As quoted on their v2.0 update,
https://play.google.com/store/apps/details?id=com.oasisfeng.greenify
What's New
v2.0 (rolling out)
Greenify now works on non-root devices! Try out the non-root working mode (without automatic hibernation due to privilege restriction).
Shortcut "Hibernate All" can now be created also from main menu in Greenify.
Greatly improved the stability of auto-hibernation service, especially on Android 4.4+.
Bugfixes.
https://play.google.com/store/apps/details?id=com.oasisfeng.greenify