In other words, the rank of a pre-translation equals the number of output trees stored in it.
given a pre-translation t, u ∈ T Σ ×T k ∆ and i ∈ [k], we call u i the i th translation of t. An alignment for the pre-translation t, u is an injective mapping ψ : an alignment should request each translation of a particular subtree at most once and if it requests the i th translation, then it should also request all previous translations.