Yep -Besedin is one of the acrobatic skaters from COI.
I'm not particularly surprised they broke up. She hadn't planned to skate this year and only the fans brought her back to skating. If she had planned to skate competitively again, she probably would have had that cyst removed. Just seems as though she decided to try skating competitively again for the fans and for Peter - not for herself. When they withdrew at Nats, she spoke a lot about being upset about letting down Peter and the fans, but the last factor was her personal disappointment.
As for Peter, I'm sure he'll be able to find a new partner. There's definitely a lack of male ice dancers. Also, Ice dancing has quite a bit of longevity. While the hydroblading moves are probably tough on the knees, overall it's not as strenous on them as jumping.
So, good luck to both in whatever they persue.