Requirement req_max: If the p_max graph of an extensible constraint is nonempty, any derivation sequence of productions that is applied to the constraint's p_base graph cannot produce a graph that includes the p_max graph without producing the p_max graph before.

The p_base specification states the only consistent way to connect a nonextensible constraint with variables. Therefore, a whole p_base structure can be established by an addition production at once. Multiple similar nonextensible constraints between the same elements can be prohibited by an NAC for the addition production. This is not a vital structural constraint but saves from redundancy.

In conclusion, there must be one addition production per nonextensible constraint, which is constructed in the following way:

Construction P_{nonextensiblea}: The right-hand side of the addition production is equal to the constraint's embedding graph p_base. The left-hand side of the production contains the vertices of the right-hand side without the constraint itself, and an NAC that contains the right-hand side without the vertices that are connected to the constraint. In addition, the left-hand side includes an NAC for each included extensible constraint to prevent from exceeding this constraint's p_max graph. These NACs consist of a constraint's maximal embedding graph p_max such that the constraint is unified with the constraint of the left-hand side (NAC without the constraint itself).

Production P_Lessa in the figure below shows the addition production for the Less constraint.

The left-hand side of the addition production requires that the other vertices of p_base are already existent. To prevent from deadlocks, it must be possible to create the other vertices of p_base independently of the nonextensible constraint. This is enforced by

Requirement req_ne: The occurrence of a nonextensible constraint is only allowed in its addition and deletion production.

This requirement also ensures that the p_base specification is always satisfied, as no production can connect or disconnect vertices from the constraint.

To guarantee that an extensional constraint in the graph cannot be changed by productions below its minimal configuration p_base, it must be ensured that

Requirement req_min: Edges to an extensible constraint can only be deleted (without deleting the constraint itself), if at least the constraint's p_base graph is preserved.

There must also be one deletion production per nonextensible constraint. It withdraws the addition of the corresponding P_{nonextensiblea} production:

Construction P_{nonextensibled}: The left-hand side of a deletion production is equal to the embedding graph p_base. The right-hand side of the production contains the vertices of the left-hand side without the constraint itself. In addition, the left-hand side includes a PAC for each included extensible constraint to prevent from falling below this constraint's p_base graph. These PACs consist of a constraint's embedding graph p_base such that the constraint is unified with the constraint of the left-hand side (PAC without the constraint itself).

Production P_Lessd in figure above shows the deletion production for the Less constraint.