Given State Table
q | x=0 x=1 | z
--------------------------------
A | B E | 0
B | D A | 1
C | G A | 0
D | F G | 1
E | B C | 0
F | D G | 1
G | D E | 1
The SP partition is also ouput consistent. The smallest equivalent system is given below
q | x=0 x=1 | z
------------------------------------
A | B A | 0
B | D A | 1
D | D B | 1