On universally catenarian pairs

If 1≤n<∞ and Rsubset of or equal toS are integral domains, then (R,S) is called an n-catenarian pair if for each intermediate ring T (that is each ring T such that Rsubset of or equal toTsubset of or equal toS) the polynomial ring in n indeterminates, T[n] is catenarian. This implies that (R,S) is m-catenarian for all m