How long does it take to break down in someone's compost (backyard)?

That depends on the conditions; i.e. temperature, humidity, other organic matter, and the actual effort put forth by the homeowner in working their compost. Both ASTM D6400 (commercial compost) and EIN 13432 (home compost) require the packaging to disintegrate to a certain extent and to certain particle size within 84 days. Home composting requires disintegration in 120 days.