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=1
  
  interpretation:
   [rev](x0) = 2x0,
   
   [flatten](x0) = x0,
   
   [++](x0, x1) = x0 + x1 + 4,
   
   [nil] = 3,
   
   [unit](x0) = x0
  orientation:
   flatten(nil()) = 3 >= 3 = nil()
   
   flatten(unit(x)) = x >= x = flatten(x)
   
   flatten(++(x,y)) = x + y + 4 >= x + y + 4 = ++(flatten(x),flatten(y))
   
   flatten(++(unit(x),y)) = x + y + 4 >= x + y + 4 = ++(flatten(x),flatten(y))
   
   flatten(flatten(x)) = x >= x = flatten(x)
   
   rev(nil()) = 6 >= 3 = nil()
   
   rev(unit(x)) = 2x >= x = unit(x)
   
   rev(++(x,y)) = 2x + 2y + 8 >= 2x + 2y + 4 = ++(rev(y),rev(x))
   
   rev(rev(x)) = 4x >= x = x
   
   ++(x,nil()) = x + 7 >= x = x
   
   ++(nil(),y) = y + 7 >= y = y
   
   ++(++(x,y),z) = x + y + z + 8 >= x + y + z + 8 = ++(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(unit(x)) -> unit(x)
   rev(rev(x)) -> x
   ++(++(x,y),z) -> ++(x,++(y,z))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                  
    [rev](x0) = x0
                  ,
    
                    [1 0 1]  
    [flatten](x0) = [0 1 0]x0
                    [0 1 0]  ,
    
                   [1 0 1]       
    [++](x0, x1) = [0 1 0]x0 + x1
                   [0 1 0]       ,
    
            [0]
    [nil] = [1]
            [1],
    
                 [1 0 1]     [1]
    [unit](x0) = [0 1 0]x0 + [0]
                 [0 0 0]     [0]
   orientation:
                     [1]    [0]        
    flatten(nil()) = [1] >= [1] = nil()
                     [1]    [1]        
    
                       [1 0 1]    [1]    [1 0 1]              
    flatten(unit(x)) = [0 1 0]x + [0] >= [0 1 0]x = flatten(x)
                       [0 1 0]    [0]    [0 1 0]              
    
                       [1 1 1]    [1 0 1]     [1 1 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]    [1]    [1 1 1]    [1 0 1]                             
    flatten(++(unit(x),y)) = [0 1 0]x + [0 1 0]y + [0] >= [0 1 0]x + [0 1 0]y = ++(flatten(x),flatten(y))
                             [0 1 0]    [0 1 0]    [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]              
    
                   [1 0 1]    [1]    [1 0 1]    [1]          
    rev(unit(x)) = [0 1 0]x + [0] >= [0 1 0]x + [0] = unit(x)
                   [0 0 0]    [0]    [0 0 0]    [0]          
    
                            
    rev(rev(x)) = x >= x = x
                            
    
                    [1 1 1]    [1 0 1]         [1 0 1]    [1 0 1]                     
    ++(++(x,y),z) = [0 1 0]x + [0 1 0]y + z >= [0 1 0]x + [0 1 0]y + z = ++(x,++(y,z))
                    [0 1 0]    [0 1 0]         [0 1 0]    [0 1 0]                     
   problem:
    flatten(++(x,y)) -> ++(flatten(x),flatten(y))
    flatten(flatten(x)) -> flatten(x)
    rev(unit(x)) -> unit(x)
    rev(rev(x)) -> x
    ++(++(x,y),z) -> ++(x,++(y,z))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [rev](x0) = x0 + 1,
     
     [flatten](x0) = x0,
     
     [++](x0, x1) = 4x0 + x1 + 4,
     
     [unit](x0) = 4x0 + 4
    orientation:
     flatten(++(x,y)) = 4x + y + 4 >= 4x + y + 4 = ++(flatten(x),flatten(y))
     
     flatten(flatten(x)) = x >= x = flatten(x)
     
     rev(unit(x)) = 4x + 5 >= 4x + 4 = unit(x)
     
     rev(rev(x)) = x + 2 >= x = x
     
     ++(++(x,y),z) = 16x + 4y + z + 20 >= 4x + 4y + z + 8 = ++(x,++(y,z))
    problem:
     flatten(++(x,y)) -> ++(flatten(x),flatten(y))
     flatten(flatten(x)) -> flatten(x)
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [flatten](x0) = 2x0 + 3,
      
      [++](x0, x1) = x0 + 2x1 + 6
     orientation:
      flatten(++(x,y)) = 2x + 4y + 15 >= 2x + 4y + 15 = ++(flatten(x),flatten(y))
      
      flatten(flatten(x)) = 4x + 9 >= 2x + 3 = flatten(x)
     problem:
      flatten(++(x,y)) -> ++(flatten(x),flatten(y))
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [flatten](x0) = 6x0 + 1,
       
       [++](x0, x1) = 5x0 + 5x1 + 2
      orientation:
       flatten(++(x,y)) = 30x + 30y + 13 >= 30x + 30y + 12 = ++(flatten(x),flatten(y))
      problem:
       
      Qed