Upgrade Path from 2.1.0

I'm working with a client who has a custom application which was written using CodeIgniter v 2.1.0 and they want to upgrade the CodeIgniter environment as well as the PHP version that the application is sitting on (5.6.37) and the MySQL MariaDB (10.2.17).

Can I do a jump straight to 3.1.9 or do I need to go to 3.0.x first (doing all of the associated activities mentioned in the Release Notes) and then consider further upgrading the technical environment?

Any suggestions/hints/things to look out for when dealing with a system which has been neglected for this amount of time?

Thanks for any and all assistance.