NO

Problem:
 zeros() -> cons(0(),n__zeros())
 and(tt(),X) -> activate(X)
 length(nil()) -> 0()
 length(cons(N,L)) -> s(length(activate(L)))
 take(0(),IL) -> nil()
 take(s(M),cons(N,IL)) -> cons(N,n__take(M,activate(IL)))
 zeros() -> n__zeros()
 take(X1,X2) -> n__take(X1,X2)
 activate(n__zeros()) -> zeros()
 activate(n__take(X1,X2)) -> take(X1,X2)
 activate(X) -> X

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [n__take](x0, x1) = x0 + 2x1,
   
   [take](x0, x1) = 2x0 + 4x1,
   
   [s](x0) = x0,
   
   [length](x0) = 2x0,
   
   [nil] = 0,
   
   [activate](x0) = 2x0,
   
   [and](x0, x1) = 4x0 + 4x1 + 1,
   
   [tt] = 1,
   
   [cons](x0, x1) = 4x0 + 2x1,
   
   [n__zeros] = 2,
   
   [0] = 0,
   
   [zeros] = 4
  orientation:
   zeros() = 4 >= 4 = cons(0(),n__zeros())
   
   and(tt(),X) = 4X + 5 >= 2X = activate(X)
   
   length(nil()) = 0 >= 0 = 0()
   
   length(cons(N,L)) = 4L + 8N >= 4L = s(length(activate(L)))
   
   take(0(),IL) = 4IL >= 0 = nil()
   
   take(s(M),cons(N,IL)) = 8IL + 2M + 16N >= 8IL + 2M + 4N = cons(N,n__take(M,activate(IL)))
   
   zeros() = 4 >= 2 = n__zeros()
   
   take(X1,X2) = 2X1 + 4X2 >= X1 + 2X2 = n__take(X1,X2)
   
   activate(n__zeros()) = 4 >= 4 = zeros()
   
   activate(n__take(X1,X2)) = 2X1 + 4X2 >= 2X1 + 4X2 = take(X1,X2)
   
   activate(X) = 2X >= X = X
  problem:
   zeros() -> cons(0(),n__zeros())
   length(nil()) -> 0()
   length(cons(N,L)) -> s(length(activate(L)))
   take(0(),IL) -> nil()
   take(s(M),cons(N,IL)) -> cons(N,n__take(M,activate(IL)))
   take(X1,X2) -> n__take(X1,X2)
   activate(n__zeros()) -> zeros()
   activate(n__take(X1,X2)) -> take(X1,X2)
   activate(X) -> X
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                        [1 0 1]     [1 1 0]  
    [n__take](x0, x1) = [1 0 0]x0 + [0 0 1]x1
                        [0 1 1]     [0 0 0]  ,
    
                     [1 0 1]     [1 1 0]  
    [take](x0, x1) = [1 0 0]x0 + [0 0 1]x1
                     [1 1 1]     [0 0 1]  ,
    
              [1 0 0]  
    [s](x0) = [0 0 0]x0
              [0 1 1]  ,
    
                   [1 0 0]     [0]
    [length](x0) = [0 0 0]x0 + [0]
                   [0 0 0]     [1],
    
            [1]
    [nil] = [0]
            [0],
    
                     [1 0 0]  
    [activate](x0) = [0 1 0]x0
                     [0 1 1]  ,
    
                     [1 0 0]     [1 0 0]  
    [cons](x0, x1) = [0 0 0]x0 + [0 1 0]x1
                     [0 1 0]     [0 1 1]  ,
    
                 [0]
    [n__zeros] = [0]
                 [1],
    
          [0]
    [0] = [0]
          [1],
    
              [0]
    [zeros] = [0]
              [1]
   orientation:
              [0]    [0]                       
    zeros() = [0] >= [0] = cons(0(),n__zeros())
              [1]    [1]                       
    
                    [1]    [0]      
    length(nil()) = [0] >= [0] = 0()
                    [1]    [1]      
    
                        [1 0 0]    [1 0 0]    [0]    [1 0 0]    [0]                         
    length(cons(N,L)) = [0 0 0]L + [0 0 0]N + [0] >= [0 0 0]L + [0] = s(length(activate(L)))
                        [0 0 0]    [0 0 0]    [1]    [0 0 0]    [1]                         
    
                   [1 1 0]     [1]    [1]        
    take(0(),IL) = [0 0 1]IL + [0] >= [0] = nil()
                   [0 0 1]     [1]    [0]        
    
                            [1 1 0]     [1 1 1]    [1 0 0]     [1 1 0]     [1 0 1]    [1 0 0]                                   
    take(s(M),cons(N,IL)) = [0 1 1]IL + [1 0 0]M + [0 1 0]N >= [0 1 1]IL + [1 0 0]M + [0 0 0]N = cons(N,n__take(M,activate(IL)))
                            [0 1 1]     [1 1 1]    [0 1 0]     [0 1 1]     [1 1 1]    [0 1 0]                                   
    
                  [1 0 1]     [1 1 0]      [1 0 1]     [1 1 0]                   
    take(X1,X2) = [1 0 0]X1 + [0 0 1]X2 >= [1 0 0]X1 + [0 0 1]X2 = n__take(X1,X2)
                  [1 1 1]     [0 0 1]      [0 1 1]     [0 0 0]                   
    
                           [0]    [0]          
    activate(n__zeros()) = [0] >= [0] = zeros()
                           [1]    [1]          
    
                               [1 0 1]     [1 1 0]      [1 0 1]     [1 1 0]                
    activate(n__take(X1,X2)) = [1 0 0]X1 + [0 0 1]X2 >= [1 0 0]X1 + [0 0 1]X2 = take(X1,X2)
                               [1 1 1]     [0 0 1]      [1 1 1]     [0 0 1]                
    
                  [1 0 0]          
    activate(X) = [0 1 0]X >= X = X
                  [0 1 1]          
   problem:
    zeros() -> cons(0(),n__zeros())
    length(cons(N,L)) -> s(length(activate(L)))
    take(0(),IL) -> nil()
    take(s(M),cons(N,IL)) -> cons(N,n__take(M,activate(IL)))
    take(X1,X2) -> n__take(X1,X2)
    activate(n__zeros()) -> zeros()
    activate(n__take(X1,X2)) -> take(X1,X2)
    activate(X) -> X
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                         [1 0 1]     [1 0 0]     [0]
     [n__take](x0, x1) = [1 1 0]x0 + [1 0 0]x1 + [0]
                         [0 0 0]     [0 0 0]     [1],
     
                      [1 0 1]     [1 0 0]     [0]
     [take](x0, x1) = [1 1 0]x0 + [1 0 0]x1 + [1]
                      [0 0 0]     [0 0 0]     [1],
     
               [1 0 1]  
     [s](x0) = [0 0 0]x0
               [0 0 0]  ,
     
                    [1 0 0]  
     [length](x0) = [0 0 0]x0
                    [0 0 0]  ,
     
             [0]
     [nil] = [0]
             [0],
     
                      [1 0 0]  
     [activate](x0) = [0 1 1]x0
                      [0 1 1]  ,
     
                      [1 1 0]     [1 0 0]  
     [cons](x0, x1) = [0 0 0]x0 + [0 0 1]x1
                      [0 0 0]     [0 0 0]  ,
     
                  [1]
     [n__zeros] = [0]
                  [1],
     
           [0]
     [0] = [0]
           [1],
     
               [1]
     [zeros] = [1]
               [0]
    orientation:
               [1]    [1]                       
     zeros() = [1] >= [1] = cons(0(),n__zeros())
               [0]    [0]                       
     
                         [1 0 0]    [1 1 0]     [1 0 0]                          
     length(cons(N,L)) = [0 0 0]L + [0 0 0]N >= [0 0 0]L = s(length(activate(L)))
                         [0 0 0]    [0 0 0]     [0 0 0]                          
     
                    [1 0 0]     [1]    [0]        
     take(0(),IL) = [1 0 0]IL + [1] >= [0] = nil()
                    [0 0 0]     [1]    [0]        
     
                             [1 0 0]     [1 0 1]    [1 1 0]    [0]    [1 0 0]     [1 0 1]    [1 1 0]    [0]                                  
     take(s(M),cons(N,IL)) = [1 0 0]IL + [1 0 1]M + [1 1 0]N + [1] >= [0 0 0]IL + [0 0 0]M + [0 0 0]N + [1] = cons(N,n__take(M,activate(IL)))
                             [0 0 0]     [0 0 0]    [0 0 0]    [1]    [0 0 0]     [0 0 0]    [0 0 0]    [0]                                  
     
                   [1 0 1]     [1 0 0]     [0]    [1 0 1]     [1 0 0]     [0]                 
     take(X1,X2) = [1 1 0]X1 + [1 0 0]X2 + [1] >= [1 1 0]X1 + [1 0 0]X2 + [0] = n__take(X1,X2)
                   [0 0 0]     [0 0 0]     [1]    [0 0 0]     [0 0 0]     [1]                 
     
                            [1]    [1]          
     activate(n__zeros()) = [1] >= [1] = zeros()
                            [1]    [0]          
     
                                [1 0 1]     [1 0 0]     [0]    [1 0 1]     [1 0 0]     [0]              
     activate(n__take(X1,X2)) = [1 1 0]X1 + [1 0 0]X2 + [1] >= [1 1 0]X1 + [1 0 0]X2 + [1] = take(X1,X2)
                                [1 1 0]     [1 0 0]     [1]    [0 0 0]     [0 0 0]     [1]              
     
                   [1 0 0]          
     activate(X) = [0 1 1]X >= X = X
                   [0 1 1]          
    problem:
     zeros() -> cons(0(),n__zeros())
     length(cons(N,L)) -> s(length(activate(L)))
     take(s(M),cons(N,IL)) -> cons(N,n__take(M,activate(IL)))
     take(X1,X2) -> n__take(X1,X2)
     activate(n__zeros()) -> zeros()
     activate(n__take(X1,X2)) -> take(X1,X2)
     activate(X) -> X
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                          [1 0 1]     [1 0 0]     [0]
      [n__take](x0, x1) = [0 0 1]x0 + [0 0 0]x1 + [1]
                          [0 0 0]     [0 0 0]     [1],
      
                       [1 0 1]     [1 0 0]     [1]
      [take](x0, x1) = [0 0 1]x0 + [0 0 0]x1 + [1]
                       [0 0 0]     [0 0 0]     [1],
      
                [1 1 0]  
      [s](x0) = [0 0 0]x0
                [0 0 1]  ,
      
                     [1 0 0]     [1]
      [length](x0) = [0 0 0]x0 + [0]
                     [0 0 0]     [1],
      
                       [1 0 1]  
      [activate](x0) = [0 1 0]x0
                       [0 0 1]  ,
      
                       [1 0 0]     [1 0 1]  
      [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                       [0 0 0]     [0 0 0]  ,
      
                   [1]
      [n__zeros] = [0]
                   [0],
      
            [0]
      [0] = [0]
            [0],
      
                [1]
      [zeros] = [0]
                [0]
     orientation:
                [1]    [1]                       
      zeros() = [0] >= [0] = cons(0(),n__zeros())
                [0]    [0]                       
      
                          [1 0 1]    [1 0 0]    [1]    [1 0 1]    [1]                         
      length(cons(N,L)) = [0 0 0]L + [0 0 0]N + [0] >= [0 0 0]L + [0] = s(length(activate(L)))
                          [0 0 0]    [0 0 0]    [1]    [0 0 0]    [1]                         
      
                              [1 0 1]     [1 1 1]    [1 0 0]    [1]    [1 0 1]     [1 0 1]    [1 0 0]    [1]                                  
      take(s(M),cons(N,IL)) = [0 0 0]IL + [0 0 1]M + [0 0 0]N + [1] >= [0 0 0]IL + [0 0 0]M + [0 0 0]N + [0] = cons(N,n__take(M,activate(IL)))
                              [0 0 0]     [0 0 0]    [0 0 0]    [1]    [0 0 0]     [0 0 0]    [0 0 0]    [0]                                  
      
                    [1 0 1]     [1 0 0]     [1]    [1 0 1]     [1 0 0]     [0]                 
      take(X1,X2) = [0 0 1]X1 + [0 0 0]X2 + [1] >= [0 0 1]X1 + [0 0 0]X2 + [1] = n__take(X1,X2)
                    [0 0 0]     [0 0 0]     [1]    [0 0 0]     [0 0 0]     [1]                 
      
                             [1]    [1]          
      activate(n__zeros()) = [0] >= [0] = zeros()
                             [0]    [0]          
      
                                 [1 0 1]     [1 0 0]     [1]    [1 0 1]     [1 0 0]     [1]              
      activate(n__take(X1,X2)) = [0 0 1]X1 + [0 0 0]X2 + [1] >= [0 0 1]X1 + [0 0 0]X2 + [1] = take(X1,X2)
                                 [0 0 0]     [0 0 0]     [1]    [0 0 0]     [0 0 0]     [1]              
      
                    [1 0 1]          
      activate(X) = [0 1 0]X >= X = X
                    [0 0 1]          
     problem:
      zeros() -> cons(0(),n__zeros())
      length(cons(N,L)) -> s(length(activate(L)))
      take(s(M),cons(N,IL)) -> cons(N,n__take(M,activate(IL)))
      activate(n__zeros()) -> zeros()
      activate(n__take(X1,X2)) -> take(X1,X2)
      activate(X) -> X
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [n__take](x0, x1) = x0 + x1,
       
       [take](x0, x1) = 4x0 + 4x1 + 2,
       
       [s](x0) = x0,
       
       [length](x0) = 5x0 + 7,
       
       [activate](x0) = 4x0 + 2,
       
       [cons](x0, x1) = 2x0 + 4x1 + 2,
       
       [n__zeros] = 0,
       
       [0] = 0,
       
       [zeros] = 2
      orientation:
       zeros() = 2 >= 2 = cons(0(),n__zeros())
       
       length(cons(N,L)) = 20L + 10N + 17 >= 20L + 17 = s(length(activate(L)))
       
       take(s(M),cons(N,IL)) = 16IL + 4M + 8N + 10 >= 16IL + 4M + 2N + 10 = cons(N,n__take(M,activate(IL)))
       
       activate(n__zeros()) = 2 >= 2 = zeros()
       
       activate(n__take(X1,X2)) = 4X1 + 4X2 + 2 >= 4X1 + 4X2 + 2 = take(X1,X2)
       
       activate(X) = 4X + 2 >= X = X
      problem:
       zeros() -> cons(0(),n__zeros())
       length(cons(N,L)) -> s(length(activate(L)))
       take(s(M),cons(N,IL)) -> cons(N,n__take(M,activate(IL)))
       activate(n__zeros()) -> zeros()
       activate(n__take(X1,X2)) -> take(X1,X2)
      Unfolding Processor:
       loop length: 3
       terms:
        length(cons(N,n__zeros()))
        s(length(activate(n__zeros())))
        s(length(zeros()))
       context: s([])
       substitution:
        N -> 0()
       Qed