Ok, you can remove all db tables and files for sure.
First you can try uninstall in Extensions -> Extension Manager -> Manage
If you uninstall ARTIO Booking (Location: Administrator), it should remove all files and folders. Database can be removed manually, but it is not so necessary. When you will install Book it! 2, it should also modify old database tables.
If you can not uninstall it in admin Extension Manager, then you can try manual uninstallation:
How to unistall component manually (for Joomla 2.5.11):
Delete these folders/files:
1. administrator/components/com_booking
2. administrator/language/{lang-code}/{lang-code}.com_booking.ini
3. administrator/language/{lang-code}/{lang-code}.com_booking.common.ini
4. administrator/language/{lang-code}/{lang-code}.com_booking.menu.ini
5. administrator/language/{lang-code}/{lang-code}.com_booking.sys.ini
6. components/com_booking
7. modules/mod_booking_customer_info
8. modules/mod_booking_search
9. plugins/search/booking
10. plugins/user/booking
11. plugins/cciDEALPlatformCustomPayment
12. language/{lang-code}/{lang-code}.com_booking.ini
13. language/{lang-code}/{lang-code}.mod_booking_customer_info.ini
14. language/{lang-code}/{lang-code}.mod_booking_search.ini
Database:
We do not remove database tables for Booking, because we want to save older data.
But there are data about installed component which we have to remove:
1. DB Table #__extensions, you can find rows by name:
ARTIO Booking Customer Info - (type=module)
ARTIO Booking Search - (type=module)
cciDEAL Platfotm Payment Plugin for ARTIO Booking - (type=plugin)
Search - Booking - (type=plugin)
User_ARTIO_Booking - (type=plugin)
booking - (type=component)
These rows should be at the end of the table if the component was last thing you installed in Joomla
2. DB Table #__menu, you can find rows by combination of menutype and path
All rows should have menutype 'main' and path starts with 'artio-booking'.
But if you have not Booking in administration menu, it is possible that there will be no rows for Booking component.
This should be all for manual uninstallation.