Yes of course there is anaerobic decomposition. It's not what we usually call composting though. Here's a little bit of info:
Anaerobic Compost is made with organisms that do not like air. These are the creatures that in nature do their work in the dank places we humans tend to avoid. Swamps, bogs, deep cold lakes etc. They will work on compost, but they work slowly. They tend to release noxious gases that are quite disagreeable. If you have ever left a bag of grass clippings and then tore it open a week later you have had a close encounter of the third kind with these creatures....Anaerobic piles will tend to have more likelihood to have an overabundance of nitrogen causing the dark slimy feel due to the fact that the organisms in such a pile have less of a need for nitrogen and high energy. They work slower, and the nitrogen will tend to convert to ammonia making a bit of a smelly mess. https://www.rivenrock.com/composttypes.htm
Anaerobic composting basically consists of piling up a bunch of organic materials, then letting them sit and rot, [while covered]. Pretty gross, huh? Well truthfully, yes, it is. Anaerobic bacteria are slow and inefficient, which means that your compost pile will have to sit there for at least a year, maybe longer, before the materials at the very bottom are fully composted. Second of all, microbes that do the decaying in anaerobic composting produce methane and sulfate gasses as a byproduct, something which we humans find very offensive. https://tomato-tips.com/aerobic-vs-anaerobic-composting-whats-the-difference.html
Here's a little bit about your styrofoam:
What is it?
Polystyrene is a petroleum-based plastic made from the styrene monomer. Most people know it under the name Styrofoam, which is actually the trade name of a polystyrene foam product used for housing insulation. Polystyrene is a light-weight material, about 95% air, with very good insulation properties and is used in all types of products from cups that keep your beverages hot or cold to packaging material that keep your computers safe during shipping.
Why not use it?
The biggest environmental health concern associated with polystyrene is the danger associated with Styrene, the basic building block of polystyrene. Styrene is used extensively in the manufacture of plastics, rubber, and resins. About 90,000 workers, including those who make boats, tubs and showers, are potentially exposed to styrene. Acute health effects are generally irritation of the skin, eyes, and upper respiratory tract, and gastrointestinal effects. Chronic exposure affects the central nervous system showing symptoms such as depression, headache, fatigue, and weakness, and can cause minor effects on kidney function and blood. Styrene is classified as a possible human carcinogen by the EPA and by the International Agency for Research on Cancer (IARC). A voluntary compliance program has been adopted by industries using styrene. The US Department of Labor, Occupational Safety & Health Administration unsuccessfully (a federal court overturned the ruling in 1992) tried to limit the amount of worker exposure to styrene to 50 parts per million (ppm). According to the Styrene Information and Research Center (SIRC), they still encourage their member companies to comply with the 50 ppm exposure limit. This program would reduce styrene exposures to a 50 ppm TWA with a 100 ppm (15 minute) ceiling.
-OSHA (US Dept of Labor, Occupational Safety & Health Administration)
A 1986 EPA report on solid waste named the polystyrene manufacturing process as the 5th largest creator of hazardous waste.Ã‚Â· The National Bureau of Standards Center for Fire Research identified 57 chemical byproducts released during the combustion of polystyrene foam. The process of making polystyrene pollutes the air and creates large amounts of liquid and solid waste.
Toxic chemicals leach out of these products into the food that they contain (especially when heated in a microwave). These chemicals threaten human health and reproductive systems.
it goes on from there https://www.earthresource.org/campaigns/capp/capp-styrofoam.html
Polystyrene contains the toxic substances Styrene and Benzene, suspected carcinogens and neurotoxins that are hazardous to human beings. Polystyrene food containers leach the toxin Styrene when they come into contact with warm food or drink, alcohol, oils and acidic foods causing contamination and posing a health risk to people. Over 100 US and Canadian, as well as some European and Asian cities have banned polystyrene food packaging as a result of negative impact to humans and the environment. https://www.way-to-go.org/doc/PolystyreneFactSheets.pdf