Complex sentence: After the Battle of Champion's Hill John McClernand's corps chased the remaining confederates towards Vicksburg, on May 17th of 1863, they arrived at the rebel defenses in front of the Big Black River.
Split into simpler sentences: After the Battle of Champion's Hill John McClernand's corps chased the remaining confederates towards Vicksburg. On May 17,1863, they arrived at the rebel defenses in front of the Big Black River.