<?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="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="1" name="CVC4" version="1.5" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="Alt-Ergo" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="verifythis_2016_tree_traversal.mlw"/>
<theory name="TreeShape" proved="true">
 <goal name="ext_set&#39;vc" expl="VC for ext_set" proved="true">
 <proof prover="0"><result status="valid" time="0.19" steps="500"/></proof>
 </goal>
 <goal name="ext_cur&#39;vc" expl="VC for ext_cur" proved="true">
 <proof prover="0"><result status="valid" time="0.00" steps="5"/></proof>
 </goal>
 <goal name="unicity&#39;vc" expl="VC for unicity" proved="true">
 <proof prover="0"><result status="valid" time="0.03" steps="160"/></proof>
 </goal>
 <goal name="not_below&#39;vc" expl="VC for not_below" proved="true">
 <proof prover="0"><result status="valid" time="1.06" steps="6227"/></proof>
 </goal>
</theory>
<theory name="Recursive" proved="true">
 <goal name="markTree&#39;vc" expl="VC for markTree" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="markTree&#39;vc.0" expl="exceptional postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.00" steps="11"/></proof>
  </goal>
  <goal name="markTree&#39;vc.1" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="14"/></proof>
  </goal>
  <goal name="markTree&#39;vc.2" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.00" steps="19"/></proof>
  </goal>
  <goal name="markTree&#39;vc.3" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="21"/></proof>
  </goal>
  <goal name="markTree&#39;vc.4" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.00" steps="23"/></proof>
  </goal>
  <goal name="markTree&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.00" steps="15"/></proof>
  </goal>
  <goal name="markTree&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="23"/></proof>
  </goal>
  <goal name="markTree&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="17"/></proof>
  </goal>
  <goal name="markTree&#39;vc.8" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="25"/></proof>
  </goal>
  <goal name="markTree&#39;vc.9" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.00" steps="35"/></proof>
  </goal>
  <goal name="markTree&#39;vc.10" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.00" steps="22"/></proof>
  </goal>
  <goal name="markTree&#39;vc.11" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="22"/></proof>
  </goal>
  <goal name="markTree&#39;vc.12" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="22"/></proof>
  </goal>
  <goal name="markTree&#39;vc.13" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="24"/></proof>
  </goal>
  <goal name="markTree&#39;vc.14" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="24"/></proof>
  </goal>
  <goal name="markTree&#39;vc.15" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="26"/></proof>
  </goal>
  <goal name="markTree&#39;vc.16" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="21"/></proof>
  </goal>
  <goal name="markTree&#39;vc.17" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="29"/></proof>
  </goal>
  <goal name="markTree&#39;vc.18" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="23"/></proof>
  </goal>
  <goal name="markTree&#39;vc.19" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="31"/></proof>
  </goal>
  <goal name="markTree&#39;vc.20" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.10" steps="259"/></proof>
  </goal>
  <goal name="markTree&#39;vc.21" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="7"/></proof>
  </goal>
  <goal name="markTree&#39;vc.22" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="7"/></proof>
  </goal>
  <goal name="markTree&#39;vc.23" expl="unreachable point" proved="true">
  <proof prover="0"><result status="valid" time="0.00" steps="11"/></proof>
  </goal>
  <goal name="markTree&#39;vc.24" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="39"/></proof>
  </goal>
  <goal name="markTree&#39;vc.25" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="24"/></proof>
  </goal>
  <goal name="markTree&#39;vc.26" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.00" steps="2"/></proof>
  </goal>
  <goal name="markTree&#39;vc.27" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.00" steps="34"/></proof>
  </goal>
  <goal name="markTree&#39;vc.28" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="19472"/></proof>
  </goal>
  <goal name="markTree&#39;vc.29" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="129"/></proof>
  </goal>
  <goal name="markTree&#39;vc.30" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="36"/></proof>
  </goal>
  <goal name="markTree&#39;vc.31" expl="variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="55"/></proof>
  </goal>
  <goal name="markTree&#39;vc.32" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="77"/></proof>
  </goal>
  <goal name="markTree&#39;vc.33" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="61"/></proof>
  </goal>
  <goal name="markTree&#39;vc.34" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.05" steps="148"/></proof>
  </goal>
  <goal name="markTree&#39;vc.35" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="2"/></proof>
  </goal>
  <goal name="markTree&#39;vc.36" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.03" steps="366"/></proof>
  </goal>
  <goal name="markTree&#39;vc.37" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="58"/></proof>
  </goal>
  <goal name="markTree&#39;vc.38" expl="variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="77"/></proof>
  </goal>
  <goal name="markTree&#39;vc.39" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.03" steps="164"/></proof>
  </goal>
  <goal name="markTree&#39;vc.40" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.04" steps="170"/></proof>
  </goal>
  <goal name="markTree&#39;vc.41" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.13" steps="618"/></proof>
  </goal>
  <goal name="markTree&#39;vc.42" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="2"/></proof>
  </goal>
  <goal name="markTree&#39;vc.43" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.09" steps="357"/></proof>
  </goal>
  <goal name="markTree&#39;vc.44" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.12" steps="81"/></proof>
  </goal>
  <goal name="markTree&#39;vc.45" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.28" steps="717"/></proof>
  </goal>
  <goal name="markTree&#39;vc.46" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="40"/></proof>
  </goal>
  <goal name="markTree&#39;vc.47" expl="exceptional postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="2"/></proof>
  </goal>
  <goal name="markTree&#39;vc.48" expl="exceptional postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="2"/></proof>
  </goal>
  <goal name="markTree&#39;vc.49" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="38"/></proof>
  </goal>
  <goal name="markTree&#39;vc.50" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="45"/></proof>
  </goal>
  <goal name="markTree&#39;vc.51" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.06" steps="121"/></proof>
  </goal>
  <goal name="markTree&#39;vc.52" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="23"/></proof>
  </goal>
  <goal name="markTree&#39;vc.53" expl="exceptional postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="2"/></proof>
  </goal>
  <goal name="markTree&#39;vc.54" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.00" steps="5"/></proof>
  </goal>
  <goal name="markTree&#39;vc.55" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.00" steps="6"/></proof>
  </goal>
  <goal name="markTree&#39;vc.56" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="2"/></proof>
  </goal>
  <goal name="markTree&#39;vc.57" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="17"/></proof>
  </goal>
  <goal name="markTree&#39;vc.58" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="8"/></proof>
  </goal>
  <goal name="markTree&#39;vc.59" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="8"/></proof>
  </goal>
  <goal name="markTree&#39;vc.60" expl="loop variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2"/></proof>
  </goal>
  <goal name="markTree&#39;vc.61" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.00" steps="2"/></proof>
  </goal>
  <goal name="markTree&#39;vc.62" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.00" steps="2"/></proof>
  </goal>
  <goal name="markTree&#39;vc.63" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="47"/></proof>
  </goal>
  <goal name="markTree&#39;vc.64" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="18"/></proof>
  </goal>
  <goal name="markTree&#39;vc.65" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="28"/></proof>
  </goal>
  <goal name="markTree&#39;vc.66" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="28"/></proof>
  </goal>
  <goal name="markTree&#39;vc.67" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="29"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Iterative" proved="true">
 <goal name="stack_size_pos&#39;vc" expl="VC for stack_size_pos" proved="true">
 <proof prover="0"><result status="valid" time="0.07" steps="162"/></proof>
 </goal>
 <goal name="opening&#39;vc" expl="VC for opening" proved="true">
 <proof prover="0"><result status="valid" time="0.03" steps="92"/></proof>
 </goal>
 <goal name="closing&#39;vc" expl="VC for closing" proved="true">
 <proof prover="0"><result status="valid" time="0.27" steps="655"/></proof>
 </goal>
 <goal name="continuing&#39;vc" expl="VC for continuing" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="continuing&#39;vc.0" expl="unreachable point" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="16"/></proof>
  </goal>
  <goal name="continuing&#39;vc.1" expl="unreachable point" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="16"/></proof>
  </goal>
  <goal name="continuing&#39;vc.2" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.03" steps="61"/></proof>
  </goal>
  <goal name="continuing&#39;vc.3" expl="assertion" proved="true">
  <proof prover="0" timelimit="1"><result status="valid" time="0.10" steps="325"/></proof>
  </goal>
  <goal name="continuing&#39;vc.4" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.03" steps="71"/></proof>
  </goal>
  <goal name="continuing&#39;vc.5" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.29" steps="765"/></proof>
  </goal>
  <goal name="continuing&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="22"/></proof>
  </goal>
  <goal name="continuing&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="36"/></proof>
  </goal>
  <goal name="continuing&#39;vc.8" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.25" steps="402"/></proof>
  </goal>
  <goal name="continuing&#39;vc.9" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="20"/></proof>
  </goal>
  <goal name="continuing&#39;vc.10" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.07" steps="135"/></proof>
  </goal>
  <goal name="continuing&#39;vc.11" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.30" steps="911"/></proof>
  </goal>
  <goal name="continuing&#39;vc.12" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.12" steps="255"/></proof>
  </goal>
  <goal name="continuing&#39;vc.13" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.14" steps="354"/></proof>
  </goal>
  <goal name="continuing&#39;vc.14" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="21"/></proof>
  </goal>
  <goal name="continuing&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.04" steps="72"/></proof>
  </goal>
  <goal name="continuing&#39;vc.16" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.76" steps="674"/></proof>
  </goal>
  <goal name="continuing&#39;vc.17" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="20"/></proof>
  </goal>
  <goal name="continuing&#39;vc.18" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.06" steps="179"/></proof>
  </goal>
  <goal name="continuing&#39;vc.19" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.39" steps="1107"/></proof>
  </goal>
  <goal name="continuing&#39;vc.20" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.30" steps="385"/></proof>
  </goal>
  <goal name="continuing&#39;vc.21" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.29" steps="405"/></proof>
  </goal>
  <goal name="continuing&#39;vc.22" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="21"/></proof>
  </goal>
  <goal name="continuing&#39;vc.23" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.03" steps="63"/></proof>
  </goal>
  <goal name="continuing&#39;vc.24" expl="assertion" proved="true">
  <proof prover="0"><result status="valid" time="0.27" steps="490"/></proof>
  </goal>
  <goal name="continuing&#39;vc.25" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="46"/></proof>
  </goal>
  <goal name="continuing&#39;vc.26" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.62" steps="1277"/></proof>
  </goal>
  <goal name="continuing&#39;vc.27" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="23"/></proof>
  </goal>
  <goal name="continuing&#39;vc.28" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="28"/></proof>
  </goal>
  <goal name="continuing&#39;vc.29" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.03" steps="56"/></proof>
  </goal>
  <goal name="continuing&#39;vc.30" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="43"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="markTree&#39;vc" expl="VC for markTree" proved="true">
 <proof prover="0"><result status="valid" time="0.86" steps="1601"/></proof>
 </goal>
</theory>
</file>
</why3session>
