9 [DNF construction and simplification phase]
11 {x:[x,y,z] in [A,B,C]}
13 [Constructing the query graph]
16 {x:[x,y,z] in [A,B,C]}
18 [Quantifier elimination phase]
20 {x:[x,y,z] in [A,B,C]}
22 [Disjunction removal phase]
24 {x:[x,y,z] in [A,B,C]}
26 [Conjunctive query decomposition phase]
29 {x:[x,y,z] in [A,B,C]}
31 [Projection recognition phase]
33 {x: x in A | (exists z in C. (exists y in B. true))}
35 [Simple find/count query decomposition phase]
37 {x: x in A | (exists z in C. (exists y in B. true))}
39 [Reiterating the transformation]
41 {x: x in A | (exists z in C. (exists y in B. true))}
45 {x: x in A | (exists z in C. (exists y in B. true))}
47 [DNF construction and simplification phase]
49 {x: x in A | (exists z in C.(nonempty B))}
51 [Constructing the query graph]
54 {x: x in A | (exists z in C.(nonempty B))}
56 [Quantifier elimination phase]
58 if((nonempty C) and(nonempty B)) then A else {}
60 [Disjunction removal phase]
62 if((nonempty C) and(nonempty B)) then A else {}
64 [Conjunctive query decomposition phase]
67 if((nonempty C) and(nonempty B)) then A else {}
69 [Projection recognition phase]
71 if((nonempty C) and(nonempty B)) then A else {}
73 [Simple find/count query decomposition phase]
76 if((nonempty C) and(nonempty B)) then A else {}