have you actually made sure that os-prober is responsible?
you should troubleshoot that by either temporarily uninstalling it, or disabling it from grub config somehow (your task to find out how).

fwiw, os-prober does exactly that: it probes a partition until it finds some markers that telli which OS is installed.
it makes sense to me that this can take a long time if it doesn't find anyhthing, because it will search through the whole partition byte by byte.

Thanks for replying.

I run journalctl and it seems that there is only one place when the updater posing 11 minutes, after debugging sdb3.

I pasted only the relevant section here.

I ran the update without internet connection, but it made no difference.

Hi ondoho,

I uninstalled the os-prober, and ran the updater but in that case the other systems are not searched.

I looked at the long journalctl document and every operation is very fast, except the updater poses in one place (see the previous post) for 11 minutes. But why, that’s the question.

here's 11 minutes; it would seem a partition with an arch linux system is responsible.
do you have archlinux installed somewhere?

so this would be the WHAT - of course that still doesn't tell us about the WHY.

edit:
here's an older answer that might explain the WHY:
https://bbs.archlinux.org/viewtopic.php?id=155298
i guess you have to click & read all secondary links to fully understand .

this reminds me, i think you never told us what distro you're running this from.

FWIW I just fired up an Arch system that also has Mint and Win10 on the disks. mkconfig took only seconds.
grub-mount does exist on that sysstem.

Hi ondoho,

I am running os-prober from archlinux. I have only arch systems installed on my computer. So here we have a case when arch has problem updating arch; I have Manjaro also installed but that one also based on arch.

Now, I am in the process of installing debian. Will see how debian handles the update.

I report back soon.

Thanks for the link. I try the idea suggested in the post and I let you know the result.

if debian fails at this or not, that doesn't prove anything, because the os-prober program is the same across both distros.
i also don't remember which "idea" was "suggested".

I installed debian stretch. I installed debian because I am more familiar with it and the link you gave me indicated that os-prober developed by debian. I ran the update and the situation is similar to that of arch.
The debian updater hangs two times but it updates a bit faster, about 6 minutes.
Here is the relevant data: