YES

Problem:
 __(__(X,Y),Z) -> __(X,__(Y,Z))
 __(X,nil()) -> X
 __(nil(),X) -> X
 U11(tt()) -> U12(tt())
 U12(tt()) -> tt()
 isNePal(__(I,__(P,I))) -> U11(tt())
 activate(X) -> X

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                    [1 0 0]     [1]
   [activate](x0) = [1 1 1]x0 + [1]
                    [0 0 1]     [1],
   
                   [1 0 0]     [0]
   [isNePal](x0) = [0 0 0]x0 + [1]
                   [0 0 0]     [1],
   
               [1 0 0]  
   [U12](x0) = [0 0 0]x0
               [0 0 1]  ,
   
               [1 0 0]     [0]
   [U11](x0) = [0 0 0]x0 + [0]
               [0 0 0]     [1],
   
          [0]
   [tt] = [0]
          [1],
   
           [1]
   [nil] = [0]
           [0],
   
                         
   [__](x0, x1) = x0 + x1
                         
  orientation:
                                                         
   __(__(X,Y),Z) = X + Y + Z >= X + Y + Z = __(X,__(Y,Z))
                                                         
   
                     [1]         
   __(X,nil()) = X + [0] >= X = X
                     [0]         
   
                     [1]         
   __(nil(),X) = X + [0] >= X = X
                     [0]         
   
               [0]    [0]            
   U11(tt()) = [0] >= [0] = U12(tt())
               [1]    [1]            
   
               [0]    [0]       
   U12(tt()) = [0] >= [0] = tt()
               [1]    [1]       
   
                            [2 0 0]    [1 0 0]    [0]    [0]            
   isNePal(__(I,__(P,I))) = [0 0 0]I + [0 0 0]P + [1] >= [0] = U11(tt())
                            [0 0 0]    [0 0 0]    [1]    [1]            
   
                 [1 0 0]    [1]         
   activate(X) = [1 1 1]X + [1] >= X = X
                 [0 0 1]    [1]         
  problem:
   __(__(X,Y),Z) -> __(X,__(Y,Z))
   U11(tt()) -> U12(tt())
   U12(tt()) -> tt()
   isNePal(__(I,__(P,I))) -> U11(tt())
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                    [1 1 0]     [0]
    [isNePal](x0) = [0 0 0]x0 + [1]
                    [0 0 0]     [1],
    
                [1 0 0]     [0]
    [U12](x0) = [0 0 0]x0 + [0]
                [0 0 0]     [1],
    
                [1 0 0]     [0]
    [U11](x0) = [0 0 0]x0 + [1]
                [0 0 1]     [0],
    
           [0]
    [tt] = [0]
           [1],
    
                   [1 0 0]     [1 0 0]     [0]
    [__](x0, x1) = [0 1 1]x0 + [1 0 1]x1 + [0]
                   [0 0 0]     [0 0 0]     [1]
   orientation:
                    [1 0 0]    [1 0 0]    [1 0 0]    [0]    [1 0 0]    [1 0 0]    [1 0 0]    [0]                
    __(__(X,Y),Z) = [0 1 1]X + [1 0 1]Y + [1 0 1]Z + [1] >= [0 1 1]X + [1 0 0]Y + [1 0 0]Z + [1] = __(X,__(Y,Z))
                    [0 0 0]    [0 0 0]    [0 0 0]    [1]    [0 0 0]    [0 0 0]    [0 0 0]    [1]                
    
                [0]    [0]            
    U11(tt()) = [1] >= [0] = U12(tt())
                [1]    [1]            
    
                [0]    [0]       
    U12(tt()) = [0] >= [0] = tt()
                [1]    [1]       
    
                             [3 1 1]    [2 0 0]    [1]    [0]            
    isNePal(__(I,__(P,I))) = [0 0 0]I + [0 0 0]P + [1] >= [1] = U11(tt())
                             [0 0 0]    [0 0 0]    [1]    [1]            
   problem:
    __(__(X,Y),Z) -> __(X,__(Y,Z))
    U11(tt()) -> U12(tt())
    U12(tt()) -> tt()
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [U12](x0) = 2x0,
     
     [U11](x0) = x0 + 2,
     
     [tt] = 2,
     
     [__](x0, x1) = x0 + x1 + 4
    orientation:
     __(__(X,Y),Z) = X + Y + Z + 8 >= X + Y + Z + 8 = __(X,__(Y,Z))
     
     U11(tt()) = 4 >= 4 = U12(tt())
     
     U12(tt()) = 4 >= 2 = tt()
    problem:
     __(__(X,Y),Z) -> __(X,__(Y,Z))
     U11(tt()) -> U12(tt())
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                  [1 0 0]  
      [U12](x0) = [0 0 0]x0
                  [0 0 0]  ,
      
                  [1 0 1]  
      [U11](x0) = [0 0 0]x0
                  [0 0 0]  ,
      
             [0]
      [tt] = [0]
             [1],
      
                     [1 0 0]     [1 0 0]  
      [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                     [0 0 0]     [0 0 0]  
     orientation:
                      [1 0 0]    [1 0 0]    [1 0 0]     [1 0 0]    [1 0 0]    [1 0 0]                 
      __(__(X,Y),Z) = [0 0 0]X + [0 0 0]Y + [0 0 0]Z >= [0 0 0]X + [0 0 0]Y + [0 0 0]Z = __(X,__(Y,Z))
                      [0 0 0]    [0 0 0]    [0 0 0]     [0 0 0]    [0 0 0]    [0 0 0]                 
      
                  [1]    [0]            
      U11(tt()) = [0] >= [0] = U12(tt())
                  [0]    [0]            
     problem:
      __(__(X,Y),Z) -> __(X,__(Y,Z))
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [__](x0, x1) = 2x0 + x1 + 1
      orientation:
       __(__(X,Y),Z) = 4X + 2Y + Z + 3 >= 2X + 2Y + Z + 2 = __(X,__(Y,Z))
      problem:
       
      Qed