On universally catenarian pairs

If 1≤n<∞1≤n<∞ and R⊆SR⊆S are integral domains, then (R,S)(R,S) is called an nn-catenarian pair if for each intermediate ring TT (that is each ring TT such that R⊆T⊆SR⊆T⊆S) the polynomial ring in nn indeterminates, T[n]T[n] is catenarian. This implies that (R,S)(R,S) is mm-catenarian for all m