Cai's Counterexample

Trying to come up with a counterexample for the "smallest variable first" strategy, Cai suggested the following table:

w x y z
-------
1 1 1 1
2 1 1 1
2 2 2 2
2 3 3 3

Here is the output of my algorithm:

w: A<1, 2>
x: B<3, 2, 1>
y: B<3, 2, 1>
z: A<1, B<3,2,1>>

And here is the table generated by this choices

  w x y z
  -------
+ 1 3 3 1
  2 1 1 1
  1 1 1 1
  2 2 2 2
+ 1 2 2 1
  2 3 3 3

As one can easily see there are additional rows.