Disadvantages of this crypto system
A chemical simulation based proof of work? Interesting, but let's ignore how the mathematics work for generating a solution based on my input key being "rhubarb". And zero knowledge based verification of said vegetable? Seems tricky. Must we assume that a 'simulation' is akin to a one way function/hash/mining?  

But I would focus on #8, valuation.  A floating currency is set by the market environment, not individual consumers on a per contract basis.  How can Bob set a realistic price for your ChemiCoin(TM)? Especially as they're not underwritten by tangible assets.  I think that I'd mow your lawn for 100 ChemiCoin(TM). But if no one else values them similarly, I've effectively consumed my resources for no reward.  That's bad capitalism and realisation would be neigh on impossible.

#8, part 2. How can Alice validate execution of the contract if the other party is not reciprocating with ChemiCoin(TM) transactions on the ledger?  Did I really mow your lawn?

And on #13.  What use treasure if it can't be spent? At least the Pharaohs could spend their accumulated gold and jewels in the Underworld.  The more ChemiCoin(TM) I possess, the more I want to spend them. But they depreciate accordingly.  So why amass them in the first place?  I may be getting poorer the richer I get, and don't mean  morally.

It all seems very tricky mathematically and economically, with a highly divisive set of cryptographic ideas.