<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session shape_version="6">
<prover id="1" name="Alt-Ergo" version="2.3.3" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="4" name="CVC4" version="1.8" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="5" name="Z3" version="4.8.10" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="huffman_with_two_queues.mlw"/>
<theory name="Top" proved="true">
 <goal name="add_last" proved="true">
 <proof prover="1"><result status="valid" time="0.02" steps="59"/></proof>
 </goal>
 <goal name="sorted_tail" proved="true">
 <proof prover="1"><result status="valid" time="0.07" steps="78"/></proof>
 <proof prover="4"><result status="valid" time="0.69" steps="73398"/></proof>
 </goal>
 <goal name="sorted_tail_tail" proved="true">
 <proof prover="1"><result status="valid" time="0.06" steps="82"/></proof>
 <proof prover="4"><result status="valid" time="0.58" steps="68466"/></proof>
 </goal>
 <goal name="huffman_coding&#39;vc" expl="VC for huffman_coding" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="huffman_coding&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="6"/></proof>
  <proof prover="4"><result status="valid" time="0.06" steps="13933"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="19"/></proof>
  <proof prover="4"><result status="valid" time="0.08" steps="17325"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="8"/></proof>
  <proof prover="4"><result status="valid" time="0.06" steps="13811"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="46"/></proof>
  <proof prover="4"><result status="valid" time="0.08" steps="17320"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="16"/></proof>
  <proof prover="4"><result status="valid" time="0.06" steps="14202"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.5" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="16"/></proof>
  <proof prover="4"><result status="valid" time="0.06" steps="14284"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.6" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="17"/></proof>
  <proof prover="4"><result status="valid" time="0.06" steps="14343"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.7" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="26"/></proof>
  <proof prover="4"><result status="valid" time="0.08" steps="15188"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.8" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="72"/></proof>
  <proof prover="4"><result status="valid" time="0.13" steps="24548"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.9" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="32"/></proof>
  <proof prover="4"><result status="valid" time="0.08" steps="17642"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.10" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="34"/></proof>
  <proof prover="4"><result status="valid" time="0.10" steps="17839"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.11" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="36"/></proof>
  <proof prover="4"><result status="valid" time="0.10" steps="17693"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.12" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="86"/></proof>
  <proof prover="4"><result status="valid" time="0.09" steps="17816"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.13" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="3.12" steps="1255"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.14" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="38"/></proof>
  <proof prover="4"><result status="valid" time="0.06" steps="15132"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.15" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="37"/></proof>
  <proof prover="4"><result status="valid" time="0.06" steps="15185"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.16" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="24"/></proof>
  <proof prover="4"><result status="valid" time="0.07" steps="15071"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.17" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="76"/></proof>
  <proof prover="4"><result status="valid" time="0.12" steps="24583"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.18" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="36"/></proof>
  <proof prover="4"><result status="valid" time="0.10" steps="17600"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.19" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="38"/></proof>
  <proof prover="4"><result status="valid" time="0.10" steps="17661"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.20" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="34"/></proof>
  <proof prover="4"><result status="valid" time="0.06" steps="14874"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.21" expl="loop invariant preservation" proved="true">
  <transf name="assert" proved="true" arg1="(sorted y1[2..])">
   <goal name="huffman_coding&#39;vc.21.0" expl="asserted formula" proved="true">
   <transf name="assert" proved="true" arg1="(length y1 &gt;= 2)">
    <goal name="huffman_coding&#39;vc.21.0.0" expl="asserted formula" proved="true">
    <proof prover="1"><result status="valid" time="0.01" steps="34"/></proof>
    <proof prover="4"><result status="valid" time="0.07" steps="15216"/></proof>
    </goal>
    <goal name="huffman_coding&#39;vc.21.0.1" expl="asserted formula" proved="true">
    <transf name="split_all_full" proved="true" >
     <goal name="huffman_coding&#39;vc.21.0.1.0" expl="asserted formula" proved="true">
     <proof prover="1"><result status="valid" time="0.02" steps="42"/></proof>
     <proof prover="4"><result status="valid" time="0.10" steps="19774"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
   <goal name="huffman_coding&#39;vc.21.1" expl="loop invariant preservation" proved="true">
   <proof prover="1"><result status="valid" time="0.24" steps="190"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="huffman_coding&#39;vc.22" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="36"/></proof>
  <proof prover="4"><result status="valid" time="0.06" steps="14973"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.23" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="36"/></proof>
  <proof prover="4"><result status="valid" time="0.06" steps="15042"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.24" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="2.28" steps="1058"/></proof>
  <proof prover="4"><result status="valid" time="1.62" steps="202016"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.25" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="50"/></proof>
  <proof prover="4"><result status="valid" time="0.06" steps="15377"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.26" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="123"/></proof>
  <proof prover="4"><result status="valid" time="0.13" steps="24424"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.27" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="56"/></proof>
  <proof prover="4"><result status="valid" time="0.10" steps="17974"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.28" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="58"/></proof>
  <proof prover="4"><result status="valid" time="0.10" steps="18113"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.29" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="60"/></proof>
  <proof prover="4"><result status="valid" time="0.10" steps="18010"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.30" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="92"/></proof>
  <proof prover="4"><result status="valid" time="0.10" steps="18104"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.31" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="2.91" steps="2065"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.32" expl="loop invariant preservation" proved="true">
  <proof prover="5"><result status="valid" time="0.21" steps="517418"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.33" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.42" steps="277"/></proof>
  <proof prover="4"><result status="valid" time="0.32" steps="56603"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.34" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="47"/></proof>
  <proof prover="4"><result status="valid" time="0.09" steps="17190"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.35" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="44"/></proof>
  <proof prover="4"><result status="valid" time="0.09" steps="17857"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.36" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.09" steps="359"/></proof>
  <proof prover="4"><result status="valid" time="0.14" steps="26685"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.37" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="45"/></proof>
  <proof prover="4"><result status="valid" time="0.10" steps="18230"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.38" expl="loop invariant preservation" proved="true">
  <transf name="split_all_full" proved="true" >
   <goal name="huffman_coding&#39;vc.38.0" expl="loop invariant preservation" proved="true">
   <transf name="inline_goal" proved="true" >
    <goal name="huffman_coding&#39;vc.38.0.0" expl="loop invariant preservation" proved="true">
    <proof prover="1"><result status="valid" time="0.03" steps="167"/></proof>
    <proof prover="4"><result status="valid" time="0.11" steps="20864"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="huffman_coding&#39;vc.39" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="49"/></proof>
  <proof prover="4"><result status="valid" time="0.10" steps="18291"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.40" expl="loop invariant preservation" proved="true">
  <transf name="split_all_full" proved="true" >
   <goal name="huffman_coding&#39;vc.40.0" expl="loop invariant preservation" proved="true">
   <proof prover="1"><result status="valid" time="1.20" steps="1881"/></proof>
   <proof prover="4"><result status="valid" time="1.54" steps="221397"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="huffman_coding&#39;vc.41" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.96" steps="863"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.42" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.68" steps="550"/></proof>
  <proof prover="4"><result status="valid" time="2.00" steps="238493"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.43" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="2.72" steps="2211"/></proof>
  <proof prover="4"><result status="valid" time="2.13" steps="291636"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.44" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="46"/></proof>
  <proof prover="4"><result status="valid" time="0.06" steps="15284"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.45" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="118"/></proof>
  <proof prover="4"><result status="valid" time="0.12" steps="24627"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.46" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="55"/></proof>
  <proof prover="4"><result status="valid" time="0.10" steps="17897"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.47" expl="loop invariant preservation" proved="true">
  <transf name="split_all_full" proved="true" >
   <goal name="huffman_coding&#39;vc.47.0" expl="loop invariant preservation" proved="true">
   <proof prover="1"><result status="valid" time="0.02" steps="57"/></proof>
   <proof prover="4"><result status="valid" time="0.09" steps="20510"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="huffman_coding&#39;vc.48" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="56"/></proof>
  <proof prover="4"><result status="valid" time="0.06" steps="15094"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.49" expl="loop invariant preservation" proved="true">
  <transf name="split_all_full" proved="true" >
   <goal name="huffman_coding&#39;vc.49.0" expl="loop invariant preservation" proved="true">
   <proof prover="1"><result status="valid" time="0.30" steps="274"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="huffman_coding&#39;vc.50" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.31" steps="208"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.51" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="1.59" steps="1201"/></proof>
  <proof prover="4"><result status="valid" time="1.19" steps="169751"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.52" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="2.21" steps="1616"/></proof>
  <proof prover="4"><result status="valid" time="1.30" steps="167907"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.53" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="36"/></proof>
  <proof prover="4"><result status="valid" time="0.09" steps="17194"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.54" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="55"/></proof>
  <proof prover="4"><result status="valid" time="0.09" steps="17878"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.55" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.10" steps="371"/></proof>
  <proof prover="4"><result status="valid" time="0.13" steps="26747"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.56" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="45"/></proof>
  <proof prover="4"><result status="valid" time="0.09" steps="18292"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.57" expl="loop invariant preservation" proved="true">
  <transf name="split_all_full" proved="true" >
   <goal name="huffman_coding&#39;vc.57.0" expl="loop invariant preservation" proved="true">
   <proof prover="1"><result status="valid" time="0.02" steps="91"/></proof>
   <proof prover="4"><result status="valid" time="0.09" steps="20912"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="huffman_coding&#39;vc.58" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="65"/></proof>
  <proof prover="4"><result status="valid" time="0.08" steps="18353"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.59" expl="loop invariant preservation" proved="true">
  <transf name="split_all_full" proved="true" >
   <goal name="huffman_coding&#39;vc.59.0" expl="loop invariant preservation" proved="true">
   <proof prover="1"><result status="valid" time="0.53" steps="1073"/></proof>
   <proof prover="4"><result status="valid" time="1.74" steps="217909"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="huffman_coding&#39;vc.60" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="1.88" steps="2163"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.61" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.62" steps="558"/></proof>
  <proof prover="4"><result status="valid" time="1.80" steps="226737"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.62" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.96" steps="1280"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.63" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.19" steps="388"/></proof>
  <proof prover="4"><result status="valid" time="0.14" steps="25660"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
