Hmm. The push representation makes sense because solve progress is entirely dependent on it. And the movement state tree can be reduced to the push tree, which would only prune useless paths. The push tree can probably also be pruned for moves that leave to softlock, but I wonder whether it can be reduced to a different representation still. Push tree already requires us to maintain a mask of where we can move to, so it's not computationally free. I can imagine representing box pushes as every position we can push it to in the current setup, but that would also make it more computationally expensive.

I feel like there's an interesting tradeoff of storing/computing cheap representations vs exploring a smaller tree.