homework and exercises - Finding the acceleration of Block attached using tricky string setup

Below shown is a setup, and block B starts from rest and moves towards right with a constant acceleration. Does the acceleration differ for the blocks ? I am a bit confused because of the tricky string setup. If after time t, the velocity of A with respect to B becomes v, then what would be the acceleration of A ?

My understanding is : After time t, Block B will be brought to rest instantaneously resulting in non-zero relative velocity which otherwise will continue to be 0.