First, for every tree t ∈ L, let R t contain all the rules p(l) → r, where p = p(l) → r is a new state with p ∈ P , minimal normalized tree l ∈ T Σ (X), and an instance r ∈ T ∆ (P (X)) of t such that Figure 12: Useful rules for the composition M ; N of Example 8, where s, s ∈ {α, β} and ρ ∈ P σ(z2,z3) .
m ξ ⇒ m r for some ξ that is not an instance of t. we construct each rule of R t by applying existing rules of R m in sequence to generate a (minimal) right-hand side that is an instance of t. We thus potentially make the right-hand sides of m bigger by joining several existing rules into a single rule.