Nope, a single rule still has an infinite number of possibilities. As an example, multiplying both sides of the equation with an arbitrary constant produces a n

Nope, a single rule still has an infinite number of possibilities. As an example, multiplying both sides of the equation with an arbitrary constant produces a new valid equation, and there's an infinite number of constants to multiply with. (Bonus point: You get to choose what kind of infinity - countable or uncountable) The reason a move tree[1] in a chess game has a finite number of nodes is not due to the finite number of possible transforms, but due to the fact that the number of possible board states is finite. [1] graph, really.