Does a slow ipod 4 under warranty qualify for replacement if no solutions help the problem?

Ive restored it to brand new... tryed every solution out there but my ipod is slow and apps constantly crash ... you name the fix... i assure you i have done it.

I bought my ipod 4 only 6 months ago so its still under warranty. Can i get it replaced? has anyone had this problem too and got a replacement?