In converting to chomsky, can i simplify the unit production S->Z of this language?

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S -> wZx | WyX | Z | yX | Wy | y 
W -> wW | w
X -> xX | x 
Z -> zZ | z

Making it

S -> wZx | WyX | zZ | z| yX | Wy | y 
W -> wW | w
X -> xX | x 

is just wrong. So i'm wondering if this unit production should just stay as it is

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