tanumshede,
One way would be to:
1) Create a green stroke/nofill Rounded Rectangle with the desired Radius of the green bend and a Stroke Weight equalling the desired width,
2) Object>Path>Offset Path by the Stroke Weight/width,
3) Change the Stroke Color of the outer Rounded Rectangle,
4) Create a path crossing both Rounded Rectangles where the paths are to end and Object>Path>Divide Objects Below and delete the unwanted parts, using the Direct Selection Tool (at least) for the straight segments from the cutting path.
North America
Europe, Middle East and Africa
Asia Pacific