The Maintenance plan failed when it was trying to rebuild the index [index_one] ON [dbo].[table_one] due to a deadlock. The best place to check is the Maintenance Plan Log file which could give you more information on what tables or indexes the operation had succeded.

It is not recommended to do the rebuilds diuring the Office Hours. Do those rebuilds during the night or during the weekend.

Thank You,

Best Regards,

SQLBuddy