What do you call a mildly-context sensitive grammar in which the LHS must appear in the grammar spec?

Question

For instance: $$ S \rightarrow aAbAb \\ aAb \rightarrow AAa \\ A \rightarrow Aa | a $$ $aAb$ is alright to have on the left-hand side since it occurs directly in the grammar spec. Further indirectly created sentential forms with $aAb$ are not expanded but become non-terminating. This makes it easier to parse than a general context-sensitive grammar because you know the valid occurrences beforehand. If this grammar can somehow be reduced to a context-free grammar, I'm not interested because I've found use for specifying the grammar this way.