BDI (Bounded Depth Increase) is a new decidable first-order clause class. It strictly includes known classes such as PVD. The arity of function and predicate symbols as well as the shape of atoms is not restricted in BDI. Instead the shape of ‘cycles’ in resolution inferences is restricted so that the depth of generated clauses may increase but is still finitely bound. The BDI class is motivated by real-world problems where function terms are used to represent record structures. We show that the hyper-resolution calculus modulo redundancy elimination terminates on BDI clause sets. Employing this result to the ordered resolution calculus, we can also prove termination of ordered resolution on BDI, yielding a more efficient decision procedure.