Michael wrote:
>Define \$$(a, b, c) \leq (a', b', c')\$$ if and only if \$$a \gt a', b \gt b' \, and \, c \lt c'\$$.

I assume you are using the opposite convention I was using above where \$$x \le y \$$ means "If we have \$$x\$$ we can get \$$y\$$". I'm also assuming that you meant \$$(a, b, c) \leq (a', b', c')\$$ if and only if \$$a \ge a', b \ge b' \, and \, c \le c'\$$, since under your original definition \$$(a,b,c) \not\le (a,b,c)\$$ since \$$a \not\gt a\$$, \$$b \not\gt b\$$ and \$$c \not\lt c \$$.

Using this modified definition it is indeed the case that \$$(2,1,0) \le (0,0,1) \$$ as desired. But it is also the case that \$$(2,1,0) \le (0,0,8) \$$ which violates conservation of mass (probably undesired) as well as \$$(1,1,0) \le (0,0,1) \$$ which does not take the stoichiometry of the reaction into account (probably also undesired).

As far as I understood the question we need to take the set of all possible complexes into account, not just the ones resulting from valid applications of the Petri net.