We denote R as the variable rule, P as the phrase pair (f j 2 j 1 , e i 2 i 1 ), and X k as the kth sub-phrase pair that is replaced with X.
the inside probability of a variable rule is calculated as: We tried to follow the constraints of Chiang (2007): (1) unaligned words are not allowed at the edges of phrases; (2) a rule must have at least one pair of aligned words.