Raspberry canes in compost?

Was just chopping up some old autumn raspberry canes - decided to put 'em in the compost heap for good "browns", and I notice a couple of them were beginning to sprout.

Question, I know you can root your own canes for next season - am I likely to get lots of raspberries growing in the compost heap, or will they break down OK? Should I tip them rather than compost?

I cut them into approx 10cm pieces...hoping in a year or so they'll have broken down?

Advice please?

Phill