/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(),n__f(s(0())))
 f(s(0())) -> f(p(s(0())))
 p(s(0())) -> 0()
 f(X) -> n__f(X)
 activate(n__f(X)) -> f(X)
 activate(X) -> X

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                    [1 0 0]     [1]
   [activate](x0) = [0 1 1]x0 + [0]
                    [0 0 1]     [0],
   
             [1 0 0]     [0]
   [p](x0) = [0 0 0]x0 + [0]
             [0 0 0]     [1],
   
                    [1 0 0]     [1 0 0]  
   [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                    [0 0 0]     [0 0 0]  ,
   
                [1 0 0]  
   [n__f](x0) = [1 0 0]x0
                [0 1 1]  ,
   
             [1 0 0]     [0]
   [s](x0) = [0 0 0]x0 + [1]
             [0 0 0]     [0],
   
             [1 0 0]     [1]
   [f](x0) = [1 1 1]x0 + [0]
             [0 1 1]     [0],
   
         [0]
   [0] = [0]
         [0]
  orientation:
            [1]    [0]                         
   f(0()) = [0] >= [0] = cons(0(),n__f(s(0())))
            [0]    [0]                         
   
               [1]    [1]               
   f(s(0())) = [1] >= [1] = f(p(s(0())))
               [1]    [1]               
   
               [0]    [0]      
   p(s(0())) = [0] >= [0] = 0()
               [1]    [0]      
   
          [1 0 0]    [1]    [1 0 0]           
   f(X) = [1 1 1]X + [0] >= [1 0 0]X = n__f(X)
          [0 1 1]    [0]    [0 1 1]           
   
                       [1 0 0]    [1]    [1 0 0]    [1]       
   activate(n__f(X)) = [1 1 1]X + [0] >= [1 1 1]X + [0] = f(X)
                       [0 1 1]    [0]    [0 1 1]    [0]       
   
                 [1 0 0]    [1]         
   activate(X) = [0 1 1]X + [0] >= X = X
                 [0 0 1]    [0]         
  problem:
   f(s(0())) -> f(p(s(0())))
   p(s(0())) -> 0()
   activate(n__f(X)) -> f(X)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                     [1 0 1]  
    [activate](x0) = [0 0 0]x0
                     [0 1 0]  ,
    
              [1 0 0]     [0]
    [p](x0) = [0 0 0]x0 + [1]
              [0 0 0]     [0],
    
                 [1 1 0]  
    [n__f](x0) = [0 1 0]x0
                 [0 0 1]  ,
    
              [1 0 0]     [0]
    [s](x0) = [0 0 0]x0 + [1]
              [0 0 0]     [1],
    
              [1 0 1]  
    [f](x0) = [0 0 0]x0
              [0 1 0]  ,
    
          [0]
    [0] = [0]
          [0]
   orientation:
                [1]    [0]               
    f(s(0())) = [0] >= [0] = f(p(s(0())))
                [1]    [1]               
    
                [0]    [0]      
    p(s(0())) = [1] >= [0] = 0()
                [0]    [0]      
    
                        [1 1 1]     [1 0 1]        
    activate(n__f(X)) = [0 0 0]X >= [0 0 0]X = f(X)
                        [0 1 0]     [0 1 0]        
   problem:
    p(s(0())) -> 0()
    activate(n__f(X)) -> f(X)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                      [1 0 1]  
     [activate](x0) = [0 0 0]x0
                      [0 0 0]  ,
     
               [1 0 0]     [1]
     [p](x0) = [0 0 0]x0 + [0]
               [0 0 0]     [0],
     
                  [1 0 0]     [0]
     [n__f](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]  
     [f](x0) = [0 0 0]x0
               [0 0 0]  ,
     
           [0]
     [0] = [0]
           [0]
    orientation:
                 [1]    [0]      
     p(s(0())) = [0] >= [0] = 0()
                 [0]    [0]      
     
                         [1 0 0]    [1]    [1 0 0]        
     activate(n__f(X)) = [0 0 0]X + [0] >= [0 0 0]X = f(X)
                         [0 0 0]    [0]    [0 0 0]        
    problem:
     
    Qed