Gain is related to Increase. Split is a type of Increase. 
Let is related to Give. Give is a synonym of Dedicate. Dedicate is a type of Assign. Assign is related to Appoint. 
Gain <--RelatedTo--> Increase <--IsA-- Split 
Let <--RelatedTo--> Give <--Synonym--> Dedicate --IsA--> Assign <--RelatedTo--> Appoint 