Complex sentence: After another tour leg supporting the remix album "Further Down the Spiral", Nine Inch Nails contributed to the Alternative Nation Festival in Australia and subsequently embarked on the Dissonance Tour, which included 26 separate performances with co-headliner David Bowie.
Split into simpler sentences: After another tour leg supporting the remix album "Further Down the Spiral", Nine Inch Nails contributed to the Alternative Nation Festival in Australia. Following the three-date alternative music festival, Nine Inch Nails embarked on the Dissonance Tour, which included 26 separate performances with co-headliner David Bowie.