Once the word alignment is fixed, the final permutation is uniquely determined, so we can safely discard that factor.
we have: For the sole remaining factor P(T|C, S), we make the assumption that a segmented query T = q 1 … q K is generated from left to right by transforming each phrase c 1 …c K independently: where is a phrase transformation probability, the estimation of which will be described in Section 5.2.