From the AGR:

"2.6.0.4 While a split card is in a player’s hand, deck, discard pile, or removed from game area (See 4.0 Zones of Play) it may be targeted by a card or effect that targets either side of the card."

Basically, a split counts as BOTH types while in out of play zones. So a split attack/anything always counts as an attack while in the deck or discard pile. So Split attacks stop the Contemplation loop.