Roll condition ifelse in R data frame

Question

I have a data frame with two columns in R and I want to create a third column that will roll by 2 in both columns and check if a condition is satisfied or not as described in the table below. The condition is a rolling ifelse and goes like this :

IF -A1<B3<A1 TRUE ELSE FALSE

IF -A2<B4<A2 TRUE ELSE FALSE

IF -A3<B5<A3 TRUE ELSE FALSE

IF -A4<B6<A4 TRUE ELSE FALSE

A	B	CHECK
1	4	NA
2	5	NA
3	6	FALSE
4	1	TRUE
5	-4	FALSE
6	1	TRUE

How can I do it in R? Is there a base R's function or within the dplyr framework ?