windows - Task Scheduler - Running a task logged off without admin rights

I have two user accounts, one is an admin and the other is a regular user, but only the second account has permissions to run a certain application.

Windows 8.1
User1: Admin
User2: Only user with access to run application X

Basically, I want to schedule a task to run the application each morning, but User2 is unable to run the tasks with "Run with highest privileges".

Is it possible to grant permission to User2 using User1? I've used icacls to grant permission to the Windows\Tasks and Windows\System32\Tasks folders to User2.

If only an administrator is able to run the task, is it possible to run a batch on User1 than runs application X as User2? Whilst logged off.

Thanks!