For Dataset 4, Guyon et al. [31] first reconstructed a reference tree using Maximum Likelihood (ML) method based on the large (LSU) and the small (SSU) ribosomal subunits sequences (i.e., the traditional alignment method). Then they compared the results using four alignment free string distances for complete genome phylogeny. The four distances are Maximum Significant Matches (MSM) distance, k-word (KW) distance (i.e., the Markov model in [11] ), Average Common Substring (ACS) distance and Compression (ZL) distance. Guyon et al. [31] found the MSM distance out performs the other three distances and the KW cannot give good phylogenetic topology for the 62 alpha-proteobacteria (see Figure 3 in [31] ). We tested our dynamical language approach with pseudo-distance in [5] and the two proper distances in this paper on Dataset 4. We found that amino acid sequences of all protein-coding genes from genomes give better results than those given by the whole DNA sequences and all protein-coding DNA sequences. We evaluated the dynamical language approach with pseudo-distance in [5] and the two proper distances in this paper on the amino acid sequences of all protein-coding genes from genomes for K = 3, 4, 5 and 6. We found the trees using the new distance metrics have the same topology as the trees using the old "distance" for the same value of K, and the topology of trees for K = 5 and 6 are the same and the best. Here we present the tree for K = 6 using dynamical language approach with chord distance in Figure 5 . As shown in Figure 5 , all Rhizobiales (Bartonellaceae, Brucellaceae, Rhizobiaceae and Phyllobacteriaceae) (A), Rhizobiales (Bradyrhizobiaceae) (B), Rickettsiales (Rickettsiaceae and Anaplasmataceae) (C), Rhodospirillales (D), Sphingomonadales (E); Rhodobacterales (Rhodobacteraceae) (F) group into correct branches respectively. Even inside each lineage (groups A to F), our phylogentic topology is more similar to that of ML reference tree (the right side tree in Figure 1 of [31] ) than that obtained by the MSM distance (the best result in [31] ). After comparing our Figure 5 with the tree obtained using KW distance (i.e., the Markov model in [11] ) (the tree in Figure 3 of [31] ), our dynamical language model performs much better than the KW distance.