The chemical reaction for combustion of methane is:
CH4 + 2 O2 → CO2 + 2 H2O (ΔH = −891 kJ/mol (at standard conditions))
Any reaction converting CO2 back into methane will consume 891 kJ/mol if 100% efficient. And no process is 100% efficient. So (and thermodynamics guarantees this result, hence no 'perpetual motion' machines) converting the same chemical reaction back and forth must ALWAYS result in a net energy LOSS. I'm a physicist, not a chemist, but this is pretty basic stuff.
Sounds like enough energy to keep the stack blowing eh!
I have no doubt they will be utterly mystified!