Run two templates for same node (XSLT)

I have some xml files like the following. They contain all different tree structures and some elements do have attributes.

<root>
  <element n="A">
    <element n="B">
      <attribute a="1"/>
      <attribute a="2"/>
    </element>
    <element n="C">
      <element n="D">
        <attribute a="3"/>
      </element>
    </element>
  </element>
</root>

I want to transform these files using XSLT to get the following output. I have to keep the tree structure and also create a list of all elements with their attributes:

<root>
  <structure>
    <newElement n="A">
      <newElement n="B">
        <newAttribute a="1"/>
        <newAttribute a="2"/>
      </newElement>
      <newElement n="C">
        <newElement n="D">
          <newAttribute a="3"/>
        </newElement>
      </newElement>
    </newElement>
  </structure>
  <list>
    <listElement n="A"/>
    <listElement n="B">
      <listAttribute a="1"/>
      <listAttribute a="2"/>
    </listElement>
    <listElement n="C"/>
    <listElement n="D">
      <listAttribute a="3"/>
    </listElement>
  </list>
</root>

I try to run two different templates "e1" and "e2" for one node "element" but it doesn't work. It seems that the first template is ignored. So what do I have to change?

<?xml version="1.0" encoding="UTF-8"?>
<xsl:stylesheet version="1.0" xmlns:xsl="http://ift.tt/tCZ8VR">

<xsl:template match="/">
  <root>
    <structure>
      <xsl:apply-templates name="e1"/>
    </structure>
    <list>
      <xsl:apply-templates name="e2"/>
    </list>
  </root>
</xsl:template>

<xsl:template match="element" name="e1">
  <newElement>
    <xsl:attribute name="n">
      <xsl:value-of select="@n"/>
    </xsl:attribute>
    <xsl:apply-templates name="a1"/>
    <xsl:apply-templates name="e1"/>
  </newElement>
</xsl:template>

<xsl:template match="attribute" name="a1">
  <newAttribute>
    <xsl:attribute name="a">
      <xsl:value-of select="@a"/>
    </xsl:attribute>
  </newAttribute>
</xsl:template>

<xsl:template match="element" name="e2">
  <listElement>
    <xsl:attribute name="n">
      <xsl:value-of select="@n"/>
    </xsl:attribute>
    <xsl:apply-templates name="a2"/>
  </listElement>
  <xsl:apply-templates select="element"/>
</xsl:template>

<xsl:template match="attribute" name="a2">
  <listAttribute>
    <xsl:attribute name="a">
      <xsl:value-of select="@a"/>
    </xsl:attribute>
  </listAttribute>
</xsl:template>

</xsl:stylesheet>