Quite right. Magic is required to convert ALL waste to methane. But there is the possiblity of methane production. What's the science of that say?

Let's look into it;

David House states in his excellent book that 1000 lbs of human waste produces about 0.6 cubic meters of biogas. Now a short ton is 2,000 pounds. A metric ton is 2,204.62 pounds and one cubic meter equals a thousand litres.

So, that's 1,323.6 litres of biogas at standard temperature and pressure (STP) for each ton of human feces processed.

Now at STP 22.4 litres of a gas equate to one molar gram for the gas. 59.08 molar grams of gas per metric ton of feces.

Now on a volume basis, biogas consists 40% carbon dioxide and 60% methane - with small quantities of materials like hydrogen sulphide - all of must be removed to get pure methane.

Methane's molecular weight is 16. Carbon dioxide's molecular weight is 44. So, methane is 60% of the volume or 35.45 moles of that gas. Times 16 grams per mole that's 567.2 GRAMS per METRIC TON of feces! 40% carbon dioxide is 23.63 moles of that gas - times 44 grams per mole that's 1,039.7 GRAMS per METRIC TONS of feces!

On average humans eliminate 128 g of fresh feces per person per day with a pH value of around 6.6. Fresh feces contains

75% water and
21% organic solids,
5% bacterial biomass
5% nitogenous matter
5% carbohydrate
3% fats
2% other
4% calcium and iron phosphates

100 persons produce 12.8 kg per day. On a 280 day trip 100 persons produce 3.58 metric tons. In an efficient anaerobic digester (which has its own mass and must be carried aboard ship) this produces 2.03 KILOGRAMS of methane gas over the entire 280 day period.

Since the anaerobic digester is likely to weigh more than 2.03 kg its inclusion in the process is a net negative.

Now;

(1) Removing the water and purifying it for reuse, saves a substantial amount of water, 2.685 metric tons! Removing 9.637 litres of water PER DAY from 12.8 kg per day - is likely to involve a device far smaller than 2.685 tons - so this is a NET GAIN.

(2) Reducing the fats, carbohydrates, biomass, to water and carbon dioxide, and then reducing water to hydrogen and oxygen, and the carbon dioxide using the hydrogen to methane then to carbon and water, produces useful products that may be recycled - and also produce a net gain.

(3) Reducing the nitrogenous matter - to hydrogen and nitrogen gas - that may be used in a closed cycle system also produces a net gain.

(4) leaving dried ash consisting of calcium and iron phosphates that may be stored for later use on Mars.

So, a one ton system that recycles water and oxygen and eliminates CO2 produces carbon black that is used to absorb odours, and make phosphate powders that may fertilise plant growth on Mars, allows us to reduce bringing along 9.6 metric tons of consumables.

So, this is what we can expect from a well-designed system.