Regular grammar

A right-linear regular grammar has productions of the forms $A\to wB$ and $A\to w$, where $A,B$ are variables and $w$ is a terminal word.

Every sentential form reachable from the start variable of a right-linear grammar is either a terminal word $w$ or $wA$, where $A$ is the unique variable and occurs at the right end.

A variable $A$ is accessible when $S{\Rightarrow }^{\ast }wA$ for some terminal word $w$.

A variable $A$ is looping when $A{\Rightarrow }^{\ast }wA$ for some terminal word $w$ through a nonempty derivation.

A variable $A$ is terminable when $A{\Rightarrow }^{\ast }w$ for some terminal word $w$.

If a finite right-linear grammar generates an infinite language, some variable is accessible, looping, and terminable. It is the repeated variable on a sufficiently long accepting derivation.