On the difference of the Burnside groups $B(2;5)$ and $B_0(2;5)$

An algorithm for calculating elements and relations in Burnside groups is described. A comparative analysis of the groups $B(2;5)$ and $B_0(2;5)$ is carried out. It is shown that these groups coincide in the minimal word format up to words of length 29. For lengths of 30–35, relations are found in the group $B_0(2;5)$ such that a violation of at least one of them in $B(2;5)$ would mean the infinity of this group.