Nodes labeled by component databases have sets of successor nodes each labeled by one of the components. These nodes are called AND nodes because in order to process the compound database to termination all of the component database must be processed to termination. so this node here in order to process C B Z to termination, C,B and Z needs to be processed to termination. In order  to process BM to termination both B and M needs to be processed to termination; so  on and so forth. Another important  thing that one needs to realize is that the successor nodes labeled by the result of rule application. Like here when I have D and L or I have B and M as  I applied rule onto C .They are referred to as the ‘OR’ nodes. Because , in order to process a component database to termination , the database resulting from only either this or this must be processed to termination. These are referred to as ‘OR’ nodes The structure called AND-OR graphs  are useful for depicting the activity of production systems. So these are the nodes , these are the or nodes. So the decomposable production system if you see these nodes that I have marked now as AND here are important because if a component database is ; all of the component databases need to be moved to termination. So, that is the and node here .That is the and node. This is the and node. Both  of them needs to be moved to the termination. So, finally we can say that the notion of decomposable production system encompass a technique often called problem Reduction in AI. We have reduced the problem  of taking C B Z to termination. To the problem of taking C, B and Z individually to termination.

Goal of decomposable production system

Problem Reduction idea usually involves replacing a problem goal by a set of   sub goals such that if the sub goals are solved, the main goal is also solved.

Explaining problems in terms of decomposable production system allows us to be indefinite about whether we are decomposing problem goals or problem states.