YES

Problem:
 div(X,e()) -> i(X)
 i(div(X,Y)) -> div(Y,X)
 div(div(X,Y),Z) -> div(Y,div(i(X),Z))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                   [1 0 0]       
   [div](x0, x1) = [0 0 1]x0 + x1
                   [0 1 0]       ,
   
         [1]
   [e] = [0]
         [0],
   
             [1 0 0]  
   [i](x0) = [0 0 1]x0
             [0 1 0]  
  orientation:
                [1 0 0]    [1]    [1 0 0]        
   div(X,e()) = [0 0 1]X + [0] >= [0 0 1]X = i(X)
                [0 1 0]    [0]    [0 1 0]        
   
                     [1 0 0]         [1 0 0]            
   i(div(X,Y)) = X + [0 0 1]Y >= X + [0 0 1]Y = div(Y,X)
                     [0 1 0]         [0 1 0]            
   
                         [1 0 0]             [1 0 0]                          
   div(div(X,Y),Z) = X + [0 0 1]Y + Z >= X + [0 0 1]Y + Z = div(Y,div(i(X),Z))
                         [0 1 0]             [0 1 0]                          
  problem:
   i(div(X,Y)) -> div(Y,X)
   div(div(X,Y),Z) -> div(Y,div(i(X),Z))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [div](x0, x1) = 4x0 + x1 + 4,
    
    [i](x0) = 4x0 + 1
   orientation:
    i(div(X,Y)) = 16X + 4Y + 17 >= X + 4Y + 4 = div(Y,X)
    
    div(div(X,Y),Z) = 16X + 4Y + Z + 20 >= 16X + 4Y + Z + 12 = div(Y,div(i(X),Z))
   problem:
    
   Qed