<?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="1.6" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="2" name="CVC4" version="1.5" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="3" name="Alt-Ergo" version="2.0.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="4" name="Z3" version="4.11.2" timelimit="1" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="verifythis_fm2012_LRS.mlw"/>
<theory name="LCP" proved="true">
 <goal name="not_common_prefix_if_last_char_are_different" proved="true">
 <proof prover="4"><result status="valid" time="0.010000" steps="10038"/></proof>
 </goal>
 <goal name="longest_common_prefix_succ" proved="true">
 <proof prover="3"><result status="valid" time="0.000000" steps="28"/></proof>
 </goal>
 <goal name="lcp&#39;vc" expl="VC for lcp" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="lcp&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3241"/></proof>
  </goal>
  <goal name="lcp&#39;vc.1" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3608"/></proof>
  </goal>
  <goal name="lcp&#39;vc.2" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3608"/></proof>
  </goal>
  <goal name="lcp&#39;vc.3" expl="loop variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="3761"/></proof>
  </goal>
  <goal name="lcp&#39;vc.4" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.880000" steps="6108258"/></proof>
  </goal>
  <goal name="lcp&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="13920"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="LCP_test" proved="true">
 <goal name="bench&#39;vc" expl="VC for bench" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="4322"/></proof>
 </goal>
</theory>
<theory name="SuffixSort" proved="true">
 <goal name="compare&#39;vc" expl="VC for compare" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="compare&#39;vc.0" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3321"/></proof>
  </goal>
  <goal name="compare&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3332"/></proof>
  </goal>
  <goal name="compare&#39;vc.2" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="4095"/></proof>
  </goal>
  <goal name="compare&#39;vc.3" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="4088"/></proof>
  </goal>
  <goal name="compare&#39;vc.4" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="4594"/></proof>
  </goal>
  <goal name="compare&#39;vc.5" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="4587"/></proof>
  </goal>
  <goal name="compare&#39;vc.6" expl="unreachable point" proved="true">
  <proof prover="3" timelimit="5"><result status="valid" time="0.010000" steps="25"/></proof>
  </goal>
  <goal name="compare&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.000000" steps="3674"/></proof>
  </goal>
  <goal name="compare&#39;vc.8" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="5242"/></proof>
  </goal>
  <goal name="compare&#39;vc.9" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.010000" steps="44"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="lcp_same_index" proved="true">
 <proof prover="2"><result status="valid" time="0.040000" steps="12932"/></proof>
 </goal>
 <goal name="le_trans" proved="true">
 <proof prover="3"><result status="valid" time="0.080000" steps="254"/></proof>
 </goal>
 <goal name="sort&#39;vc" expl="VC for sort" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="sort&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="13492"/></proof>
  </goal>
  <goal name="sort&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="16406"/></proof>
  </goal>
  <goal name="sort&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="14851"/></proof>
  </goal>
  <goal name="sort&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="14959"/></proof>
  </goal>
  <goal name="sort&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="14966"/></proof>
  </goal>
  <goal name="sort&#39;vc.5" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="14973"/></proof>
  </goal>
  <goal name="sort&#39;vc.6" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="14980"/></proof>
  </goal>
  <goal name="sort&#39;vc.7" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.070000" steps="20027"/></proof>
  </goal>
  <goal name="sort&#39;vc.8" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="15061"/></proof>
  </goal>
  <goal name="sort&#39;vc.9" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.050000" steps="17007"/></proof>
  </goal>
  <goal name="sort&#39;vc.10" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.070000" steps="17028"/></proof>
  </goal>
  <goal name="sort&#39;vc.11" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.070000" steps="20637"/></proof>
  </goal>
  <goal name="sort&#39;vc.12" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.080000" steps="20890"/></proof>
  </goal>
  <goal name="sort&#39;vc.13" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="17777"/></proof>
  </goal>
  <goal name="sort&#39;vc.14" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.050000" steps="17791"/></proof>
  </goal>
  <goal name="sort&#39;vc.15" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="17777"/></proof>
  </goal>
  <goal name="sort&#39;vc.16" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.050000" steps="18133"/></proof>
  </goal>
  <goal name="sort&#39;vc.17" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.010000" steps="109"/></proof>
  </goal>
  <goal name="sort&#39;vc.18" expl="loop variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="16130"/></proof>
  </goal>
  <goal name="sort&#39;vc.19" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.060000" steps="18647"/></proof>
  </goal>
  <goal name="sort&#39;vc.20" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.060000" steps="177"/></proof>
  </goal>
  <goal name="sort&#39;vc.21" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.070000" steps="23287"/></proof>
  </goal>
  <goal name="sort&#39;vc.22" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.200000" steps="39574"/></proof>
  </goal>
  <goal name="sort&#39;vc.23" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.680000" steps="938"/></proof>
  </goal>
  <goal name="sort&#39;vc.24" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.560000" steps="925"/></proof>
  </goal>
  <goal name="sort&#39;vc.25" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.050000" steps="17803"/></proof>
  </goal>
  <goal name="sort&#39;vc.26" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="15642"/></proof>
  </goal>
  <goal name="sort&#39;vc.27" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.130000" steps="345"/></proof>
  </goal>
  <goal name="sort&#39;vc.28" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="15693"/></proof>
  </goal>
  <goal name="sort&#39;vc.29" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="15542"/></proof>
  </goal>
  <goal name="sort&#39;vc.30" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="14903"/></proof>
  </goal>
  <goal name="sort&#39;vc.31" expl="out of loop bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="13033"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="SuffixSort_test" proved="true">
 <goal name="bench&#39;vc" expl="VC for bench" proved="true">
 <proof prover="2"><result status="valid" time="0.340000" steps="70987"/></proof>
 </goal>
</theory>
<theory name="SuffixArray" proved="true">
 <goal name="suffixArray&#39;vc" expl="VC for suffixArray" proved="true">
 <proof prover="2"><result status="valid" time="0.040000" steps="17209"/></proof>
 </goal>
 <goal name="select&#39;vc" expl="VC for select" proved="true">
 <proof prover="2"><result status="valid" time="0.040000" steps="13252"/></proof>
 </goal>
 <goal name="permut_permutation" proved="true">
 <proof prover="4"><result status="valid" time="0.030000" steps="129768"/></proof>
 </goal>
 <goal name="create&#39;vc" expl="VC for create" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="create&#39;vc.0" expl="array creation size" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="12384"/></proof>
  </goal>
  <goal name="create&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="12194"/></proof>
  </goal>
  <goal name="create&#39;vc.2" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="13219"/></proof>
  </goal>
  <goal name="create&#39;vc.3" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.020000" steps="37"/></proof>
  </goal>
  <goal name="create&#39;vc.4" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.050000" steps="12880"/></proof>
  </goal>
  <goal name="create&#39;vc.5" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.060000" steps="19567"/></proof>
  </goal>
  <goal name="create&#39;vc.6" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.040000" steps="100498"/></proof>
  </goal>
  <goal name="create&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="12462"/></proof>
  </goal>
  <goal name="create&#39;vc.8" expl="out of loop bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="16969"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="lcp&#39;vc" expl="VC for lcp" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="lcp&#39;vc.0" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.050000" steps="13345"/></proof>
  </goal>
  <goal name="lcp&#39;vc.1" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="13348"/></proof>
  </goal>
  <goal name="lcp&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.080000" steps="16737"/></proof>
  </goal>
  <goal name="lcp&#39;vc.3" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.070000" steps="17116"/></proof>
  </goal>
  <goal name="lcp&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.020000" steps="76"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="SuffixArray_test" proved="true">
 <goal name="bench&#39;vc" expl="VC for bench" proved="true">
 <proof prover="2"><result status="valid" time="0.050000" steps="19408"/></proof>
 </goal>
</theory>
<theory name="LRS" proved="true">
 <goal name="lcp_sym" proved="true">
 <proof prover="3"><result status="valid" time="0.010000" steps="40"/></proof>
 </goal>
 <goal name="le_le_common_prefix" proved="true">
 <proof prover="3"><result status="valid" time="0.050000" steps="155"/></proof>
 </goal>
 <goal name="le_le_longest_common_prefix" proved="true">
 <proof prover="2"><result status="valid" time="0.040000" steps="12938"/></proof>
 </goal>
 <goal name="lrs&#39;vc" expl="VC for lrs" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="lrs&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="13344"/></proof>
  </goal>
  <goal name="lrs&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="12870"/></proof>
  </goal>
  <goal name="lrs&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="15234"/></proof>
  </goal>
  <goal name="lrs&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="14355"/></proof>
  </goal>
  <goal name="lrs&#39;vc.4" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="14626"/></proof>
  </goal>
  <goal name="lrs&#39;vc.5" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="15063"/></proof>
  </goal>
  <goal name="lrs&#39;vc.6" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="15103"/></proof>
  </goal>
  <goal name="lrs&#39;vc.7" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.080000" steps="22575"/></proof>
  </goal>
  <goal name="lrs&#39;vc.8" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.080000" steps="22836"/></proof>
  </goal>
  <goal name="lrs&#39;vc.9" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.080000" steps="25467"/></proof>
  </goal>
  <goal name="lrs&#39;vc.10" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.340000" steps="67386"/></proof>
  </goal>
  <goal name="lrs&#39;vc.11" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="14960"/></proof>
  </goal>
  <goal name="lrs&#39;vc.12" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="14979"/></proof>
  </goal>
  <goal name="lrs&#39;vc.13" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="15030"/></proof>
  </goal>
  <goal name="lrs&#39;vc.14" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.360000" steps="81085"/></proof>
  </goal>
  <goal name="lrs&#39;vc.15" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.080000" steps="22029"/></proof>
  </goal>
  <goal name="lrs&#39;vc.16" expl="assertion" proved="true">
  <transf name="introduce_premises" proved="true" >
   <goal name="lrs&#39;vc.16.0" expl="assertion" proved="true">
   <transf name="assert" proved="true" arg1="(surjective (suffixes sa).elts a.length)">
    <goal name="lrs&#39;vc.16.0.0" expl="asserted formula" proved="true">
    <proof prover="2"><result status="valid" time="0.060000" steps="17974"/></proof>
    </goal>
    <goal name="lrs&#39;vc.16.0.1" expl="assertion" proved="true">
    <transf name="unfold" proved="true" arg1="surjective" arg2="in" arg3="h">
     <goal name="lrs&#39;vc.16.0.1.0" expl="assertion" proved="true">
     <transf name="instantiate" proved="true" arg1="h" arg2="x">
      <goal name="lrs&#39;vc.16.0.1.0.0" expl="assertion" proved="true">
      <transf name="instantiate" proved="true" arg1="h" arg2="y">
       <goal name="lrs&#39;vc.16.0.1.0.0.0" expl="assertion" proved="true">
       <proof prover="2"><result status="valid" time="0.060000" steps="16929"/></proof>
       </goal>
      </transf>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="lrs&#39;vc.17" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="15410"/></proof>
  </goal>
  <goal name="lrs&#39;vc.18" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="15421"/></proof>
  </goal>
  <goal name="lrs&#39;vc.19" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="15464"/></proof>
  </goal>
  <goal name="lrs&#39;vc.20" expl="postcondition" proved="true">
  <transf name="introduce_premises" proved="true" >
   <goal name="lrs&#39;vc.20.0" expl="postcondition" proved="true">
   <transf name="instantiate" proved="true" arg1="Assert" arg2="x,y">
    <goal name="lrs&#39;vc.20.0.0" expl="postcondition" proved="true">
    <proof prover="0"><result status="valid" time="0.060000" steps="14756"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="lrs&#39;vc.21" expl="out of loop bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="15139"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="LRS_test" proved="true">
 <goal name="bench&#39;vc" expl="VC for bench" proved="true">
 <proof prover="2"><result status="valid" time="0.040000" steps="17170"/></proof>
 </goal>
</theory>
</file>
</why3session>
