2

Does the first ability of Baral, Chief of Compliance also reduce alternative casting cost?

For example: What about the Overload cost of Cyclonic Rift - is that reduced by one colorless mana?

Or what about flashback costs - are they reduced?

5

Yes

As long as the cost involves mana, Baral will get the job done.

117.9d. If an alternative cost is being paid to cast a spell, any additional costs, cost increases, and cost reductions that affect that spell are applied to that alternative cost.

2

Yes.

Total cost
= mana cost or alternative cost
+ additional costs and cost increases
- cost reductions

That means that cost reductions are applied towards the total of the mana or alternative cost, additional costs and cost increases.

601.2f The player determines the total cost of the spell. Usually this is just the mana cost. Some spells have additional or alternative costs. Some effects may increase or reduce the cost to pay, or may provide other alternative costs. Costs may include paying mana, tapping permanents, sacrificing permanents, discarding cards, and so on. The total cost is the mana cost or alternative cost (as determined in rule 601.2b), plus all additional costs and cost increases, and minus all cost reductions. If multiple cost reductions apply, the player may apply them in any order. If the mana component of the total cost is reduced to nothing by cost reduction effects, it is considered to be {0}. It can’t be reduced to less than {0}. Once the total cost is determined, any effects that directly affect the total cost are applied. Then the resulting total cost becomes “locked in.” If effects would change the total cost after this time, they have no effect.

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