/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:
 f(0()) -> cons(0())
 f(s(0())) -> f(p(s(0())))
 p(s(0())) -> 0()

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
             [1 0 0]     [0]
   [p](x0) = [0 0 0]x0 + [0]
             [0 0 0]     [1],
   
             [1 0 0]  
   [s](x0) = [0 0 0]x0
             [0 0 0]  ,
   
                [1 0 0]  
   [cons](x0) = [0 0 0]x0
                [0 0 0]  ,
   
             [1 0 0]     [1]
   [f](x0) = [0 0 0]x0 + [0]
             [0 0 0]     [0],
   
         [0]
   [0] = [0]
         [0]
  orientation:
            [1]    [0]            
   f(0()) = [0] >= [0] = cons(0())
            [0]    [0]            
   
               [1]    [1]               
   f(s(0())) = [0] >= [0] = f(p(s(0())))
               [0]    [0]               
   
               [0]    [0]      
   p(s(0())) = [0] >= [0] = 0()
               [1]    [0]      
  problem:
   f(s(0())) -> f(p(s(0())))
   p(s(0())) -> 0()
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 0 0]     [0]
    [p](x0) = [0 0 0]x0 + [0]
              [0 0 0]     [1],
    
              [1 0 0]  
    [s](x0) = [0 0 1]x0
              [0 0 0]  ,
    
              [1 1 0]  
    [f](x0) = [0 0 0]x0
              [0 0 0]  ,
    
          [0]
    [0] = [0]
          [1]
   orientation:
                [1]    [0]               
    f(s(0())) = [0] >= [0] = f(p(s(0())))
                [0]    [0]               
    
                [0]    [0]      
    p(s(0())) = [0] >= [0] = 0()
                [1]    [1]      
   problem:
    p(s(0())) -> 0()
   Matrix Interpretation Processor: dim=3
    
    interpretation:
               [1 0 0]     [1]
     [p](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]      
     p(s(0())) = [0] >= [0] = 0()
                 [0]    [0]      
    problem:
     
    Qed