I'm going to make a slightly wacky suggestion. I wouldn't use a fully recycling system for only one person on a 40 year journey. An average US citizen eats about 1 ton of food every year, and this is widely recognised as more than is needed. For an astronaut with reduced physical activity and carefully chosen food types this can very easily be reduced to 60-70% of this (probably further). Freeze-dried and recombined with recycled water the mass that actually needs to be carried is only about 20% of this. In total about 5 tons of dried food would be needed for a 40 year journey. For comparison an Apollo Command/Service Module has a dry mass of about 11 tons and a NERVA rocket engine has a dry mass of about 34 tons.
Now you may say that 5 tons is still 5 tons, and waste should be avoided like the plague. Maybe you can imagine a bacterial faeces-to-food recycling system (yum!) that weighs less. But it is still going to be complex and bulky and weigh some not insignificant fraction of 5 tons, and wasted mass counts against you not only when accelerating your rocket up to cruise speed, but also when decelerating it at the end of your journey.
I'm guessing you aren't planning a 40 year one-way Hohmann transfer to Uranus where we can assume a relatively small capture burn, but either a round trip or some high velocity voyage with a large initial burn, high cruise speed and significant deceleration at the other end. If you take a large, bulky recycling system inside your crew compartment where it can actually be accessed, then you need to decelerate that as well. You also need to carry the extra fuel for this deceleration and accelerate that fuel to your cruise speed when you set off. It's mass relative to its remaining utility only increases during your journey. By contrast the mass relative to remaining utility for stored food remains constant.
Interestingly, your minimally treated, unrecycled waste could actually be helpful during deceleration. If you are planning a nuclear reactor for power generation then your means of propulsion should definitely be a nuclear thermal rocket engine, with the reactor being used for combined power and propulsion. In a liquid fuel rocket the energy is generated by a chemical process in the fuel itself, while in a nuclear thermal rocket the energy is generated by nuclear fission in the reactor and then transferred to an inert reaction mass, which then expands through the rocket nozzle, creating thrust. Why not put that waste to use as reaction mass during your deceleration burn?
Additionally, the stored carbohydrates in your food will liberate water vapour and carbon dioxide once metabolised (containing slightly more oxygen that you inhaled), which could help compensate for any inefficiency in your water and oxygen recycling systems. I'm finding it hard to pin down exact numbers, but it seems the total mass of faeces output by a human being is only around 10% of the food eaten. If we assume somewhere up to 80% of food eaten by mass is water, then perhaps half of the weight of the freeze-dried, stored food will be liberated as carbon dioxide and water.
Finally, the psychological value of freeze dried ice-cream to an astronaut isolated for FORTY years should not be overlooked.