<?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="CVC4" version="1.5" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="1" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="Z3" version="4.12.2" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="3" name="CVC4" version="1.4" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="4" name="Alt-Ergo" version="2.3.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="7" name="Alt-Ergo" version="2.1.0" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="optimal_replay.mlw"/>
<theory name="OptimalReplay" proved="true">
 <goal name="n&#39;vc" expl="VC for n" proved="true">
 <proof prover="4"><result status="valid" time="0.000000" steps="0"/></proof>
 </goal>
 <goal name="distance&#39;vc" expl="VC for distance" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="distance&#39;vc.0" expl="array creation size" proved="true">
  <proof prover="7"><result status="valid" time="0.010000" steps="4"/></proof>
  </goal>
  <goal name="distance&#39;vc.1" expl="index in array bounds" proved="true">
  <proof prover="7"><result status="valid" time="0.020000" steps="6"/></proof>
  </goal>
  <goal name="distance&#39;vc.2" expl="array creation size" proved="true">
  <proof prover="7"><result status="valid" time="0.010000" steps="12"/></proof>
  </goal>
  <goal name="distance&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="7"><result status="valid" time="0.010000" steps="32"/></proof>
  </goal>
  <goal name="distance&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="7"><result status="valid" time="0.020000" steps="21"/></proof>
  </goal>
  <goal name="distance&#39;vc.5" expl="loop invariant init" proved="true">
  <proof prover="7"><result status="valid" time="0.020000" steps="55"/></proof>
  </goal>
  <goal name="distance&#39;vc.6" expl="loop invariant init" proved="true">
  <proof prover="7"><result status="valid" time="0.020000" steps="31"/></proof>
  </goal>
  <goal name="distance&#39;vc.7" expl="loop invariant init" proved="true">
  <proof prover="7"><result status="valid" time="0.020000" steps="32"/></proof>
  </goal>
  <goal name="distance&#39;vc.8" expl="precondition" proved="true">
  <proof prover="7"><result status="valid" time="0.010000" steps="35"/></proof>
  </goal>
  <goal name="distance&#39;vc.9" expl="index in array bounds" proved="true">
  <proof prover="7"><result status="valid" time="0.020000" steps="39"/></proof>
  </goal>
  <goal name="distance&#39;vc.10" expl="index in array bounds" proved="true">
  <proof prover="7"><result status="valid" time="0.020000" steps="43"/></proof>
  </goal>
  <goal name="distance&#39;vc.11" expl="loop variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.040000"/></proof>
  </goal>
  <goal name="distance&#39;vc.12" expl="loop invariant preservation" proved="true">
  <proof prover="7"><result status="valid" time="0.020000" steps="83"/></proof>
  </goal>
  <goal name="distance&#39;vc.13" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.040000"/></proof>
  <proof prover="3"><result status="valid" time="0.050000"/></proof>
  </goal>
  <goal name="distance&#39;vc.14" expl="index in array bounds" proved="true">
  <proof prover="7"><result status="valid" time="0.010000" steps="41"/></proof>
  </goal>
  <goal name="distance&#39;vc.15" expl="index in array bounds" proved="true">
  <proof prover="7"><result status="valid" time="0.010000" steps="41"/></proof>
  </goal>
  <goal name="distance&#39;vc.16" expl="index in array bounds" proved="true">
  <proof prover="7"><result status="valid" time="0.020000" steps="47"/></proof>
  </goal>
  <goal name="distance&#39;vc.17" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.040000"/></proof>
  <proof prover="2"><result status="valid" time="0.010000" steps="20740"/></proof>
  <proof prover="3"><result status="valid" time="0.020000"/></proof>
  </goal>
  <goal name="distance&#39;vc.18" expl="loop invariant preservation" proved="true">
  <proof prover="1" timelimit="17"><result status="valid" time="0.780000"/></proof>
  </goal>
  <goal name="distance&#39;vc.19" expl="loop invariant preservation" proved="true">
  <transf name="unfold" proved="true" arg1="distance">
   <goal name="distance&#39;vc.19.0" expl="loop invariant preservation" proved="true">
   <transf name="split_goal_right" proved="true" >
    <goal name="distance&#39;vc.19.0.0" expl="loop invariant preservation" proved="true">
    <proof prover="0"><result status="valid" time="0.380000" steps="58168"/></proof>
    </goal>
    <goal name="distance&#39;vc.19.0.1" expl="loop invariant preservation" proved="true">
    <proof prover="3" timelimit="10" memlimit="4000"><result status="valid" time="1.390000"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="distance&#39;vc.20" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.060000"/></proof>
  </goal>
  <goal name="distance&#39;vc.21" expl="assertion" proved="true">
  <proof prover="7" timelimit="36"><result status="valid" time="0.000000" steps="33"/></proof>
  </goal>
  <goal name="distance&#39;vc.22" expl="out of loop bounds" proved="true">
  <proof prover="7"><result status="valid" time="0.020000" steps="14"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
