YES

Problem:
 flatten(nil()) -> nil()
 flatten(unit(x)) -> flatten(x)
 flatten(++(x,y)) -> ++(flatten(x),flatten(y))
 flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y))
 flatten(flatten(x)) -> flatten(x)
 rev(nil()) -> nil()
 rev(unit(x)) -> unit(x)
 rev(++(x,y)) -> ++(rev(y),rev(x))
 rev(rev(x)) -> x
 ++(x,nil()) -> x
 ++(nil(),y) -> y
 ++(++(x,y),z) -> ++(x,++(y,z))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
               [1 0 1]  
   [rev](x0) = [1 0 1]x0
               [0 1 0]  ,
   
                         
   [++](x0, x1) = x0 + x1
                         ,
   
                [1 1 1]     [0]
   [unit](x0) = [1 1 1]x0 + [1]
                [0 0 0]     [1],
   
                   [1 0 0]  
   [flatten](x0) = [0 1 0]x0
                   [0 1 0]  ,
   
           [0]
   [nil] = [1]
           [1]
  orientation:
                    [0]    [0]        
   flatten(nil()) = [1] >= [1] = nil()
                    [1]    [1]        
   
                      [1 1 1]    [0]    [1 0 0]              
   flatten(unit(x)) = [1 1 1]x + [1] >= [0 1 0]x = flatten(x)
                      [1 1 1]    [1]    [0 1 0]              
   
                      [1 0 0]    [1 0 0]     [1 0 0]    [1 0 0]                             
   flatten(++(x,y)) = [0 1 0]x + [0 1 0]y >= [0 1 0]x + [0 1 0]y = ++(flatten(x),flatten(y))
                      [0 1 0]    [0 1 0]     [0 1 0]    [0 1 0]                             
   
                            [1 1 1]    [1 0 0]    [0]    [1 0 0]    [1 0 0]                             
   flatten(++(unit(x),y)) = [1 1 1]x + [0 1 0]y + [1] >= [0 1 0]x + [0 1 0]y = ++(flatten(x),flatten(y))
                            [1 1 1]    [0 1 0]    [1]    [0 1 0]    [0 1 0]                             
   
                         [1 0 0]     [1 0 0]              
   flatten(flatten(x)) = [0 1 0]x >= [0 1 0]x = flatten(x)
                         [0 1 0]     [0 1 0]              
   
                [1]    [0]        
   rev(nil()) = [1] >= [1] = nil()
                [1]    [1]        
   
                  [1 1 1]    [1]    [1 1 1]    [0]          
   rev(unit(x)) = [1 1 1]x + [1] >= [1 1 1]x + [1] = unit(x)
                  [1 1 1]    [1]    [0 0 0]    [1]          
   
                  [1 0 1]    [1 0 1]     [1 0 1]    [1 0 1]                     
   rev(++(x,y)) = [1 0 1]x + [1 0 1]y >= [1 0 1]x + [1 0 1]y = ++(rev(y),rev(x))
                  [0 1 0]    [0 1 0]     [0 1 0]    [0 1 0]                     
   
                 [1 1 1]          
   rev(rev(x)) = [1 1 1]x >= x = x
                 [1 0 1]          
   
                     [0]         
   ++(x,nil()) = x + [1] >= x = x
                     [1]         
   
                     [0]         
   ++(nil(),y) = y + [1] >= y = y
                     [1]         
   
                                                         
   ++(++(x,y),z) = x + y + z >= x + y + z = ++(x,++(y,z))
                                                         
  problem:
   flatten(nil()) -> nil()
   flatten(unit(x)) -> flatten(x)
   flatten(++(x,y)) -> ++(flatten(x),flatten(y))
   flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y))
   flatten(flatten(x)) -> flatten(x)
   rev(++(x,y)) -> ++(rev(y),rev(x))
   rev(rev(x)) -> x
   ++(x,nil()) -> x
   ++(nil(),y) -> y
   ++(++(x,y),z) -> ++(x,++(y,z))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                  
    [rev](x0) = x0
                  ,
    
                          
    [++](x0, x1) = x0 + x1
                          ,
    
                 [1 0 0]     [0]
    [unit](x0) = [0 0 1]x0 + [0]
                 [0 0 1]     [1],
    
                    [1 0 1]  
    [flatten](x0) = [0 0 0]x0
                    [0 0 0]  ,
    
            [0]
    [nil] = [0]
            [0]
   orientation:
                     [0]    [0]        
    flatten(nil()) = [0] >= [0] = nil()
                     [0]    [0]        
    
                       [1 0 1]    [1]    [1 0 1]              
    flatten(unit(x)) = [0 0 0]x + [0] >= [0 0 0]x = flatten(x)
                       [0 0 0]    [0]    [0 0 0]              
    
                       [1 0 1]    [1 0 1]     [1 0 1]    [1 0 1]                             
    flatten(++(x,y)) = [0 0 0]x + [0 0 0]y >= [0 0 0]x + [0 0 0]y = ++(flatten(x),flatten(y))
                       [0 0 0]    [0 0 0]     [0 0 0]    [0 0 0]                             
    
                             [1 0 1]    [1 0 1]    [1]    [1 0 1]    [1 0 1]                             
    flatten(++(unit(x),y)) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y = ++(flatten(x),flatten(y))
                             [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]                             
    
                          [1 0 1]     [1 0 1]              
    flatten(flatten(x)) = [0 0 0]x >= [0 0 0]x = flatten(x)
                          [0 0 0]     [0 0 0]              
    
                                                     
    rev(++(x,y)) = x + y >= x + y = ++(rev(y),rev(x))
                                                     
    
                            
    rev(rev(x)) = x >= x = x
                            
    
                            
    ++(x,nil()) = x >= x = x
                            
    
                            
    ++(nil(),y) = y >= y = y
                            
    
                                                          
    ++(++(x,y),z) = x + y + z >= x + y + z = ++(x,++(y,z))
                                                          
   problem:
    flatten(nil()) -> nil()
    flatten(++(x,y)) -> ++(flatten(x),flatten(y))
    flatten(flatten(x)) -> flatten(x)
    rev(++(x,y)) -> ++(rev(y),rev(x))
    rev(rev(x)) -> x
    ++(x,nil()) -> x
    ++(nil(),y) -> y
    ++(++(x,y),z) -> ++(x,++(y,z))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                 [1 0 0]  
     [rev](x0) = [0 0 1]x0
                 [0 1 0]  ,
     
                           
     [++](x0, x1) = x0 + x1
                           ,
     
                     [1 0 0]  
     [flatten](x0) = [1 0 0]x0
                     [0 0 0]  ,
     
             [1]
     [nil] = [0]
             [0]
    orientation:
                      [1]    [1]        
     flatten(nil()) = [1] >= [0] = nil()
                      [0]    [0]        
     
                        [1 0 0]    [1 0 0]     [1 0 0]    [1 0 0]                             
     flatten(++(x,y)) = [1 0 0]x + [1 0 0]y >= [1 0 0]x + [1 0 0]y = ++(flatten(x),flatten(y))
                        [0 0 0]    [0 0 0]     [0 0 0]    [0 0 0]                             
     
                           [1 0 0]     [1 0 0]              
     flatten(flatten(x)) = [1 0 0]x >= [1 0 0]x = flatten(x)
                           [0 0 0]     [0 0 0]              
     
                    [1 0 0]    [1 0 0]     [1 0 0]    [1 0 0]                     
     rev(++(x,y)) = [0 0 1]x + [0 0 1]y >= [0 0 1]x + [0 0 1]y = ++(rev(y),rev(x))
                    [0 1 0]    [0 1 0]     [0 1 0]    [0 1 0]                     
     
                             
     rev(rev(x)) = x >= x = x
                             
     
                       [1]         
     ++(x,nil()) = x + [0] >= x = x
                       [0]         
     
                       [1]         
     ++(nil(),y) = y + [0] >= y = y
                       [0]         
     
                                                           
     ++(++(x,y),z) = x + y + z >= x + y + z = ++(x,++(y,z))
                                                           
    problem:
     flatten(nil()) -> nil()
     flatten(++(x,y)) -> ++(flatten(x),flatten(y))
     flatten(flatten(x)) -> flatten(x)
     rev(++(x,y)) -> ++(rev(y),rev(x))
     rev(rev(x)) -> x
     ++(++(x,y),z) -> ++(x,++(y,z))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [rev](x0) = 4x0 + 1,
      
      [++](x0, x1) = x0 + x1 + 4,
      
      [flatten](x0) = x0,
      
      [nil] = 0
     orientation:
      flatten(nil()) = 0 >= 0 = nil()
      
      flatten(++(x,y)) = x + y + 4 >= x + y + 4 = ++(flatten(x),flatten(y))
      
      flatten(flatten(x)) = x >= x = flatten(x)
      
      rev(++(x,y)) = 4x + 4y + 17 >= 4x + 4y + 6 = ++(rev(y),rev(x))
      
      rev(rev(x)) = 16x + 5 >= x = x
      
      ++(++(x,y),z) = x + y + z + 8 >= x + y + z + 8 = ++(x,++(y,z))
     problem:
      flatten(nil()) -> nil()
      flatten(++(x,y)) -> ++(flatten(x),flatten(y))
      flatten(flatten(x)) -> flatten(x)
      ++(++(x,y),z) -> ++(x,++(y,z))
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                             
       [++](x0, x1) = x0 + x1
                             ,
       
                       [1 0 1]  
       [flatten](x0) = [0 1 0]x0
                       [0 1 0]  ,
       
               [0]
       [nil] = [1]
               [1]
      orientation:
                        [1]    [0]        
       flatten(nil()) = [1] >= [1] = nil()
                        [1]    [1]        
       
                          [1 0 1]    [1 0 1]     [1 0 1]    [1 0 1]                             
       flatten(++(x,y)) = [0 1 0]x + [0 1 0]y >= [0 1 0]x + [0 1 0]y = ++(flatten(x),flatten(y))
                          [0 1 0]    [0 1 0]     [0 1 0]    [0 1 0]                             
       
                             [1 1 1]     [1 0 1]              
       flatten(flatten(x)) = [0 1 0]x >= [0 1 0]x = flatten(x)
                             [0 1 0]     [0 1 0]              
       
                                                             
       ++(++(x,y),z) = x + y + z >= x + y + z = ++(x,++(y,z))
                                                             
      problem:
       flatten(++(x,y)) -> ++(flatten(x),flatten(y))
       flatten(flatten(x)) -> flatten(x)
       ++(++(x,y),z) -> ++(x,++(y,z))
      Matrix Interpretation Processor: dim=1
       
       interpretation:
        [++](x0, x1) = 2x0 + x1 + 1,
        
        [flatten](x0) = 2x0
       orientation:
        flatten(++(x,y)) = 4x + 2y + 2 >= 4x + 2y + 1 = ++(flatten(x),flatten(y))
        
        flatten(flatten(x)) = 4x >= 2x = flatten(x)
        
        ++(++(x,y),z) = 4x + 2y + z + 3 >= 2x + 2y + z + 2 = ++(x,++(y,z))
       problem:
        flatten(flatten(x)) -> flatten(x)
       Matrix Interpretation Processor: dim=3
        
        interpretation:
                         [1 1 0]     [0]
         [flatten](x0) = [0 0 0]x0 + [1]
                         [0 0 0]     [0]
        orientation:
                               [1 1 0]    [1]    [1 1 0]    [0]             
         flatten(flatten(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = flatten(x)
                               [0 0 0]    [0]    [0 0 0]    [0]             
        problem:
         
        Qed