Sheet processing apparatus and image forming system

A sheet processing apparatus includes a feed-in path through which a sheet is fed, a first transport path through which a sheet fed from the feed-in path is transported, and a second transport path through which a sheet fed from the feed-in path is transported. The sheet processing apparatus also includes the following elements. A first processor sequentially stacks sheets output from the first transport path and performs first processing on a bundle of stacked sheets. A second processor sequentially stacks sheets output from the second transport path and performs second processing, which is different from the first processing, on a bundle of stacked sheets. A common retention path causes a sheet fed through the feed-in path to temporarily remain on the common retention path and causes the sheet temporarily remaining on the common retention path to be output to one of the first and second transport paths.