())
                        [2]    [2]         
      
                   [2 0 0]    [2]    [2 0 0]    [2]                                       
      conv(s(x)) = [0 0 0]x + [2] >= [0 0 0]x + [0] = cons(conv(half(s(x))),lastbit(s(x)))
                   [1 0 0]    [2]    [1 0 0]    [2]                                       
     problem:
      lastbit(s(0())) -> s(0())
      conv(s(x)) -> cons(conv(half(s(x))),lastbit(s(x)))
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                        [1 0 0]     [1 0 0]  
       [cons](x0, x1) = [0 0 0]x0 + [0 1 1]x1
                        [0 0 0]     [0 0 0]  ,
       
                    [1 0 1]     [0]
       [conv](x0) = [1 1 1]x0 + [1]
                    [0 0 0]     [0],
       
                         
       [lastbit](x0) = x0
                         ,
       
                 [1 0 0]     [0]
       [s](x0) = [0 0 1]x0 + [0]
                 [1 0 1]     [1],
       
                    [1 0 0]     [0]
       [half](x0) = [1 0 0]x0 + [1]
                    [0 0 0]     [0],
       
             [0]
       [0] = [0]
             [0]
      orientation:
                         [0]    [0]         
       lastbit(s(0())) = [0] >= [0] = s(0())
                         [1]    [1]         
       
                    [2 0 1]    [1]    [2 0 0]    [0]                                       
       conv(s(x)) = [2 0 2]x + [2] >= [1 0 2]x + [1] = cons(conv(half(s(x))),lastbit(s(x)))
                    [0 0 0]    [0]    [0 0 0]    [0]                                       
      problem:
       lastbit(s(0())) -> s(0())
      Matrix Interpretation Processor: dim=3
       
       interpretation:
                        [1 0 0]     [1]
        [lastbit](x0) = [0 0 0]x0 + [0]
                        [0 0 0]     [0],
        
                  [1 0 0]  
        [s](x0) = [0 0 0]x0
                  [0 0 0]  ,
        
              [0]
        [0] = [0]
              [0]
       orientation:
                          [1]    [0]         
        lastbit(s(0())) = [0] >= [0] = s(0())
                          [0]    [0]         
       problem:
        
       Qed