/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:
 f(0()) -> cons(0(),n__f(n__s(n__0())))
 f(s(0())) -> f(p(s(0())))
 p(s(X)) -> X
 f(X) -> n__f(X)
 s(X) -> n__s(X)
 0() -> n__0()
 activate(n__f(X)) -> f(activate(X))
 activate(n__s(X)) -> s(activate(X))
 activate(n__0()) -> 0()
 activate(X) -> X

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                    [1 0 1]     [1]
   [activate](x0) = [0 1 0]x0 + [0]
                    [0 0 1]     [0],
   
             [1 1 0]  
   [p](x0) = [1 0 0]x0
             [0 1 0]  ,
   
             [1 1 0]     [0]
   [s](x0) = [0 0 1]x0 + [1]
             [0 0 1]     [0],
   
                    [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) = [0 0 0]x0
                [0 1 1]  ,
   
                [1 1 0]     [0]
   [n__s](x0) = [0 0 1]x0 + [1]
                [0 0 1]     [0],
   
            [0]
   [n__0] = [0]
            [0],
   
             [1 1 0]  
   [f](x0) = [0 0 0]x0
             [0 1 1]  ,
   
         [0]
   [0] = [0]
         [0]
  orientation:
            [0]    [0]                               
   f(0()) = [0] >= [0] = cons(0(),n__f(n__s(n__0())))
            [0]    [0]                               
   
               [1]    [1]               
   f(s(0())) = [0] >= [0] = f(p(s(0())))
               [1]    [1]               
   
             [1 1 1]    [1]         
   p(s(X)) = [1 1 0]X + [0] >= X = X
             [0 0 1]    [1]         
   
          [1 1 0]     [1 0 0]           
   f(X) = [0 0 0]X >= [0 0 0]X = n__f(X)
          [0 1 1]     [0 1 1]           
   
          [1 1 0]    [0]    [1 1 0]    [0]          
   s(X) = [0 0 1]X + [1] >= [0 0 1]X + [1] = n__s(X)
          [0 0 1]    [0]    [0 0 1]    [0]          
   
         [0]    [0]         
   0() = [0] >= [0] = n__0()
         [0]    [0]         
   
                       [1 1 1]    [1]    [1 1 1]    [1]                 
   activate(n__f(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = f(activate(X))
                       [0 1 1]    [0]    [0 1 1]    [0]                 
   
                       [1 1 1]    [1]    [1 1 1]    [1]                 
   activate(n__s(X)) = [0 0 1]X + [1] >= [0 0 1]X + [1] = s(activate(X))
                       [0 0 1]    [0]    [0 0 1]    [0]                 
   
                      [1]    [0]      
   activate(n__0()) = [0] >= [0] = 0()
                      [0]    [0]      
   
                 [1 0 1]    [1]         
   activate(X) = [0 1 0]X + [0] >= X = X
                 [0 0 1]    [0]         
  problem:
   f(0()) -> cons(0(),n__f(n__s(n__0())))
   f(s(0())) -> f(p(s(0())))
   f(X) -> n__f(X)
   s(X) -> n__s(X)
   0() -> n__0()
   activate(n__f(X)) -> f(activate(X))
   activate(n__s(X)) -> s(activate(X))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                     [1 0 0]     [0]
    [activate](x0) = [0 1 0]x0 + [0]
                     [0 1 1]     [1],
    
              [1 0 0]  
    [p](x0) = [0 0 0]x0
              [0 0 0]  ,
    
              [1 0 0]  
    [s](x0) = [0 1 0]x0
              [0 0 0]  ,
    
                     [1 0 0]     [1 0 0]     [0]
    [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1]
                     [0 0 0]     [0 0 0]     [0],
    
                 [1 1 0]  
    [n__f](x0) = [1 1 0]x0
                 [0 0 1]  ,
    
                 [1 0 0]  
    [n__s](x0) = [0 1 0]x0
                 [0 0 0]  ,
    
             [0]
    [n__0] = [0]
             [0],
    
              [1 1 0]  
    [f](x0) = [1 1 0]x0
              [1 0 1]  ,
    
          [0]
    [0] = [1]
          [0]
   orientation:
             [1]    [0]                               
    f(0()) = [1] >= [1] = cons(0(),n__f(n__s(n__0())))
             [0]    [0]                               
    
                [1]    [0]               
    f(s(0())) = [1] >= [0] = f(p(s(0())))
                [0]    [0]               
    
           [1 1 0]     [1 1 0]           
    f(X) = [1 1 0]X >= [1 1 0]X = n__f(X)
           [1 0 1]     [0 0 1]           
    
           [1 0 0]     [1 0 0]           
    s(X) = [0 1 0]X >= [0 1 0]X = n__s(X)
           [0 0 0]     [0 0 0]           
    
          [0]    [0]         
    0() = [1] >= [0] = n__0()
          [0]    [0]         
    
                        [1 1 0]    [0]    [1 1 0]    [0]                 
    activate(n__f(X)) = [1 1 0]X + [0] >= [1 1 0]X + [0] = f(activate(X))
                        [1 1 1]    [1]    [1 1 1]    [1]                 
    
                        [1 0 0]    [0]    [1 0 0]                  
    activate(n__s(X)) = [0 1 0]X + [0] >= [0 1 0]X = s(activate(X))
                        [0 1 0]    [1]    [0 0 0]                  
   problem:
    f(X) -> n__f(X)
    s(X) -> n__s(X)
    0() -> n__0()
    activate(n__f(X)) -> f(activate(X))
    activate(n__s(X)) -> s(activate(X))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                      [1 1 0]  
     [activate](x0) = [0 0 1]x0
                      [0 0 1]  ,
     
               [1 1 0]  
     [s](x0) = [0 0 1]x0
               [0 0 1]  ,
     
                       [0]
     [n__f](x0) = x0 + [1]
                       [1],
     
                  [1 1 0]  
     [n__s](x0) = [0 0 1]x0
                  [0 0 1]  ,
     
              [0]
     [n__0] = [0]
              [0],
     
                    [1]
     [f](x0) = x0 + [1]
                    [1],
     
           [0]
     [0] = [0]
           [0]
    orientation:
                [1]        [0]          
     f(X) = X + [1] >= X + [1] = n__f(X)
                [1]        [1]          
     
            [1 1 0]     [1 1 0]           
     s(X) = [0 0 1]X >= [0 0 1]X = n__s(X)
            [0 0 1]     [0 0 1]           
     
           [0]    [0]         
     0() = [0] >= [0] = n__0()
           [0]    [0]         
     
                         [1 1 0]    [1]    [1 1 0]    [1]                 
     activate(n__f(X)) = [0 0 1]X + [1] >= [0 0 1]X + [1] = f(activate(X))
                         [0 0 1]    [1]    [0 0 1]    [1]                 
     
                         [1 1 1]     [1 1 1]                  
     activate(n__s(X)) = [0 0 1]X >= [0 0 1]X = s(activate(X))
                         [0 0 1]     [0 0 1]                  
    problem:
     s(X) -> n__s(X)
     0() -> n__0()
     activate(n__f(X)) -> f(activate(X))
     activate(n__s(X)) -> s(activate(X))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                       [1 1 0]  
      [activate](x0) = [0 1 0]x0
                       [0 0 1]  ,
      
                     [1]
      [s](x0) = x0 + [1]
                     [0],
      
                   [1 1 0]  
      [n__f](x0) = [0 0 0]x0
                   [0 0 0]  ,
      
                        [0]
      [n__s](x0) = x0 + [1]
                        [0],
      
               [0]
      [n__0] = [0]
               [0],
      
                [1 0 0]  
      [f](x0) = [0 0 0]x0
                [0 0 0]  ,
      
            [0]
      [0] = [0]
            [0]
     orientation:
                 [1]        [0]          
      s(X) = X + [1] >= X + [1] = n__s(X)
                 [0]        [0]          
      
            [0]    [0]         
      0() = [0] >= [0] = n__0()
            [0]    [0]         
      
                          [1 1 0]     [1 1 0]                  
      activate(n__f(X)) = [0 0 0]X >= [0 0 0]X = f(activate(X))
                          [0 0 0]     [0 0 0]                  
      
                          [1 1 0]    [1]    [1 1 0]    [1]                 
      activate(n__s(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = s(activate(X))
                          [0 0 1]    [0]    [0 0 1]    [0]                 
     problem:
      0() -> n__0()
      activate(n__f(X)) -> f(activate(X))
      activate(n__s(X)) -> s(activate(X))
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                        [1 0 0]  
       [activate](x0) = [0 0 0]x0
                        [0 0 0]  ,
       
                 [1 0 0]  
       [s](x0) = [0 0 0]x0
                 [0 0 0]  ,
       
                    [1 0 0]     [1]
       [n__f](x0) = [0 0 0]x0 + [0]
                    [0 0 0]     [0],
       
                    [1 0 0]     [1]
       [n__s](x0) = [0 0 0]x0 + [0]
                    [0 0 0]     [0],
       
                [0]
       [n__0] = [0]
                [0],
       
                 [1 0 0]  
       [f](x0) = [0 0 0]x0
                 [0 0 0]  ,
       
             [0]
       [0] = [0]
             [0]
      orientation:
             [0]    [0]         
       0() = [0] >= [0] = n__0()
             [0]    [0]         
       
                           [1 0 0]    [1]    [1 0 0]                  
       activate(n__f(X)) = [0 0 0]X + [0] >= [0 0 0]X = f(activate(X))
                           [0 0 0]    [0]    [0 0 0]                  
       
                           [1 0 0]    [1]    [1 0 0]                  
       activate(n__s(X)) = [0 0 0]X + [0] >= [0 0 0]X = s(activate(X))
                           [0 0 0]    [0]    [0 0 0]                  
      problem:
       0() -> n__0()
      Matrix Interpretation Processor: dim=3
       
       interpretation:
                 [0]
        [n__0] = [0]
                 [0],
        
              [1]
        [0] = [0]
              [1]
       orientation:
              [1]    [0]         
        0() = [0] >= [0] = n__0()
              [1]    [0]         
       problem:
        
       Qed