<?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="0" name="Z3" version="4.8.4" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="1" name="Z3" version="4.8.6" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="2" name="Alt-Ergo" version="2.3.0" timelimit="1" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="string_search.mlw"/>
<theory name="Occurs" proved="true">
 <goal name="occurs&#39;vc" expl="VC for occurs" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="occurs&#39;vc.0" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="24"/></proof>
  </goal>
  <goal name="occurs&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="95"/></proof>
  </goal>
  <goal name="occurs&#39;vc.2" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="25123"/></proof>
  </goal>
  <goal name="occurs&#39;vc.3" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="33"/></proof>
  </goal>
  <goal name="occurs&#39;vc.4" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="35"/></proof>
  </goal>
  <goal name="occurs&#39;vc.5" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="35"/></proof>
  </goal>
  <goal name="occurs&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.05" steps="188"/></proof>
  </goal>
  <goal name="occurs&#39;vc.7" expl="loop invariant preservation" proved="true">
  <transf name="rewrite" proved="true" arg1="&lt;-" arg2="concat_substring">
   <goal name="occurs&#39;vc.7.0" expl="loop invariant preservation" proved="true">
   <proof prover="2" timelimit="5"><result status="valid" time="3.49" steps="5928"/></proof>
   </goal>
   <goal name="occurs&#39;vc.7.1" expl="rewrite premises" proved="true">
   <proof prover="2"><result status="valid" time="0.01" steps="39"/></proof>
   </goal>
   <goal name="occurs&#39;vc.7.2" expl="rewrite premises" proved="true">
   <proof prover="2"><result status="valid" time="0.02" steps="39"/></proof>
   </goal>
   <goal name="occurs&#39;vc.7.3" expl="rewrite premises" proved="true">
   <proof prover="2"><result status="valid" time="0.01" steps="39"/></proof>
   </goal>
   <goal name="occurs&#39;vc.7.4" expl="rewrite premises" proved="true">
   <proof prover="2"><result status="valid" time="0.01" steps="39"/></proof>
   </goal>
   <goal name="occurs&#39;vc.7.5" expl="rewrite premises" proved="true">
   <proof prover="2"><result status="valid" time="0.02" steps="39"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="occurs&#39;vc.8" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.06" steps="244"/></proof>
  </goal>
  <goal name="occurs&#39;vc.9" expl="VC for occurs" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="24571"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Naive" proved="true">
 <goal name="search1&#39;vc" expl="VC for search1" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="search1&#39;vc.0" expl="integer overflow" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="17582"/></proof>
  </goal>
  <goal name="search1&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="24"/></proof>
  </goal>
  <goal name="search1&#39;vc.2" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="25411"/></proof>
  </goal>
  <goal name="search1&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="30"/></proof>
  </goal>
  <goal name="search1&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="32"/></proof>
  </goal>
  <goal name="search1&#39;vc.5" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="118"/></proof>
  </goal>
  <goal name="search1&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="22"/></proof>
  </goal>
  <goal name="search1&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="70"/></proof>
  </goal>
  <goal name="search1&#39;vc.8" expl="out of loop bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="21"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="search2&#39;vc" expl="VC for search2" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="search2&#39;vc.0" expl="integer overflow" proved="true">
  <proof prover="0"><result status="valid" time="0.03" steps="17582"/></proof>
  </goal>
  <goal name="search2&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="24"/></proof>
  </goal>
  <goal name="search2&#39;vc.2" expl="precondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="search2&#39;vc.2.0" expl="precondition" proved="true">
   <proof prover="2"><result status="valid" time="0.01" steps="26"/></proof>
   </goal>
   <goal name="search2&#39;vc.2.1" expl="precondition" proved="true">
   <proof prover="2"><result status="valid" time="0.01" steps="26"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="search2&#39;vc.3" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="27309"/></proof>
  </goal>
  <goal name="search2&#39;vc.4" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="search2&#39;vc.4.0" expl="postcondition" proved="true">
   <proof prover="2"><result status="valid" time="0.01" steps="30"/></proof>
   </goal>
   <goal name="search2&#39;vc.4.1" expl="postcondition" proved="true">
   <transf name="unfold" proved="true" arg1="matches">
    <goal name="search2&#39;vc.4.1.0" expl="postcondition" proved="true">
    <transf name="split_vc" proved="true" >
     <goal name="search2&#39;vc.4.1.0.0" expl="postcondition" proved="true">
     <proof prover="1"><result status="valid" time="0.02" steps="29511"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="search2&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="169"/></proof>
  </goal>
  <goal name="search2&#39;vc.6" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="36"/></proof>
  </goal>
  <goal name="search2&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="22"/></proof>
  </goal>
  <goal name="search2&#39;vc.8" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="70"/></proof>
  </goal>
  <goal name="search2&#39;vc.9" expl="out of loop bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="24749"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="BadShiftTable" proved="true">
 <goal name="bad_shift_table&#39;vc" expl="VC for bad_shift_table" proved="true">
 <proof prover="2"><result status="valid" time="0.03" steps="161"/></proof>
 </goal>
 <goal name="make_table&#39;vc" expl="VC for make_table" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="make_table&#39;vc.0" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.06" steps="18"/></proof>
  </goal>
  <goal name="make_table&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="21"/></proof>
  </goal>
  <goal name="make_table&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="116"/></proof>
  </goal>
  <goal name="make_table&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="27"/></proof>
  </goal>
  <goal name="make_table&#39;vc.4" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="25"/></proof>
  </goal>
  <goal name="make_table&#39;vc.5" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="25"/></proof>
  </goal>
  <goal name="make_table&#39;vc.6" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="143"/></proof>
  </goal>
  <goal name="make_table&#39;vc.7" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.11" steps="489"/></proof>
  </goal>
  <goal name="make_table&#39;vc.8" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="322"/></proof>
  </goal>
  <goal name="make_table&#39;vc.9" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="27"/></proof>
  </goal>
  <goal name="make_table&#39;vc.10" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="49"/></proof>
  </goal>
  <goal name="make_table&#39;vc.11" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.08" steps="83"/></proof>
  </goal>
  <goal name="make_table&#39;vc.12" expl="out of loop bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="18"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="shift&#39;vc" expl="VC for shift" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="shift&#39;vc.0" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="91"/></proof>
  </goal>
  <goal name="shift&#39;vc.1" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.07" steps="205"/></proof>
  </goal>
  <goal name="shift&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="30"/></proof>
  </goal>
  <goal name="shift&#39;vc.3" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="shift&#39;vc.3.0" expl="postcondition" proved="true">
   <proof prover="2"><result status="valid" time="0.01" steps="24"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="no_shift&#39;vc" expl="VC for no_shift" proved="true">
 <proof prover="2"><result status="valid" time="0.44" steps="1056"/></proof>
 </goal>
 <goal name="search&#39;vc" expl="VC for search" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="search&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="23"/></proof>
  </goal>
  <goal name="search&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="5822"/></proof>
  </goal>
  <goal name="search&#39;vc.2" expl="integer overflow" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="90559"/></proof>
  </goal>
  <goal name="search&#39;vc.3" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="33"/></proof>
  </goal>
  <goal name="search&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="37"/></proof>
  </goal>
  <goal name="search&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="39"/></proof>
  </goal>
  <goal name="search&#39;vc.6" expl="integer overflow" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="99140"/></proof>
  </goal>
  <goal name="search&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="41"/></proof>
  </goal>
  <goal name="search&#39;vc.8" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="142"/></proof>
  </goal>
  <goal name="search&#39;vc.9" expl="integer overflow" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="104789"/></proof>
  </goal>
  <goal name="search&#39;vc.10" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="45"/></proof>
  </goal>
  <goal name="search&#39;vc.11" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="93699"/></proof>
  </goal>
  <goal name="search&#39;vc.12" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="50"/></proof>
  </goal>
  <goal name="search&#39;vc.13" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="49"/></proof>
  </goal>
  <goal name="search&#39;vc.14" expl="precondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="search&#39;vc.14.0" expl="precondition" proved="true">
   <proof prover="2"><result status="valid" time="0.01" steps="45"/></proof>
   </goal>
   <goal name="search&#39;vc.14.1" expl="precondition" proved="true">
   <proof prover="2"><result status="valid" time="0.02" steps="45"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="search&#39;vc.15" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="50"/></proof>
  </goal>
  <goal name="search&#39;vc.16" expl="integer overflow" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="140635"/></proof>
  </goal>
  <goal name="search&#39;vc.17" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="212"/></proof>
  </goal>
  <goal name="search&#39;vc.18" expl="loop variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="126"/></proof>
  </goal>
  <goal name="search&#39;vc.19" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="167"/></proof>
  </goal>
  <goal name="search&#39;vc.20" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.37" steps="943"/></proof>
  </goal>
  <goal name="search&#39;vc.21" expl="postcondition" proved="true">
  <proof prover="2" timelimit="5"><result status="valid" time="0.01" steps="33"/></proof>
  </goal>
  <goal name="search&#39;vc.22" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="search&#39;vc.22.0" expl="postcondition" proved="true">
   <proof prover="2"><result status="valid" time="0.01" steps="109"/></proof>
   </goal>
   <goal name="search&#39;vc.22.1" expl="postcondition" proved="true">
   <proof prover="2"><result status="valid" time="0.01" steps="31"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
