/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:
  not(true()) -> false()
  not(false()) -> true()
  evenodd(x,0()) -> not(evenodd(x,s(0())))
  evenodd(0(),s(0())) -> false()
  evenodd(s(x),s(0())) -> evenodd(x,0())
 weak:
  rand(x) -> x
  rand(x) -> rand(s(x))

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
                [2 2]     [2]
   [rand](x0) = [1 1]x0 + [0],
   
             [1 1]  
   [s](x0) = [0 0]x0,
   
                       [2 1]     [1 1]     [0]
   [evenodd](x0, x1) = [2 1]x0 + [0 0]x1 + [1],
   
         [0]
   [0] = [1],
   
             [0]
   [false] = [0],
   
               [1 0]     [0]
   [not](x0) = [0 0]x0 + [1],
   
            [0]
   [true] = [0]
  orientation:
                 [0]    [0]          
   not(true()) = [1] >= [0] = false()
   
                  [0]    [0]         
   not(false()) = [1] >= [0] = true()
   
                    [2 1]    [1]    [2 1]    [1]                         
   evenodd(x,0()) = [2 1]x + [1] >= [0 0]x + [1] = not(evenodd(x,s(0())))
   
                         [2]    [0]          
   evenodd(0(),s(0())) = [2] >= [0] = false()
   
                          [2 2]    [1]    [2 1]    [1]                 
   evenodd(s(x),s(0())) = [2 2]x + [1] >= [2 1]x + [1] = evenodd(x,0())
   
             [2 2]    [2]         
   rand(x) = [1 1]x + [0] >= x = x
   
             [2 2]    [2]    [2 2]    [2]             
   rand(x) = [1 1]x + [0] >= [1 1]x + [0] = rand(s(x))
  problem:
   strict:
    not(true()) -> false()
    not(false()) -> true()
    evenodd(x,0()) -> not(evenodd(x,s(0())))
    evenodd(s(x),s(0())) -> evenodd(x,0())
   weak:
    rand(x) -> rand(s(x))
  Matrix Interpretation Processor: dim=2
   
   interpretation:
                 [1 0]     [0]
    [rand](x0) = [0 0]x0 + [2],
    
                
    [s](x0) = x0,
    
                        [1 0]     [2 2]  
    [evenodd](x0, x1) = [0 0]x0 + [0 0]x1,
    
          [0]
    [0] = [1],
    
              [1]
    [false] = [1],
    
                [1 2]  
    [not](x0) = [0 2]x0,
    
             [0]
    [true] = [1]
   orientation:
                  [2]    [1]          
    not(true()) = [2] >= [1] = false()
    
                   [3]    [0]         
    not(false()) = [2] >= [1] = true()
    
                     [1 0]    [2]    [1 0]    [2]                         
    evenodd(x,0()) = [0 0]x + [0] >= [0 0]x + [0] = not(evenodd(x,s(0())))
    
                           [1 0]    [2]    [1 0]    [2]                 
    evenodd(s(x),s(0())) = [0 0]x + [0] >= [0 0]x + [0] = evenodd(x,0())
    
              [1 0]    [0]    [1 0]    [0]             
    rand(x) = [0 0]x + [2] >= [0 0]x + [2] = rand(s(x))
   problem:
    strict:
     evenodd(x,0()) -> not(evenodd(x,s(0())))
     evenodd(s(x),s(0())) -> evenodd(x,0())
    weak:
     rand(x) -> rand(s(x))
   Matrix Interpretation Processor: dim=2
    
    interpretation:
                  [2 0]  
     [rand](x0) = [0 0]x0,
     
                    [0]
     [s](x0) = x0 + [1],
     
                         [2 2]     [2 0]  
     [evenodd](x0, x1) = [0 0]x0 + [0 1]x1,
     
           [0]
     [0] = [0],
     
                 [1 0]  
     [not](x0) = [0 0]x0
    orientation:
                      [2 2]     [2 2]                          
     evenodd(x,0()) = [0 0]x >= [0 0]x = not(evenodd(x,s(0())))
     
                            [2 2]    [2]    [2 2]                  
     evenodd(s(x),s(0())) = [0 0]x + [1] >= [0 0]x = evenodd(x,0())
     
               [2 0]     [2 0]              
     rand(x) = [0 0]x >= [0 0]x = rand(s(x))
    problem:
     strict:
      evenodd(x,0()) -> not(evenodd(x,s(0())))
     weak:
      rand(x) -> rand(s(x))
    Matrix Interpretation Processor: dim=5
     
     interpretation:
                   [1 0 0 0 1]     [1]
                   [1 0 0 0 0]     [0]
      [rand](x0) = [0 0 1 0 0]x0 + [0]
                   [0 0 0 0 0]     [0]
                   [0 1 1 1 1]     [0],
      
                [1 0 0 0 0]  
                [0 0 0 0 0]  
      [s](x0) = [0 0 0 0 0]x0
                [0 1 1 1 0]  
                [0 0 0 0 0]  ,
      
                          [1 0 0 0 0]     [1 1 1 0 1]     [0]
                          [0 1 1 0 0]     [0 0 0 1 0]     [0]
      [evenodd](x0, x1) = [0 0 0 0 0]x0 + [0 1 1 0 0]x1 + [1]
                          [0 1 1 1 0]     [0 0 1 0 1]     [1]
                          [0 0 0 0 0]     [0 0 0 0 0]     [1],
      
            [0]
            [1]
      [0] = [1]
            [1]
            [1],
      
                  [1 0 1 0 1]     [0]
                  [0 0 0 0 0]     [1]
      [not](x0) = [0 0 0 0 0]x0 + [0]
                  [0 1 0 0 0]     [0]
                  [0 0 0 0 0]     [0]
     orientation:
                       [1 0 0 0 0]    [3]    [1 0 0 0 0]    [2]                         
                       [0 1 1 0 0]    [1]    [0 0 0 0 0]    [1]                         
      evenodd(x,0()) = [0 0 0 0 0]x + [3] >= [0 0 0 0 0]x + [0] = not(evenodd(x,s(0())))
                       [0 1 1 1 0]    [3]    [0 1 1 0 0]    [3]                         
                       [0 0 0 0 0]    [1]    [0 0 0 0 0]    [0]                         
      
                [1 0 0 0 1]    [1]    [1 0 0 0 0]    [1]             
                [1 0 0 0 0]    [0]    [1 0 0 0 0]    [0]             
      rand(x) = [0 0 1 0 0]x + [0] >= [0 0 0 0 0]x + [0] = rand(s(x))
                [0 0 0 0 0]    [0]    [0 0 0 0 0]    [0]             
                [0 1 1 1 1]    [0]    [0 1 1 1 0]    [0]             
     problem:
      strict:
       
      weak:
       rand(x) -> rand(s(x))
     Qed