-<h1>Upward axes</h1>
-<tt> <![CDATA[<a>[ <b>[ <c>[] <d>[] <e>[ <f> [] ] ] ]]]><sub>&bcirc;</sub></tt>
-<object id="svgRBTree" data="rb_tree.svg" type="image/svg+xml" style="margin-left:7.5%;width:85%" />
-<pre>
- <tt>parent ::</tt> t ≡ ⊤<sub> (&left;_) · (&right;_)* · (&right; ẋ & t) · (( (&left; _) · &ztop;) &lor; &bcirc; )</sub>
- <tt>ancestor ::</tt> t ≡ ⊤<sub> ((&left;_) · (&right;_)* · (&right; ẋ & t))* · &bcirc; </sub>
+ <h1>Binary-tree encoding</h1>
+ <p>We use <u>regular expressions</u> over basic &left;/&right; zippers to encode upward XPath</p>
+<code style="width:50%;float:left;"> <![CDATA[<a>[ <b>[
+ <c>[]
+ <d>[]
+ <e>[ <f> [] ]
+ ]
+ ]]]>
+</code><img style="width:17.5%;" src="ex_ntree.svg" alt="ex_ntree" /><br/>
+<p class="sws-pause"><img style="margin-top:-1em;margin-left:5%;width:85%;" src="rb_tree.svg" alt="rb_tree"/></p>
+</div>
+
+<div class="sws-slide">
+<h1>Upward XPath axes</h1>
+<div style="position:absolute; width:80%; left:10%;top:15%">
+<object id="svgRBTree" data="rb_tree.svg" type="image/svg+xml" style="z-index:1;position:absolute;width:100%" />
+<object class="sws-onframe-1" id="svgRBTree1" data="rb_tree01.svg" type="image/svg+xml" style="z-index:1;position:absolute;width:100%" />
+<object class="sws-onframe-2" id="svgRBTree2" data="rb_tree02.svg" type="image/svg+xml" style="z-index:3;position:absolute;width:100%" />
+<object class="sws-onframe-3" id="svgRBTree3" data="rb_tree03.svg" type="image/svg+xml" style="z-index:4;position:absolute;width:100%" />
+<object class="sws-onframe-4" id="svgRBTree4" data="rb_tree04.svg" type="image/svg+xml" style="z-index:5;position:absolute;width:100%" />
+</div>
+<pre style="position:absolute;bottom:5%;z-index:1;"> <tt>parent ::</tt> t ≡ ⊤<sub> (&left;_) · (&right;_)* · (&right; ẋ & t) · (( (&left; _) · &ztop;) &lor; &bcirc; )</sub>
+
+<span class="sws-onframe-5"> <tt>ancestor ::</tt> t ≡ ⊤<sub> ( (&left;_) · (&right;_)* · (&right; ẋ & t) )* · &bcirc; </sub></span>
+
+
+
+
+</pre>
+<pre style="position:absolute;bottom:5%;z-index:2;">
+
+ <span class="sws-onframe-1" style="font-size:110%;color:#1fb01b;">⬆</span> <span class="sws-onframe-2" style="font-size:110%;color:#1fb01b;">⬆</span> <span class="sws-onframe-3" style="font-size:110%;color:#1fb01b;">⬆</span> <span class="sws-onframe-4" style="font-size:110%;color:#1fb01b;">⬆</span>
+
+ <span class="sws-onframe-5" style="color:#1fb01b;border-color:#1fb01b;border-top-style:dashed;border-top-width:3pt;position:relative;top:0.5em;"> parent </span>
+
+
+