forms - Can sign up/log in be unified in one button?

I'm working a form at the moment and was consider merging sign in and sign up but thought it might be confusing. Is there any precedent for this?

Example

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This has been asked before but the answer was more about the word selection and pointed to this article which I thought was a bit off the point.

Or alternatively, what if the button was dynamic i.e. if the email address was recognised they'd see a button saying 'Log in' but if it wasn't then it would say 'Sign Up':

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Answer

I think combining the two will be confusing. The reason why companies create two distinct paths is because those two are different paths.

What happens if someone thinks they have an account, and then when they don't and they start registering and they don't want that, what then? This is forcing a user to register if they don't have a login, and that's not a good idea.

Instead, just create two different paths:

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