/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem:
 first(0(),X) -> nil()
 first(s(X),cons(Y)) -> cons(Y)
 from(X) -> cons(X)

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                [1 0 0]  
   [cons](x0) = [0 0 0]x0
                [0 0 0]  ,
   
                     [1 0 0]     [1 0 0]     [1]
   [first](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                     [0 0 0]     [0 0 0]     [0],
   
             [1 0 0]  
   [s](x0) = [0 0 0]x0
             [0 0 0]  ,
   
                [1 0 0]  
   [from](x0) = [0 0 0]x0
                [0 0 0]  ,
   
         [0]
   [0] = [0]
         [0],
   
           [0]
   [nil] = [0]
           [0]
  orientation:
                  [1 0 0]    [1]    [0]        
   first(0(),X) = [0 0 0]X + [0] >= [0] = nil()
                  [0 0 0]    [0]    [0]        
   
                         [1 0 0]    [1 0 0]    [1]    [1 0 0]           
   first(s(X),cons(Y)) = [0 0 0]X + [0 0 0]Y + [0] >= [0 0 0]Y = cons(Y)
                         [0 0 0]    [0 0 0]    [0]    [0 0 0]           
   
             [1 0 0]     [1 0 0]           
   from(X) = [0 0 0]X >= [0 0 0]X = cons(X)
             [0 0 0]     [0 0 0]           
  problem:
   from(X) -> cons(X)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                 [1 0 0]  
    [cons](x0) = [0 0 0]x0
                 [0 0 0]  ,
    
                 [1 0 0]     [1]
    [from](x0) = [0 0 0]x0 + [0]
                 [0 0 1]     [0]
   orientation:
              [1 0 0]    [1]    [1 0 0]           
    from(X) = [0 0 0]X + [0] >= [0 0 0]X = cons(X)
              [0 0 1]    [0]    [0 0 0]           
   problem:
    
   Qed