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?