If you didn't have any joint accounts, didn't file taxes together, didn't have both names on leases, rent, bills, etc, then I'm pretty sure CIC doesn't consider that common-law and wouldn't need proof of the relationship ending... they wouldn't even need to know about it.
If you were trying to apply as a common-law partner without the things you mentioned, CIC would reject the application. But that doesn't mean you weren't common law, it just means you couldn't prove it.
If you were living with someone for a year-and-a-half, and having sex with this person, it was a common-law relationship. I would include it. You can include a letter explaining the extent of your involvement and how you have no legal proof it's over.