Complex sentence: Following the release of these two songs, the band embarked on the Time Machine Tour in 2010 and 2011 with the first live performances of "Caravan" and "BU2B" as part of the nightly set list.
Split into simpler sentences: Following the release of these two songs, the band embarked on the Time Machine Tour in 2010 and 2011. The tour featured the first live performances of "Caravan" and "BU2B" as part of the nightly set list.