@[Matthew](https://forum.azimuthproject.org/profile/1818/Matthew%20Doty), you're right. There's probably some statement I could make about the free symmetric monoidal preorder generated by the desired reactions, but that's just kicking the can down the road. (See Section 25.2 of John's book, [Quantum Techniques for Stochastic Mechanics](https://arxiv.org/abs/1209.3632).) Let's see if I can recover this.

(**EDIT:** Also worth noting here that my thought process went badly off track when I said that Marius' and my rules were ultimately the same. Mine was _very_ wrong.)

First, consider that every complex \$$(x, y, z)\$$ can be written uniquely as \$$(2x_q + x_r, y, z)\$$ with \$$0 \le x_r < 2\$$ -- in other words, dividing \$$x\$$ by 2 and getting a quotient and remainder. (We'd only be dividing the others by 1, so we'll leave them alone.)

Now, we say that \$$(2x_q + x_r, y, z) \le (2x'_q + x'_r, y', z')\$$ iff the following statements hold for some \$$c \in \mathbb{N}\$$:

$$c = x_q - x'_q$$
$$0 = x_r - x'_r$$
$$c = y - y'$$
$$c = z' - z$$

When \$$c = 0\$$, we get the reflexive case. As \$$c\$$ increases, we utilize more of the available resources.