The parties to any rule shall agree upon the mode of procedure, the defraying of expenses, the time when and manner in which the referees shall make their report, and the time and manner of issuing execution on the judgment or decree which the court shall enter, upon the coming in of the report; and every such agreement shall be conclusive upon the parties and upon their heirs, executors, administrators, and successors, and, if involving real estate, when notice thereof is duly recorded, upon their assigns, and a majority report of referees shall be binding and conclusive.
R.I. Gen. Laws § 9-15-4