How many times has a BIG IP box been upgraded?

It is very hard to say how many times the box was upgraded. But you can have an idea

1) Check for /var/log/liveinstall.log.x files count. Every upgrade attempt creates separate file. But files count may be more or less then actual upgrades. Every failed upgrade will create one files per attempt. If the box was upgraded to HF then there will be 2 files: 1st for main version, 2d for HF but it is still considered as one upgrade.

2) You can check how many boot location available: tmsh show sys software Again, if the new version was installed to existing boot location, then you can not tell exact numbers of updates.

3) Software upgrades does not require license reactivation all the time. If the license was reactivated recently then you can follow with upgrades as many time as you want without license reactivation. If you want to get license reactivation count, you need to open a case with F5 Support.