/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:
 filter(cons(X),0(),M) -> cons(0())
 filter(cons(X),s(N),M) -> cons(X)
 sieve(cons(0())) -> cons(0())
 sieve(cons(s(N))) -> cons(s(N))
 nats(N) -> cons(N)
 zprimes() -> sieve(nats(s(s(0()))))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
               [1]
   [zprimes] = [1]
               [1],
   
                [1 1 0]     [0]
   [nats](x0) = [0 1 0]x0 + [1]
                [0 1 1]     [0],
   
                 [1 1 0]     [0]
   [sieve](x0) = [0 0 0]x0 + [1]
                 [0 0 1]     [0],
   
             [1 0 0]  
   [s](x0) = [0 0 0]x0
             [0 1 1]  ,
   
                          [1 0 0]     [1 0 0]     [1 0 0]     [1]
   [filter](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2 + [1]
                          [0 0 1]     [0 1 0]     [0 0 0]     [0],
   
         [0]
   [0] = [1]
         [0],
   
                [1 0 0]     [0]
   [cons](x0) = [0 0 0]x0 + [1]
                [0 1 0]     [0]
  orientation:
                           [1 0 0]    [1 0 0]    [1]    [0]            
   filter(cons(X),0(),M) = [0 0 0]M + [0 0 0]X + [1] >= [1] = cons(0())
                           [0 0 0]    [0 1 0]    [1]    [1]            
   
                            [1 0 0]    [1 0 0]    [1 0 0]    [1]    [1 0 0]    [0]          
   filter(cons(X),s(N),M) = [0 0 0]M + [0 0 0]N + [0 0 0]X + [1] >= [0 0 0]X + [1] = cons(X)
                            [0 0 0]    [0 0 0]    [0 1 0]    [0]    [0 1 0]    [0]          
   
                      [1]    [0]            
   sieve(cons(0())) = [1] >= [1] = cons(0())
                      [1]    [1]            
   
                       [1 0 0]    [1]    [1 0 0]    [0]             
   sieve(cons(s(N))) = [0 0 0]N + [1] >= [0 0 0]N + [1] = cons(s(N))
                       [0 0 0]    [0]    [0 0 0]    [0]             
   
             [1 1 0]    [0]    [1 0 0]    [0]          
   nats(N) = [0 1 0]N + [1] >= [0 0 0]N + [1] = cons(N)
             [0 1 1]    [0]    [0 1 0]    [0]          
   
               [1]    [1]                         
   zprimes() = [1] >= [1] = sieve(nats(s(s(0()))))
               [1]    [1]                         
  problem:
   nats(N) -> cons(N)
   zprimes() -> sieve(nats(s(s(0()))))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                [1]
    [zprimes] = [0]
                [0],
    
                 [1 0 0]  
    [nats](x0) = [0 0 1]x0
                 [0 0 0]  ,
    
                  [1 0 0]  
    [sieve](x0) = [0 0 0]x0
                  [0 0 0]  ,
    
              [1 0 0]  
    [s](x0) = [0 0 0]x0
              [0 0 0]  ,
    
          [0]
    [0] = [0]
          [0],
    
                 [1 0 0]  
    [cons](x0) = [0 0 0]x0
                 [0 0 0]  
   orientation:
              [1 0 0]     [1 0 0]           
    nats(N) = [0 0 1]N >= [0 0 0]N = cons(N)
              [0 0 0]     [0 0 0]           
    
                [1]    [0]                         
    zprimes() = [0] >= [0] = sieve(nats(s(s(0()))))
                [0]    [0]                         
   problem:
    nats(N) -> cons(N)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                  [1 0 0]     [1]
     [nats](x0) = [0 0 0]x0 + [0]
                  [0 0 1]     [0],
     
                  [1 0 0]  
     [cons](x0) = [0 0 0]x0
                  [0 0 0]  
    orientation:
               [1 0 0]    [1]    [1 0 0]           
     nats(N) = [0 0 0]N + [0] >= [0 0 0]N = cons(N)
               [0 0 1]    [0]    [0 0 0]           
    problem:
     
    Qed