Workshop under floor insulation

Been reading plenty on insulation and vapor barriers, totally confused, here is my senario, anyone see potential problems with this?
Trying to turn an existing storage building into a heated and cooled workshop/office. The floor is too close to the ground to crawl under completely, but it is open all the way around. I can only get my head and an arm underneath. There no problems of standing water underneath stays dry.
So I was thinking of cutting and glueing 2" styrofoam insulation to the underside of the 3/4" plywood flooring between the floor joists. Then putting rubber backed indoor/outdoor carpet on top of the flooring inside. I have no way of getting a vapor barrier up next to the flooring first. I live in North Carolina so climate is moderate just humid at times. My main concern is I don't want to create a situation that might rot the floor. It is still just a detached building so not like I'm trying to insulate my house or anything but still want to avoid any future problems if I can.
Thanks for any input
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What is under the floor? If it is dirt, lay out some plastic sheeting to keep the ground moisture out.

Sounds good to me.
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I think that would be fine as long as you mean the blue colored ridged insulation. IIRC it does not need a separate vapor barrior. I Do not think you need rubber backed indoor/outdoor carpet. Use whatever floor covering will suit the use and asthetics of the room. If you skirt the outside, below the sill, use a lattice or something that will allow good vebtalation. Make sure you keep the area underneath dry. Gutters and downspouts may be worth it in the future.
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