From Nate:

Ahh, yes. I answered a question about whether or not the two effects can be used in conjunction with one another. I overlooked the "to a minimum of 1" on Kuat Reinforcements. The reduction can only go down to cost 1.

Just an error in what I thought was being asked, and because the card text was not in front of me when I replied.

And then further clarification:

Going one step further with this. Using a card with a built in minimum on it, like Kuat Reinforcements, implants that minimum regardless of the order.

For instance, if I used Kuat Reinforcements once, it does 2 things: reduces the cost by 1, and implants a minimum of 1 as the absolute lowest that card's cost can be reduced to.

If I had another, theoretical reducer that was an interrupt, that said something like "Reduce the cost of the card by 8," I could use it, but the "minimum of 1" would still be in effect, and I could not reduce any further.

So the question of what comes first is moot, if any of the effects have planted a minimum, it must be observed.

That is very, very, good to know. This should be in the next FAQ imo.+1'd