Schemas of XML documents may be updated for various reasons. If a schema is updated, then XSLT stylesheets are also affected by the schema update. To maintain the consistencies of XSLT stylesheets with updated schemas, we have to detect the XSLT rules affected by schema updates in order to determine whether the XSLT rules need to be updated accordingly. However, detecting such XSLT rules manually is a difficult and time-consuming task, since users do not always fully understand the dependencies between XSLT stylesheets and DTDs. In this paper, we consider three classes of tree transducers as subsets of XSLT, and investigate whether XSLT rules affected by DTD updates can be detected efficiently for these classes.