I can't believe that I actually took time to do some research about this: apparently Asking Alexandria was founded in 2008 (which puts it in late 2000's), and the trap genre began developing in the early 2000's. Also, the trap genre has its roots on US southern hip-hop and crunk scenes, while the metalcore genre has it's roots on extreme metal and punk.
On a side note, Sepultura is the band that have the credits for layering the foundation of metalcore, and, believe me, they're in the scene long before people was even using computers to make music. In fact, Sepultura was formed in 1984, while the TR-808 (hence the 808's used in trap) was first commercialized in 1980.
