rubber tire shreds that are "paved"? I've seen those at parks. It is like very cushy asphalt (they are glued together somehow, not loose).

I'm not sure I know what you are asking. Is the "terrace" like a patio below the deck? How about artificial grass?

The tire stuff stinks. Figuratively and literally. It doesn't stop small seedlings from weeds and trees growing in it, and it's difficult to remove leaves and other debris from it. It also smells to high heaven in the sun. There is also some controversy as to it being a negative environmental impact because of the chemicals in the tires leaching rather than a positive one because of the recycling.

There's nothing wrong with plain pine bark if you want a soft area for kids to play. But, if you want to place a table and chairs there, you need hard surfacing. You're not going to be able to carpet the world to keep kids from falling down and hurting themselves and there's nothing wrong with a nice flagstone patio under your deck and teaching the kids not to do horseplay on hard surfaces. Or just wait for the skinned knee to teach them that for themselves.