In (<cite>Siahbani et al., 2013</cite>) we discuss that LR-Hiero with beam search (Watanabe et al., 2006) does not perform at the same level of state-of-the-art Hiero (more LM calls and less translation quality). As we can see in this figure, adding new modified rules slightly increases the number of language model queries on Cs-En and De-En so that <cite>LR-Hiero+CP</cite> still works 2 to 3 times faster than Hiero.