How long it takes for roots to decompose

Recently removed huge yucca and almost 15 clumps of golden cane. Removed stumps with stump grinding.

But my whole backyard is like web of roots. Soo many intertwined roots at just 20cm depth. I tried planting some fruit trees close to where golden cane was and it took me 30 mins just to dig 30cm hole.

Just curious, how long it takes for roots to decompose? There is no stump left. Just roots.

Thanks.