The ADA compliance for carpets reads as below: 

4.5.3* Carpet
If carpet or carpet tile is used on a ground or floor surface, then it shall be securely attached; have a firm cushion, pad, or backing, or no cushion or pad; and have a level loop, textured loop, level cut pile, or level cut/uncut pile texture. The maximum pile thickness shall be 1/2 in (13 mm).

Exposed edges of carpet shall be fastened to floor surfaces and have trim along the entire length of the exposed edge. Carpet edge trim shall comply with 4.5.2.

4.5.2 Changes in Level
Changes in level up to 1/4 in (6 mm) may be vertical and without edge treatment.

Changes in level between 1/4 in and 1/2 in (6 mm and 13 mm) shall be beveled with a slope no greater than 1:2.

Changes in level greater than 1/2 in (13 mm) shall be accomplished by means of a ramp that complies with 4.7 or 4.8.

Applying this to our carpets we will list below the options that can be achieved without the need of a beveled edge treatment or a beveled slope. 

Our standard overlock binding is not beveled, so all our area rugs fall in this category. The carpet products you can work with are dependent on the type. 

Option 2