Rightmost extension defines a canonical search space in which one can enumerate all subtrees from a given set of trees.
we here consider an upper bound of the gain that allows subspace pruning in  (Morhishita, 2002), gives a convenient way of computing a tight upper bound on gain( t , y ) for any super-tree t of t. For any t ⊇ t and y ∈ {±1}, the gain of t , y is bounded by µ(t) (i.e., gain( t y ) ≤ µ(t)), where µ(t) is given by If we focus on the case y = +1, then for any t ⊇ t and y ∈ {±1}, we can efficiently prune the search space spanned by right most extension using the upper bound of gain u(t).