What about my plans - can I use the 144-Hour-Permit?

I want to fly from Germany to Shanghai (direct flight), stay there for three nights, then fly from Shanghai to Taipeh. After ten days I return from Taipeh to fly back to Shanghai, stay there for one night and then fly back to germany. In short: Frankfurt-Shanghai (3 nights) / Shanghai-Taipeh / Taipeh-Shanghai (1 night) / Shanghai-Frankfurt.