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Since the 1900s, the sense "fed up" has been used with the accusative (
ich habe deine Faulheit satt); use with the genitive (
ich bin deiner Faulheit satt), which was common in the 1800s and earlier, is marked as literary by the
Duden and
DWDS and rare in spoken language. A comparably uncommon variant using
sein with the accusative (
ich bin deine Faulheit satt) also exists.