For example, initially R is a cluster string with a single cluster R. Therefore S_t (t₁, t₂, t₃) R = (t: C_t1 < C_t2 < C_t3)
Subsequently R is a cluster string with 3 clusters. Thus S_y (y₁^o, y₂^o) (S_t (t₁, t₂, t₃) R) = (t: (v:a < b)_t1 < (v:a = b)_t2 < (v:a > b)_t3)