<?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="1.8" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="1" name="CVC4" version="1.4" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="Eprover" version="1.8-001" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="3" name="CVC4" version="1.5" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="4" name="Vampire" version="0.6" timelimit="6" steplimit="0" memlimit="1000"/>
<prover id="5" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="tree_height.mlw"/>
<theory name="HeightCPS" proved="true">
 <goal name="height_cps&#39;vc" expl="VC for height_cps" proved="true">
 <proof prover="5"><result status="valid" time="0.00" steps="48"/></proof>
 </goal>
 <goal name="height&#39;vc" expl="VC for height" proved="true">
 <proof prover="5"><result status="valid" time="0.00" steps="2"/></proof>
 </goal>
</theory>
<theory name="Iteration" proved="true">
 <goal name="sizek_nonneg" proved="true">
 <transf name="induction_ty_lex" proved="true" >
  <goal name="sizek_nonneg.0" proved="true">
  <proof prover="5" timelimit="6"><result status="valid" time="0.01" steps="15"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="helper1" proved="true">
 <proof prover="5" timelimit="6"><result status="valid" time="0.01" steps="2"/></proof>
 </goal>
 <goal name="sizew_nonneg" proved="true">
 <proof prover="2"><result status="valid" time="0.11"/></proof>
 </goal>
 <goal name="height1&#39;vc" expl="VC for height1" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="height1&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="5"><result status="valid" time="0.00" steps="9"/></proof>
  </goal>
  <goal name="height1&#39;vc.1" expl="loop variant decrease" proved="true">
  <proof prover="5"><result status="valid" time="0.00" steps="13"/></proof>
  </goal>
  <goal name="height1&#39;vc.2" expl="loop invariant preservation" proved="true">
  <proof prover="5"><result status="valid" time="0.01" steps="25"/></proof>
  </goal>
  <goal name="height1&#39;vc.3" expl="loop variant decrease" proved="true">
  <proof prover="5"><result status="valid" time="0.01" steps="15"/></proof>
  </goal>
  <goal name="height1&#39;vc.4" expl="loop invariant preservation" proved="true">
  <proof prover="5"><result status="valid" time="0.01" steps="39"/></proof>
  </goal>
  <goal name="height1&#39;vc.5" expl="unreachable point" proved="true">
  <proof prover="5"><result status="valid" time="0.01" steps="33"/></proof>
  </goal>
  <goal name="height1&#39;vc.6" expl="loop variant decrease" proved="true">
  <proof prover="5"><result status="valid" time="0.01" steps="13"/></proof>
  </goal>
  <goal name="height1&#39;vc.7" expl="loop invariant preservation" proved="true">
  <proof prover="5"><result status="valid" time="0.01" steps="32"/></proof>
  </goal>
  <goal name="height1&#39;vc.8" expl="loop variant decrease" proved="true">
  <proof prover="5"><result status="valid" time="0.01" steps="15"/></proof>
  </goal>
  <goal name="height1&#39;vc.9" expl="loop invariant preservation" proved="true">
  <proof prover="5"><result status="valid" time="0.01" steps="41"/></proof>
  </goal>
  <goal name="height1&#39;vc.10" expl="loop variant decrease" proved="true">
  <proof prover="5"><result status="valid" time="0.01" steps="14"/></proof>
  </goal>
  <goal name="height1&#39;vc.11" expl="loop invariant preservation" proved="true">
  <proof prover="5"><result status="valid" time="0.01" steps="31"/></proof>
  </goal>
  <goal name="height1&#39;vc.12" expl="loop variant decrease" proved="true">
  <proof prover="5"><result status="valid" time="0.01" steps="13"/></proof>
  </goal>
  <goal name="height1&#39;vc.13" expl="loop invariant preservation" proved="true">
  <proof prover="5"><result status="valid" time="0.01" steps="30"/></proof>
  </goal>
  <goal name="height1&#39;vc.14" expl="loop variant decrease" proved="true">
  <proof prover="5"><result status="valid" time="0.01" steps="15"/></proof>
  </goal>
  <goal name="height1&#39;vc.15" expl="loop invariant preservation" proved="true">
  <proof prover="5"><result status="valid" time="0.01" steps="41"/></proof>
  </goal>
  <goal name="height1&#39;vc.16" expl="loop variant decrease" proved="true">
  <proof prover="5"><result status="valid" time="0.00" steps="14"/></proof>
  </goal>
  <goal name="height1&#39;vc.17" expl="loop invariant preservation" proved="true">
  <proof prover="5"><result status="valid" time="0.01" steps="26"/></proof>
  </goal>
  <goal name="height1&#39;vc.18" expl="unreachable point" proved="true">
  <proof prover="5"><result status="valid" time="0.01" steps="5"/></proof>
  </goal>
  <goal name="height1&#39;vc.19" expl="postcondition" proved="true">
  <transf name="inline_all" proved="true" >
   <goal name="height1&#39;vc.19.0" expl="postcondition" proved="true">
   <proof prover="5"><result status="valid" time="0.01" steps="7"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="HeightStack" proved="true">
 <goal name="sizes_nonneg" proved="true">
 <transf name="induction_ty_lex" proved="true" >
  <goal name="sizes_nonneg.0" proved="true">
  <proof prover="4"><result status="valid" time="0.23"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="height_stack&#39;vc" expl="VC for height_stack" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="height_stack&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="5"><result status="valid" time="0.01" steps="36"/></proof>
  </goal>
  <goal name="height_stack&#39;vc.1" expl="precondition" proved="true">
  <proof prover="5"><result status="valid" time="0.00" steps="9"/></proof>
  </goal>
  <goal name="height_stack&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="5"><result status="valid" time="0.01" steps="21"/></proof>
  </goal>
  <goal name="height_stack&#39;vc.3" expl="precondition" proved="true">
  <proof prover="5"><result status="valid" time="0.01" steps="5"/></proof>
  </goal>
  <goal name="height_stack&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="1" timelimit="1"><result status="valid" time="0.07"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="height1&#39;vc" expl="VC for height1" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="height1&#39;vc.0" expl="precondition" proved="true">
  <proof prover="5"><result status="valid" time="0.00" steps="1"/></proof>
  </goal>
  <goal name="height1&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.02"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="HeightSmallSpace" proved="true">
 <goal name="height_limited&#39;vc" expl="VC for height_limited" proved="true">
 <proof prover="3"><result status="valid" time="0.31" steps="54985"/></proof>
 </goal>
 <goal name="height&#39;vc" expl="VC for height" proved="true">
 <proof prover="0"><result status="valid" time="0.03" steps="9865"/></proof>
 </goal>
</theory>
</file>
</why3session>
