Component of the cleavage and polyadenylation factor (CPF) complex, which plays a key role in polyadenylation-dependent pre-mRNA 3'-end formation and cooperates with cleavage factors including the CFIA complex and NAB4/CFIB. Component of the APT complex, which may be involved in polyadenylation-independent transcript 3'-end formation. SSU72 is required for 3'-end formation of snoRNAs. Processively dephosphorylates Ser-5 of the heptad repeats YSPTSPS in the C-terminal domain of the largest RNA polymerase II subunit (RPB1). H2O + O-phospho-L-seryl-[protein] = L-seryl-[protein] + phosphate H2O + O-phospho-L-threonyl-[protein] = L-threonyl-[protein] + phosphate Component of the cleavage and polyadenylation factor (CPF) complex, which is composed of PTI1, SYC1, SSU72, GLC7, MPE1, REF2, PFS2, PTA1, YSH1/BRR5, SWD2, CFT2/YDH1, YTH1, CFT1/YHH1, FIP1 and PAP1. Component of the APT complex, which is a subcomplex of CPF, and is composed of PTI1, SYC1, SSU72, GLC7, REF2, PTA1 and SWD2. Belongs to the SSU72 phosphatase family.