You're defaulting to html output. Set the output to xhtml:

<xsl:stylesheet version="1.0" 
        xmlns:xsl="http://www.w3.org/1999/XSL/Transform" 
        xmlns="http://www.w3.org/1999/xhtml">
  <xsl:output method="xml" 
  doctype-public="-//W3C//DTD XHTML 1.0 Strict//EN"  
doctype-system="http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"
  indent="yes"/>
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