Displays depupylase (DPUP) activity, removing conjugated Pup from target proteins; is thus involved in the recycling of Pup and may function similarly to deubiquitinases (DUBs) in eukaryotes to prevent or promote proteasomal degradation of certain proteins. Is also able to catalyze the deamidation of the C-terminal glutamine to glutamate in a variant of the prokaryotic ubiquitin-like protein Pup; however, since Pup from A.cellulolyticus possesses a C-terminal glutamate, this deamidase activity may be of no significance in vivo. ATP is required for the deamidation and depupylation reactions but is not hydrolyzed during the reactions. Protein degradation; proteasomal Pup-dependent pathway. Likely interacts with the C-terminal half of the prokaryotic ubiquitin-like protein Pup. Belongs to the Pup ligase/Pup deamidase family. Pup deamidase subfamily.