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())

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [U12](x0) = x0,
   
   [nil] = 0,
   
   [U11](x0) = x0,
   
   [isNePal](x0) = x0,
   
   [__](x0, x1) = x0 + x1 + 3,
   
   [tt] = 6
  orientation:
   __(__(X,Y),Z) = X + Y + Z + 6 >= X + Y + Z + 6 = __(X,__(Y,Z))
   
   __(X,nil()) = X + 3 >= X = X
   
   __(nil(),X) = X + 3 >= X = X
   
   U11(tt()) = 6 >= 6 = U12(tt())
   
   U12(tt()) = 6 >= 6 = tt()
   
   isNePal(__(I,__(P,I))) = 2I + P + 6 >= 6 = U11(tt())
  problem:
   __(__(X,Y),Z) -> __(X,__(Y,Z))
   U11(tt()) -> U12(tt())
   U12(tt()) -> tt()
   isNePal(__(I,__(P,I))) -> U11(tt())
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [U12](x0) = x0,
    
    [U11](x0) = x0 + 1,
    
    [isNePal](x0) = 2x0 + 2,
    
    [__](x0, x1) = x0 + x1,
    
    [tt] = 0
   orientation:
    __(__(X,Y),Z) = X + Y + Z >= X + Y + Z = __(X,__(Y,Z))
    
    U11(tt()) = 1 >= 0 = U12(tt())
    
    U12(tt()) = 0 >= 0 = tt()
    
    isNePal(__(I,__(P,I))) = 4I + 2P + 2 >= 1 = U11(tt())
   problem:
    __(__(X,Y),Z) -> __(X,__(Y,Z))
    U12(tt()) -> tt()
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                 [1 0 0]     [1]
     [U12](x0) = [0 0 0]x0 + [1]
                 [0 0 0]     [0],
     
                    [1 0 0]     [1 0 0]     [0]
     [__](x0, x1) = [0 1 1]x0 + [0 0 1]x1 + [0]
                    [0 0 0]     [0 0 0]     [1],
     
            [0]
     [tt] = [0]
            [0]
    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 + [0 0 1]Y + [0 0 1]Z + [1] >= [0 1 1]X + [0 0 0]Y + [0 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]                
     
                 [1]    [0]       
     U12(tt()) = [1] >= [0] = tt()
                 [0]    [0]       
    problem:
     __(__(X,Y),Z) -> __(X,__(Y,Z))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                     [1 0 1]     [1 0 0]     [1]
      [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                     [1 0 0]     [0 0 1]     [1]
     orientation:
                      [2 0 1]    [1 0 1]    [1 0 0]    [3]    [1 0 1]    [1 0 1]    [1 0 0]    [2]                
      __(__(X,Y),Z) = [0 0 0]X + [0 0 0]Y + [0 0 0]Z + [0] >= [0 0 0]X + [0 0 0]Y + [0 0 0]Z + [0] = __(X,__(Y,Z))
                      [1 0 1]    [1 0 0]    [0 0 1]    [2]    [1 0 0]    [1 0 0]    [0 0 1]    [2]                
     problem:
      
     Qed