Discreteness criterion in SL(2,$bc$) by a test map

In the paper (Osaka J. Math. {bf 46}: 403-409, 2009), Yang conjectured that a non-elementary subgroup $G$ of $SL(2, bc)$ containing elliptic elements is discrete if for each elliptic element $gin G$ the group $< f, g >$ is discrete, where $fin SL(2,bc)$ is a test map which is loxodromic or elliptic. The purpose of this paper is to give an affirmative answer to this question.