[harerazer]

This is essentially calculating the Kolmogorov complexity of whatever the final state of memory wrt to the constrained assembly (and giving the associated program). Since the any program in the constrained assembly always halts, this is possible a la brute force.

It also doesn't seem particularly interesting because it doesn't allow the programs to get input. Obviously that makes things much more difficult wrt to proving program equivalence.

[manasij7479]

Input's and other side effects are not too tricky to handle.

In most cases, you just slice the program to isolate pure computation, and just optimize that.

Most traditional compiler optimizations stick to that as well, the exceptions to this rule are carefully engineered.