The Attempt at a Solution
How is the regions in the given decomposition both type 1 and type 2 regions at the same time? Take the region at the upper right hand side as an example. It can't be neither type 1 and type 2 regions because the functions that are bounding the curve are not continuous. e.g. If I take the rightmost point as x=b, leftmost line as x=a, the lower function bounding y is not continuous.