How long does it take for fecal matter to decompose?

A long, long time. Just like a compost heap, when you have moisture and warmth, the process takes less time. Out there in the wilds, you have a great variety of moisture levels and temps. Here in Wyoming, where I am, there are low levels of moisture and long winters, so fecal matter can be dug up years later-with lots of nasty pathogens still active. It would be a different story in, say, the swampy land of South Carolina. In the end, it becomes of great importance where we place our excreta. Dig down 6 to 8 inches at least 200 feet from a water source-and hide the spot well.