  Recently, Shestakov-Umirbaev solved Nagata's conjecture on an automorphism of
a polynomial ring. To solve the conjecture, they defined notions called
reductions of types I--IV for automorphisms of a polynomial ring. An
automorphism admitting a reduction of type I was first found by
Shestakov-Umirbaev. Using a computer, van den Essen--Makar-Limanov--Willems
gave a family of such automorphisms. In this paper, we present a new
construction of such automorphisms using locally nilpotent derivations. As a
consequence, we discover that there exists an automorphism admitting a
reduction of type I which satisfies some degree condition for each possible
value.
