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All damage is dealt at once, therefore for your question O will be dealt 2 damage, but since toughness reduces damage by 1, O is dealt 1 damage.
Since Armor Piercing states damage dealt by this character may not be reduced below 1, and since O would be dealt 1 damage even after toughness for the above example, Armor Piercing won't effect the result, so O is dealt 1 damage.
So, in your example, O would be dealt 2 damage, reduced to 1 by Toughness: O takes 1 damage.
Same thing with Armor Piercing.
But let's take the same example, and say O has Invulnerability instead of Toughness: he'd still be dealt 2 damage, which should be reduced to 0 by Invulnerability, but because of AP, it is only reduced to 1: O takes 1 damage.