A,2    1,B     -2    0
  3    3        3    3
  2    2        2    2
  0   -1      L,1    3,M

----------------------------
In the left rectangle, from top, eliminate y_3,x_3,y_2,x_2
to get

 1   0
 0  -1

In the right rectangle, from bottom, eliminate x_0,x_1,y_0,y_1
to get

-2  0
 0  2
-----------------------------

Suppose we reconstruct from the bottom: start from the codim 2 complete
intersection in x_0,y_0,x_1,y_1,A,B,L,M

add x_2 via the pentagram (x_1,x_0,y_0,y_1,x_2)
add y_2 via the pentagram (x_2,x_1,y_0,y_1,y_2), eliminate x_0
add x_3 via the pentagram (x_2,y_0,y_1,y_2,x_3), eliminate x_1
add y_3 via the pentagram (x_3,x_2,y_1,y_2,y_3), eliminate y_0

On the other hand, suppose we reconstruct from the top: start from
the codim 2 complete intersection in x_3,y_3,x_2,y_2,A,B,L,M

add y_1 via the pentagram (y_2,y_3,x_3,x_2,y_1)
add y_0 via the pentagram (y_1,y_2,x_3,x_2,y_0), eliminate y_3
add x_1 via the pentagram (y_0,y_1,y_2,x_2,x_1), eliminate x_3
add x_0 via the pentagram (y_0,y_1,x_2,x_1,x_0), eliminate y_2