“…In each row, the first column (column toc(d 1 )) specifies the form of the target of the conclusion of the -defining rule d 1 (e.g., x in case of row 3), the second column (column toc(d 2 )) specifies the form of the target of the conclusion of the -defining rule d 2 (e.g., x y in case of row 3), if the conditions in the column further requirements are satisfied (e.g., in row 3, among all possible -defining rules only d 1 can satisfy premises x a → x and y a → y ), then the result of the transition of terms (p q) r and (p r) (q r) is specified by the term given in column result (e.g., p q in row 3). The requirement idempotent means that the operator can be proved idempotent, e.g., by means of the rule format offered in [1].…”