MSG Method ground case The first two steps

Finally, create a logic algorithm LA(r) from the msgs of the obtained compatible subsets (suppose there are c of them)  

Note that this algorithm actually also works for atom sets, by virtue of Definition 10-5 and Definition 10-7. 

This algorithm is non-deterministic, finite, and never fails. Moreover, the synthesized logic algorithm is non-deterministic in general, and finite, but may fail. For instance, considering Example 10-2, the atom pcCompress eXe,2]X) is covered by both disjuncts of the synthesized logic algorithm, namely via the answer substitutions X/[e,3] and X/[c,l,, 2].  

Proof 10-3 Trivial, from Theorem 10-2, Definition 10-9, and Algorithm 10-1. 10.3.4 Illustration 

Let s illustrate the described method on some sample problems. 

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Figure 10-1 MSG Method (ground case) The first two steps...

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