Is there any Blackmagic pruduct for time shift?

I would like a fullHD product for time shift.
Like continusly recording and in the same time playback 10sec "time" shifted the same material.
I have a BMPC 4k and a BMMSC 4k so it's HD-SDI environment.
I'm planning to buy an ATEM Television Studio Pro HD for mixing.
Is it possibile whit any of Blackmagic recorder the time shift playback like I need?
Thanks
Andrew

Not directly. I have used the H.264 Pro Recorder with some Windows software to do this.
https://ianmorrish.wordpress.com/2016/11/19/instant-replay-time-shift-on-the-cheap/
This lets me feed the delayed source back into the ATEM while having a recorded file at the same time (using .TS file and REFs file system for reliability).
If you just want to delay the program out for live streaming then OBS (with a Decklink card) can do this using a memory buffer for playback while recording at the same time.

Anything else, especially UHD, seems very expensive (although professional).

http://www.softron.tv/

I used a BM mini-recorder and mini-monitor with their products to do something similar on one MacBook Pro - it will record to a growing file and play it back. They have trial versions. You need 'movie recorder' and 'on the air video' apps.

I'm pretty sure you need 2 BM devices to be able to record and play at the same time.

Thank you very much Ian!!
last night I had a test and it works fine with MX Light ...demo
setup: a BM TV Studio a PC with a simple HDD

I would like to ask you how to control vlc with the x key
please describe the process

I tried with "specify timecode" CTRL+t it works, but not that comfortable

Thank you!
Best
Andrew