So far we have only compared the CTW codeword length resulting from
our source sequence 
to the ideal codeword length relative to the
actual source.
We have shown that this codeword length is upper bounded by the ideal
codeword length plus an upper bound for the individual redundancy in
terms of the sequence length T and the number of parameters 
of the actual source.
If however this was generated by some other tree source
the same bound on the codeword length applies but now with the ideal
codelength and redundancy as determined by the other source.
Hence upper bounds like this, for all tree sources, hold for the CTW
codeword length and the CTW algorithm minimizes, over all tree
sources, the sum of the corresponding ideal codeword length and
redundancy.
This can be considered as minimum description length (MDL) behavior,
if we realize that the redundancy is needed to describe the source
model and parameters.