MATH.11:2 - Problem

Trying more sequences can leave a reachability question unresolved. A proposed formula may hold in the first few calculations but fail at a later step or a different branch. Guessing that an unweighted total stays constant can also fail when a rule replaces two units of one kind with three of another.

The difficulty is to obtain a relation from the actual rules and explain why it survives sequences of arbitrary finite length. A useful relation must then answer the question: a constant function is always preserved, but cannot distinguish a reachable proposal from an impossible one.

The result is a constructed invariant with its preservation argument and a consequence for the stated task. A failed search within the chosen expression family can instead identify a reason to change that family or try another method.