/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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NO

Problem:
 nats() -> adx(zeros())
 zeros() -> cons(n__0(),n__zeros())
 incr(cons(X,Y)) -> cons(n__s(activate(X)),n__incr(activate(Y)))
 adx(cons(X,Y)) -> incr(cons(activate(X),n__adx(activate(Y))))
 hd(cons(X,Y)) -> activate(X)
 tl(cons(X,Y)) -> activate(Y)
 0() -> n__0()
 zeros() -> n__zeros()
 s(X) -> n__s(X)
 incr(X) -> n__incr(X)
 adx(X) -> n__adx(X)
 activate(n__0()) -> 0()
 activate(n__zeros()) -> zeros()
 activate(n__s(X)) -> s(X)
 activate(n__incr(X)) -> incr(X)
 activate(n__adx(X)) -> adx(X)
 activate(X) -> X

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [s](x0) = x0,
   
   [0] = 0,
   
   [tl](x0) = 4x0 + 5,
   
   [hd](x0) = 2x0 + 4,
   
   [n__adx](x0) = 2x0,
   
   [n__incr](x0) = x0,
   
   [n__s](x0) = x0,
   
   [activate](x0) = x0,
   
   [incr](x0) = x0,
   
   [cons](x0, x1) = x0 + 2x1,
   
   [n__zeros] = 0,
   
   [n__0] = 0,
   
   [adx](x0) = 2x0,
   
   [zeros] = 0,
   
   [nats] = 0
  orientation:
   nats() = 0 >= 0 = adx(zeros())
   
   zeros() = 0 >= 0 = cons(n__0(),n__zeros())
   
   incr(cons(X,Y)) = X + 2Y >= X + 2Y = cons(n__s(activate(X)),n__incr(activate(Y)))
   
   adx(cons(X,Y)) = 2X + 4Y >= X + 4Y = incr(cons(activate(X),n__adx(activate(Y))))
   
   hd(cons(X,Y)) = 2X + 4Y + 4 >= X = activate(X)
   
   tl(cons(X,Y)) = 4X + 8Y + 5 >= Y = activate(Y)
   
   0() = 0 >= 0 = n__0()
   
   zeros() = 0 >= 0 = n__zeros()
   
   s(X) = X >= X = n__s(X)
   
   incr(X) = X >= X = n__incr(X)
   
   adx(X) = 2X >= 2X = n__adx(X)
   
   activate(n__0()) = 0 >= 0 = 0()
   
   activate(n__zeros()) = 0 >= 0 = zeros()
   
   activate(n__s(X)) = X >= X = s(X)
   
   activate(n__incr(X)) = X >= X = incr(X)
   
   activate(n__adx(X)) = 2X >= 2X = adx(X)
   
   activate(X) = X >= X = X
  problem:
   nats() -> adx(zeros())
   zeros() -> cons(n__0(),n__zeros())
   incr(cons(X,Y)) -> cons(n__s(activate(X)),n__incr(activate(Y)))
   adx(cons(X,Y)) -> incr(cons(activate(X),n__adx(activate(Y))))
   0() -> n__0()
   zeros() -> n__zeros()
   s(X) -> n__s(X)
   incr(X) -> n__incr(X)
   adx(X) -> n__adx(X)
   activate(n__0()) -> 0()
   activate(n__zeros()) -> zeros()
   activate(n__s(X)) -> s(X)
   activate(n__incr(X)) -> incr(X)
   activate(n__adx(X)) -> adx(X)
   activate(X) -> X
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [s](x0) = x0,
    
    [0] = 0,
    
    [n__adx](x0) = 2x0,
    
    [n__incr](x0) = x0,
    
    [n__s](x0) = x0,
    
    [activate](x0) = x0,
    
    [incr](x0) = x0,
    
    [cons](x0, x1) = 2x0 + 2x1,
    
    [n__zeros] = 0,
    
    [n__0] = 0,
    
    [adx](x0) = 2x0,
    
    [zeros] = 0,
    
    [nats] = 4
   orientation:
    nats() = 4 >= 0 = adx(zeros())
    
    zeros() = 0 >= 0 = cons(n__0(),n__zeros())
    
    incr(cons(X,Y)) = 2X + 2Y >= 2X + 2Y = cons(n__s(activate(X)),n__incr(activate(Y)))
    
    adx(cons(X,Y)) = 4X + 4Y >= 2X + 4Y = incr(cons(activate(X),n__adx(activate(Y))))
    
    0() = 0 >= 0 = n__0()
    
    zeros() = 0 >= 0 = n__zeros()
    
    s(X) = X >= X = n__s(X)
    
    incr(X) = X >= X = n__incr(X)
    
    adx(X) = 2X >= 2X = n__adx(X)
    
    activate(n__0()) = 0 >= 0 = 0()
    
    activate(n__zeros()) = 0 >= 0 = zeros()
    
    activate(n__s(X)) = X >= X = s(X)
    
    activate(n__incr(X)) = X >= X = incr(X)
    
    activate(n__adx(X)) = 2X >= 2X = adx(X)
    
    activate(X) = X >= X = X
   problem:
    zeros() -> cons(n__0(),n__zeros())
    incr(cons(X,Y)) -> cons(n__s(activate(X)),n__incr(activate(Y)))
    adx(cons(X,Y)) -> incr(cons(activate(X),n__adx(activate(Y))))
    0() -> n__0()
    zeros() -> n__zeros()
    s(X) -> n__s(X)
    incr(X) -> n__incr(X)
    adx(X) -> n__adx(X)
    activate(n__0()) -> 0()
    activate(n__zeros()) -> zeros()
    activate(n__s(X)) -> s(X)
    activate(n__incr(X)) -> incr(X)
    activate(n__adx(X)) -> adx(X)
    activate(X) -> X
   Matrix Interpretation Processor: dim=3
    
    interpretation:
               [1 0 0]  
     [s](x0) = [1 0 1]x0
               [0 0 0]  ,
     
           [0]
     [0] = [0]
           [0],
     
                    [1 0 1]  
     [n__adx](x0) = [0 0 0]x0
                    [0 1 0]  ,
     
                     [1 1 0]  
     [n__incr](x0) = [0 0 0]x0
                     [0 0 0]  ,
     
                  [1 0 0]  
     [n__s](x0) = [1 0 1]x0
                  [0 0 0]  ,
     
                      [1 0 1]  
     [activate](x0) = [0 1 0]x0
                      [1 0 1]  ,
     
                  [1 1 0]  
     [incr](x0) = [0 0 0]x0
                  [1 1 0]  ,
     
                      [1 0 0]     [1 1 0]  
     [cons](x0, x1) = [0 0 1]x0 + [0 0 1]x1
                      [1 0 1]     [1 0 1]  ,
     
                  [0]
     [n__zeros] = [1]
                  [1],
     
              [0]
     [n__0] = [0]
              [0],
     
                 [1 1 1]  
     [adx](x0) = [0 0 0]x0
                 [1 1 1]  ,
     
               [1]
     [zeros] = [1]
               [1]
    orientation:
               [1]    [1]                          
     zeros() = [1] >= [1] = cons(n__0(),n__zeros())
               [1]    [1]                          
     
                       [1 0 1]    [1 1 1]     [1 0 1]    [1 1 1]                                                
     incr(cons(X,Y)) = [0 0 0]X + [0 0 0]Y >= [0 0 0]X + [0 0 0]Y = cons(n__s(activate(X)),n__incr(activate(Y)))
                       [1 0 1]    [1 1 1]     [1 0 1]    [1 1 1]                                                
     
                      [2 0 2]    [2 1 2]     [2 0 2]    [2 1 2]                                               
     adx(cons(X,Y)) = [0 0 0]X + [0 0 0]Y >= [0 0 0]X + [0 0 0]Y = incr(cons(activate(X),n__adx(activate(Y))))
                      [2 0 2]    [2 1 2]     [2 0 2]    [2 1 2]                                               
     
           [0]    [0]         
     0() = [0] >= [0] = n__0()
           [0]    [0]         
     
               [1]    [0]             
     zeros() = [1] >= [1] = n__zeros()
               [1]    [1]             
     
            [1 0 0]     [1 0 0]           
     s(X) = [1 0 1]X >= [1 0 1]X = n__s(X)
            [0 0 0]     [0 0 0]           
     
               [1 1 0]     [1 1 0]              
     incr(X) = [0 0 0]X >= [0 0 0]X = n__incr(X)
               [1 1 0]     [0 0 0]              
     
              [1 1 1]     [1 0 1]             
     adx(X) = [0 0 0]X >= [0 0 0]X = n__adx(X)
              [1 1 1]     [0 1 0]             
     
                        [0]    [0]      
     activate(n__0()) = [0] >= [0] = 0()
                        [0]    [0]      
     
                            [1]    [1]          
     activate(n__zeros()) = [1] >= [1] = zeros()
                            [1]    [1]          
     
                         [1 0 0]     [1 0 0]        
     activate(n__s(X)) = [1 0 1]X >= [1 0 1]X = s(X)
                         [1 0 0]     [0 0 0]        
     
                            [1 1 0]     [1 1 0]           
     activate(n__incr(X)) = [0 0 0]X >= [0 0 0]X = incr(X)
                            [1 1 0]     [1 1 0]           
     
                           [1 1 1]     [1 1 1]          
     activate(n__adx(X)) = [0 0 0]X >= [0 0 0]X = adx(X)
                           [1 1 1]     [1 1 1]          
     
                   [1 0 1]          
     activate(X) = [0 1 0]X >= X = X
                   [1 0 1]          
    problem:
     zeros() -> cons(n__0(),n__zeros())
     incr(cons(X,Y)) -> cons(n__s(activate(X)),n__incr(activate(Y)))
     adx(cons(X,Y)) -> incr(cons(activate(X),n__adx(activate(Y))))
     0() -> n__0()
     s(X) -> n__s(X)
     incr(X) -> n__incr(X)
     adx(X) -> n__adx(X)
     activate(n__0()) -> 0()
     activate(n__zeros()) -> zeros()
     activate(n__s(X)) -> s(X)
     activate(n__incr(X)) -> incr(X)
     activate(n__adx(X)) -> adx(X)
     activate(X) -> X
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                [1 0 1]  
      [s](x0) = [0 0 0]x0
                [0 0 0]  ,
      
            [0]
      [0] = [0]
            [0],
      
                     [1 1 0]     [0]
      [n__adx](x0) = [0 0 0]x0 + [1]
                     [0 0 0]     [0],
      
                      [1 0 0]  
      [n__incr](x0) = [0 0 0]x0
                      [0 0 0]  ,
      
                   [1 0 1]  
      [n__s](x0) = [0 0 0]x0
                   [0 0 0]  ,
      
                       [1 1 0]  
      [activate](x0) = [0 1 1]x0
                       [0 0 1]  ,
      
                   [1 0 0]  
      [incr](x0) = [0 0 0]x0
                   [0 0 0]  ,
      
                       [1 1 1]     [1 1 1]  
      [cons](x0, x1) = [0 1 1]x0 + [0 1 1]x1
                       [0 1 0]     [0 0 0]  ,
      
                   [0]
      [n__zeros] = [0]
                   [0],
      
               [0]
      [n__0] = [0]
               [0],
      
                  [1 1 0]     [1]
      [adx](x0) = [0 0 0]x0 + [1]
                  [0 0 0]     [0],
      
                [0]
      [zeros] = [0]
                [0]
     orientation:
                [0]    [0]                          
      zeros() = [0] >= [0] = cons(n__0(),n__zeros())
                [0]    [0]                          
      
                        [1 1 1]    [1 1 1]     [1 1 1]    [1 1 0]                                                
      incr(cons(X,Y)) = [0 0 0]X + [0 0 0]Y >= [0 0 0]X + [0 0 0]Y = cons(n__s(activate(X)),n__incr(activate(Y)))
                        [0 0 0]    [0 0 0]     [0 0 0]    [0 0 0]                                                
      
                       [1 2 2]    [1 2 2]    [1]    [1 2 2]    [1 2 1]    [1]                                              
      adx(cons(X,Y)) = [0 0 0]X + [0 0 0]Y + [1] >= [0 0 0]X + [0 0 0]Y + [0] = incr(cons(activate(X),n__adx(activate(Y))))
                       [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]    [0]                                              
      
            [0]    [0]         
      0() = [0] >= [0] = n__0()
            [0]    [0]         
      
             [1 0 1]     [1 0 1]           
      s(X) = [0 0 0]X >= [0 0 0]X = n__s(X)
             [0 0 0]     [0 0 0]           
      
                [1 0 0]     [1 0 0]              
      incr(X) = [0 0 0]X >= [0 0 0]X = n__incr(X)
                [0 0 0]     [0 0 0]              
      
               [1 1 0]    [1]    [1 1 0]    [0]            
      adx(X) = [0 0 0]X + [1] >= [0 0 0]X + [1] = n__adx(X)
               [0 0 0]    [0]    [0 0 0]    [0]            
      
                         [0]    [0]      
      activate(n__0()) = [0] >= [0] = 0()
                         [0]    [0]      
      
                             [0]    [0]          
      activate(n__zeros()) = [0] >= [0] = zeros()
                             [0]    [0]          
      
                          [1 0 1]     [1 0 1]        
      activate(n__s(X)) = [0 0 0]X >= [0 0 0]X = s(X)
                          [0 0 0]     [0 0 0]        
      
                             [1 0 0]     [1 0 0]           
      activate(n__incr(X)) = [0 0 0]X >= [0 0 0]X = incr(X)
                             [0 0 0]     [0 0 0]           
      
                            [1 1 0]    [1]    [1 1 0]    [1]         
      activate(n__adx(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = adx(X)
                            [0 0 0]    [0]    [0 0 0]    [0]         
      
                    [1 1 0]          
      activate(X) = [0 1 1]X >= X = X
                    [0 0 1]          
     problem:
      zeros() -> cons(n__0(),n__zeros())
      incr(cons(X,Y)) -> cons(n__s(activate(X)),n__incr(activate(Y)))
      adx(cons(X,Y)) -> incr(cons(activate(X),n__adx(activate(Y))))
      0() -> n__0()
      s(X) -> n__s(X)
      incr(X) -> n__incr(X)
      activate(n__0()) -> 0()
      activate(n__zeros()) -> zeros()
      activate(n__s(X)) -> s(X)
      activate(n__incr(X)) -> incr(X)
      activate(n__adx(X)) -> adx(X)
      activate(X) -> X
     Unfolding Processor:
      loop length: 5
      terms:
       incr(cons(X,n__adx(cons(x22945,n__zeros()))))
       cons(n__s(activate(X)),n__incr(activate(n__adx(cons(x22945,n__zeros())))))
       cons(n__s(activate(X)),n__incr(adx(cons(x22945,n__zeros()))))
       cons(n__s(activate(X)),n__incr(incr(cons(activate(x22945),n__adx(activate(n__zeros()))))))
       cons(n__s(activate(X)),n__incr(incr(cons(activate(x22945),n__adx(zeros())))))
      context: cons(n__s(activate(X)),n__incr([]))
      substitution:
       X -> activate(x22945)
       x22945 -> n__0()
      Qed