Helmut Seidl. **Parameter Reduction of Higher Level Grammars**. *Theor. Comput. Sci.*, 55(1):47-85, 1987.

A higher level (OI-)grammar is called terminating, if for every accessible term there is at least one terminal term which can be derived from . A grammar is called parameter-reduced, if it is terminating and has no superfluous parameters. For every grammar of level which generates at least one term we construct grammars and such that and generate the same language as G but are terminating and paramter-reduced, respectively. We introduce a hierarchy of restrictions to the deletion capability of the grammars which allow a gradual decrease in the complexity of the algorithms from n-iterated exponential time to polynomial time.