/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:
 strict:
  average(s(x),y) -> average(x,s(y))
  average(x,s(s(s(y)))) -> s(average(s(x),y))
  average(0(),0()) -> 0()
  average(0(),s(0())) -> 0()
  average(0(),s(s(0()))) -> s(0())
 weak:
  rand(x) -> x
  rand(x) -> rand(s(x))

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
                [1 2]     [2]
   [rand](x0) = [0 1]x0 + [0],
   
         [0]
   [0] = [0],
   
                       [1 2]     [1 2]     [2]
   [average](x0, x1) = [0 0]x0 + [0 0]x1 + [0],
   
             [1 2]  
   [s](x0) = [0 0]x0
  orientation:
                     [1 2]    [1 2]    [2]    [1 2]    [1 2]    [2]                  
   average(s(x),y) = [0 0]x + [0 0]y + [0] >= [0 0]x + [0 0]y + [0] = average(x,s(y))
   
                           [1 2]    [1 2]    [2]    [1 2]    [1 2]    [2]                     
   average(x,s(s(s(y)))) = [0 0]x + [0 0]y + [0] >= [0 0]x + [0 0]y + [0] = s(average(s(x),y))
   
                      [2]    [0]      
   average(0(),0()) = [0] >= [0] = 0()
   
                         [2]    [0]      
   average(0(),s(0())) = [0] >= [0] = 0()
   
                            [2]    [0]         
   average(0(),s(s(0()))) = [0] >= [0] = s(0())
   
             [1 2]    [2]         
   rand(x) = [0 1]x + [0] >= x = x
   
             [1 2]    [2]    [1 2]    [2]             
   rand(x) = [0 1]x + [0] >= [0 0]x + [0] = rand(s(x))
  problem:
   strict:
    average(s(x),y) -> average(x,s(y))
    average(x,s(s(s(y)))) -> s(average(s(x),y))
   weak:
    rand(x) -> rand(s(x))
  Matrix Interpretation Processor: dim=2
   
   interpretation:
                 [1 0]     [0]
    [rand](x0) = [2 0]x0 + [1],
    
                        [1 1]     [1 1]  
    [average](x0, x1) = [0 2]x0 + [0 1]x1,
    
                   [0]
    [s](x0) = x0 + [1]
   orientation:
                      [1 1]    [1 1]    [1]    [1 1]    [1 1]    [1]                  
    average(s(x),y) = [0 2]x + [0 1]y + [2] >= [0 2]x + [0 1]y + [1] = average(x,s(y))
    
                            [1 1]    [1 1]    [3]    [1 1]    [1 1]    [1]                     
    average(x,s(s(s(y)))) = [0 2]x + [0 1]y + [3] >= [0 2]x + [0 1]y + [3] = s(average(s(x),y))
    
              [1 0]    [0]    [1 0]    [0]             
    rand(x) = [2 0]x + [1] >= [2 0]x + [1] = rand(s(x))
   problem:
    strict:
     average(s(x),y) -> average(x,s(y))
    weak:
     rand(x) -> rand(s(x))
   Matrix Interpretation Processor: dim=5
    
    interpretation:
                  [1 0 1 0 0]     [1]
                  [0 0 1 0 0]     [0]
     [rand](x0) = [0 0 0 1 0]x0 + [0]
                  [0 0 0 0 0]     [0]
                  [0 0 0 0 0]     [0],
     
                         [1 1 0 0 1]     [1 0 1 0 0]     [0]
                         [1 0 1 0 1]     [0 0 1 1 0]     [0]
     [average](x0, x1) = [1 0 1 1 0]x0 + [0 0 1 1 0]x1 + [1]
                         [0 0 0 1 1]     [0 1 0 0 0]     [1]
                         [0 0 0 0 0]     [1 0 1 0 0]     [0],
     
               [1 0 1 0 0]     [0]
               [0 0 0 0 0]     [1]
     [s](x0) = [0 0 0 0 0]x0 + [0]
               [0 0 0 1 0]     [0]
               [1 1 0 1 1]     [1]
    orientation:
                       [2 1 1 1 1]    [1 0 1 0 0]    [2]    [1 1 0 0 1]    [1 0 1 0 0]    [0]                  
                       [2 1 1 1 1]    [0 0 1 1 0]    [1]    [1 0 1 0 1]    [0 0 0 1 0]    [0]                  
     average(s(x),y) = [1 0 1 1 0]x + [0 0 1 1 0]y + [1] >= [1 0 1 1 0]x + [0 0 0 1 0]y + [1] = average(x,s(y))
                       [1 1 0 2 1]    [0 1 0 0 0]    [2]    [0 0 0 1 1]    [0 0 0 0 0]    [2]                  
                       [0 0 0 0 0]    [1 0 1 0 0]    [0]    [0 0 0 0 0]    [1 0 1 0 0]    [0]                  
     
               [1 0 1 0 0]    [1]    [1 0 1 0 0]    [1]             
               [0 0 1 0 0]    [0]    [0 0 0 0 0]    [0]             
     rand(x) = [0 0 0 1 0]x + [0] >= [0 0 0 1 0]x + [0] = rand(s(x))
               [0 0 0 0 0]    [0]    [0 0 0 0 0]    [0]             
               [0 0 0 0 0]    [0]    [0 0 0 0 0]    [0]             
    problem:
     strict:
      
     weak:
      rand(x) -> rand(s(x))
    Qed