How Cayley diagram change without requirement that actions are determined?

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The question is from the book "Visual group theory" by Nathan Carter. The book doesn't give an answer to this exercise so I post it here. It is the Exercise 2.14 at the page 24 of the pdf book.

Literally it says:

Exercise 2.14. Chapter 1 required groups to satisfy Rule 1.5, which states, "There is a predefined list of actions that never changes." How does this rule impact the appearance of Cayley diagrams? (Or how would diagrams be different if this rule were not a requirement?)

Earlier the book gives the definition of a group in the following way: A group is a set of actions satisfying the following rules:

Rule 1.5. There is a predefined list of actions that never changes.

Rule 1.6. Every action is reversible.

Rule 1.7. Every action is deterministic.

Rule 1.8. Any sequence of consecutive actions is also an action.