**Puzzle TF3.** Let \$$(X,\leq,\otimes,I)\$$ be a symmetric monoidal poset, and \$$\\in X\$$ an arbitrary element. (I'm only naming the element suggestively, no further properties should be required.) Now for given \$$x,y\in X\$$, define \$$\mathcal{X}(x,y)\$$ to be the smallest natural number \$$n\$$ such that \$$x \leq y \otimes \^{\otimes n}\$$ if such an \$$n\$$ exists, and \$$\infty\$$ otherwise. Prove that this makes \$$X\$$ into a **Cost**-enriched category! What is its resource-theoretic interpretation?