Definition:Golden Mean Number System/Simplification

Definition
Consider the golden mean number system. Let $x \in \R_{\ge 0}$ have a representation which includes the string $011$, say:
 * $x = p011q$

where $p$ and $q$ are strings in $\left\{ {0, 1}\right\}$.

From 100 in Golden Mean Number System equals 011, $x$ can also be written as:
 * $x = p100q$

The expression $p100q$ is a simplification of $p011q$