Algorithm 2.

How to construct any explanation between an arbitrary pair of groups, t_i→j, using the set of basis explanations relative to the reference group, t₁, . . . , t_l−1

Input: i, j

if i == 1 then

Return: tj

else if j == 1 then

Return: $t_i^{-1}$

else

Return: $t_j\circ t_i^{-1}$

end if