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Rules are optimized one by one, but the result is obtained as if all rules are optimized at once. On the other hand, the guarantee of optimality is sacrificed to prevent combinatorial explosion. For example, let us consider two rules (a)(b)(c) and (b)(c)(d). Suppose the join structure (a)((b)(c)) is chosen for the first rule. According to the above algorithm, the cost of ((b)(c)) in the first rule is calculated by dividing the original cost by 2, but in the second rule, the cost is counted as 0.

Tokens are input into the root node in the descending order of G. Each node processes tokens as follows. Chapter 2. 7: Decomposition Process el) If both rules are contained in the root node, move one of t h e m to the root node of its left subtree, and the other to the root node of its right subtree. ) c2) If one of two rules is contained in the root node and the other is contained in its right (left) subtree, move the rule contained in the node to the root node of its left (right) subtree. ) c3) If both rules are each contained in its left (right) subtree, pass the token to the root node of its left (right) subtree.

C l a s s l ) and ( c l a s s 2 ) remain, ( c l a s s l ) remains, (class2) remains, or no WME remains. From the above observations, the paired-rule (or pairwise) conditions [Ishida and Stolfo, 1985], which can detect the interference between instantiations in paired P-nodes, are formally described as follows. [ P a i r e d - R u l e Conditions] There is a possibility of interference between the two instantiations in P-node PA and P-node PB, if there exists a W-node that satisfies any of the following conditions: A1) '+'changed ('-'changed) by PA and '-'referenced ('+'referenced) by PB.

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