[Apprentice123]

Simplification the grammar
S -> XYZ
X -> AXA | BXB | Z | E
Y -> AYB | BYA | Z | E
A -> a
B -> b
Z -> Zu | Zv | E


First step: Deleting empty productions
I find:

S -> XYZ | XY | XZ | YZ | X | Y | Z
X -> AXA | BXB | Z | AA | BB
Y -> AYB | BYA | Z | AB | BA
A -> a
B -> b
Z -> Zu | Zv | u | v

The first step is correct?

[mostyfriedman]

by simplification, do you mean putting it in Chomsky normal form?