In the query S_t (t₁, t₂,..., t_n) R, R is a cluster string representing (a portion of) the virtul world. The above query is interpreted as follows:

Procedure Query_Interpretor( S_t (t₁, t₂,..., t_n) R)
Step 1: Apply cut_t to each existing cluster in R to find its sub-clusters C_t1, C_t2, ..., C_tn.
Step 2: For each sub-cluster C_i, if t_i^c is closed it is treated as a single object. If t_i^o is open it is treated as a set of objects. Re-encode R according to S_t.

In the beginning R is a cluster string with a single cluster R. Therefore S_t (t₁, t₂, t₃) R = (t: C_t1 < C_t2 < C_t3)
Now R is a cluster string with 3 clusters. Thus S_x (x₁^o, x₂^o) (S_t (t₁, t₂, t₃) R) = (t: (u:a<b) < (u:a<b) < (u:a<b))