  The reductivity of a spherical curve is the minimal number of a local
transformation called an inverse-half-twisted splice required to obtain a
reducible spherical curve from the spherical curve. It is unknown if there
exists a spherical curve whose reductivity is four. In this paper, an
unavoidable set of configurations for a spherical curve with reductivity four
is given by focusing on 5-gons. It has also been unknown if there exists a
reduced spherical curve which has no 2-gons and 3-gons of type A, B and C. This
paper gives the answer to the question by constructing such a spherical curve.
