Unequal Accelerations in Double Atwood Machine

[id the sloth]

I have a simple question about the Double Atwood machine.

I am able to follow the solution but one thing makes no sense to me. The accelerations for block A and block B are:

Why aren't these equal? If they aren't, doesn't that mean the rope stretches? Or is this just an effect of assuming a massless rope?

 

[id the sloth]

In the few minutes since posting this, I have realized my mistake.

a_b and a_a are not equal because that pulley is attached to a second pulley. When that pulley A and B are attached to moves up and down, it will add a term to both a_b and a_a, making them unequal.