More formally, we call two hyperedges e 1 and e 2 are competing hyperedges, if their corresponding rules r(e 1 ) = ⟨γ 1 , α 1 ⟩ and r(e 2 ) = ⟨γ 2 , α 2 ⟩ : This means they give different translations for a same source side.
we use C(e) to represent the set of competing hyperedges of e. Two derivations t 1 = ⟨V 1 , E 1 ⟩ and t 2 = ⟨V 2 , E 2 ⟩ are competing derivations if there exists e 1 ∈ E 1 and e 2 ∈ E 2 : 2 derivations t 1 and t 2 only differ in e 1 and e 2 , and these two hyperedges are competing hyperedges.