MyBB Community Forums

Keep an eye on GetSimple
http://get-simple.info/forums/index.php
It's a micro CMS on a GPLv3 license that doesn't use MySQL and is only a few files.
Porting to use MyBB tables shouldn't prove too difficult.
it's open source as well on Github:
https://github.com/GetSimpleCMS/GetSimpleCMS

Try it

I have tried it. but get a little difficulty when trying to integrate the template "MyBB" with "GetSimple"

Nah, just leave a space for either in your navigation and have both in their own subfolders or just rewrite some of GetSimple to work in the same folder as MyBB. Making a matching theme wouldn't be difficult.. I'm doing it right now.

Edit:
By tables I meant Database tables.. meaning having GetSimple use a comment function that parses/credentials users in the MyBB users table.

It's been 9 years since my last reply to this thread . just to let you know, it turns out that using Get-Simple is quite easy. can be combined with MyBB too

Forum with MyBB : https://www.indolokal.com
Forum with Get-Simple : https://www.indolokal.id