Commutative production systems

Question

For the following production systems, how can I test and justify whether they are commutative or not?

Production System 1

Knowledge Base :

If A & B then C,

If C then D,

If A & D then E

Initial Working memory : {A,B}

Production System 2

Knowledge Base :

If A & B then C,

If X & Y then C,

If A then E,

If B then F

Initial Working memory : {A,B,X,Y}