What is the test for federal habeas relief under the AEDPA?

Death Penalty Act of 1996 ("AEDPA"), 28 U.S.C. 2254(d). AEDPA limits "the availability of federal habeas relief ... with respect to claims previously adjudicated on the merits in state-court proceedings." Harrington v. Richter , 562 U.S. 86, 92, 131 S.Ct. 770, 178 L.Ed.2d 624 (2011). The statute "bars relitigation" of such claims subject only to two exceptions. Id. at 98, 131 S.Ct. 770. Under AEDPA, federal habeas relief remains unavailable unless the state adjudication of the claim:

28 U.S.C. 2254(d).