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How do you parse lujvo into the component rafsi?



I'm working on an algorithm for breaking a lujvo into its component parts.  (My goal: given an unknown lujvo, break it up into parts and display the definitions of each of those parts.)  Chapter 4, section 11 of the grammar book ("The lujvo-making algorithm") talks about creating lujvo, but my question is about the reverse.  Is there a place where this is simply described?
 
If there's not, let me try this: I've tried to compose a grammar that defines a lujvo.  Could someone critique it?
 
lujvo  =  InitialRafsi  TermainlRafsi
InitialRafsi  =  Rafsi  InitialRafsi  |  <null>
Rafsi  =  4Rafsi  |  3Rafsi
 
TerminalRafsi  =  CCV | CVV| CVCCV | CCVCV
4Rafsi  =  CVCCy | CCVCy
3Rafsi  =  CVV | CCV | CVVr| CVVn | CVC | CVCy
 
Must the parsing of the unknown lujvo begin from the right?  or left?  or is it unambiguous regardless?  Given a 4Rafsi of the form CVCCy or CCVCy, I'm assuming that there's only one gismu with those first 4 letters -- right? 
 
Any other suggestions for how to do the parsing?
 
Thanks.