The advantage of any checked memory management scheme, be it a runtime thing like a tracing gc or a fancy type system, is not to give a tighter over-approximati

The advantage of any checked memory management scheme, be it a runtime thing like a tracing gc or a fancy type system, is not to give a tighter over-approximation of liveness but to guarantee that you never under-approximate it. In other words, preventing memory leaks is undecidable, but you can at least be sure you're not freeing useful memory.