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'''while''' <tex>\mathtt{S} \ne \varnothing</tex>
<tex>(C, a) \leftarrow</tex> '''pop'''(<tex>\mathtt{S}</tex>)
<tex>T \leftarrow \{R \ | \ R \in \mathtt{P}, \ R</tex> '''split splits by''' <tex>(C, a) \}</tex>
'''for each''' <tex>R</tex> '''in''' <tex>T</tex>
<tex> R_1, R_2 \leftarrow </tex> '''split'''(<tex>R, C, a</tex>)
<tex>T' \leftarrow \{R \ | \ R \in \mathtt{P}, \ R \cap \mathtt{Inverse} \neq \varnothing\}</tex>
'''for each''' <tex>R</tex> '''in''' <tex>T'</tex>
'''if''' <tex>R</tex> '''split splits by''' <tex>(C, a)</tex>
<tex> R_1, R_2 \leftarrow </tex> '''split'''(<tex>R, C, a</tex>)
'''replace''' <tex>R</tex> '''in''' <tex>\mathtt{P}</tex> '''with''' <tex>R_1</tex> '''and''' <tex>R_2</tex>
