This technique yields an O((n+m)log M) algorithm for compressed pattern matching, where n (m) is the size of the compressed representation of the text (pattern, respectively),
while M is the size of the decompressed pattern. Since M is at most 2^m, this substantially improves the previously best O(m^2 n) algorithm.
The technique seems to be quite general and can be applied to several different problems related to SLP-compressed strings.