<?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="4.12.2" timelimit="1" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="decrease1.mlw"/>
<theory name="Decrease1" proved="true">
 <goal name="decrease1_induction&#39;vc" expl="VC for decrease1_induction" proved="true">
 <proof prover="0"><result status="valid" time="0.010000" steps="10225"/></proof>
 </goal>
 <goal name="search&#39;vc" expl="VC for search" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="search&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="652"/></proof>
  </goal>
  <goal name="search&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="907"/></proof>
  </goal>
  <goal name="search&#39;vc.2" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="9251"/></proof>
  </goal>
  <goal name="search&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="10910"/></proof>
  </goal>
  <goal name="search&#39;vc.4" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="9358"/></proof>
  </goal>
  <goal name="search&#39;vc.5" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="9431"/></proof>
  </goal>
  <goal name="search&#39;vc.6" expl="loop variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="9655"/></proof>
  </goal>
  <goal name="search&#39;vc.7" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="9554"/></proof>
  </goal>
  <goal name="search&#39;vc.8" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="10921"/></proof>
  </goal>
  <goal name="search&#39;vc.9" expl="loop variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="9598"/></proof>
  </goal>
  <goal name="search&#39;vc.10" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="9500"/></proof>
  </goal>
  <goal name="search&#39;vc.11" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="10768"/></proof>
  </goal>
  <goal name="search&#39;vc.12" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="9982"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="search_rec&#39;vc" expl="VC for search_rec" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="search_rec&#39;vc.0" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="8149"/></proof>
  </goal>
  <goal name="search_rec&#39;vc.1" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="8824"/></proof>
  </goal>
  <goal name="search_rec&#39;vc.2" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="8897"/></proof>
  </goal>
  <goal name="search_rec&#39;vc.3" expl="variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="9043"/></proof>
  </goal>
  <goal name="search_rec&#39;vc.4" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="9052"/></proof>
  </goal>
  <goal name="search_rec&#39;vc.5" expl="variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="8996"/></proof>
  </goal>
  <goal name="search_rec&#39;vc.6" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="9012"/></proof>
  </goal>
  <goal name="search_rec&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="17080"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
