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<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v2//EN" "http://why3.lri.fr/why3session.dtd">
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<why3session shape_version="4">
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 <prover id="0" name="Alt-Ergo" version="0.95.1"/>
 <prover id="1" name="CVC3" version="2.4.1"/>
 <prover id="2" name="CVC4" version="1.2"/>
 <prover id="3" name="Coq" version="8.4pl2"/>
 <file name="../there_and_back_again.mlw" verified="true"
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  expanded="true">
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  <theory name="Convolution" locfile="../there_and_back_again.mlw"
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   loclnum="14" loccnumb="7" loccnume="18"
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   verified="true">
   <goal name="WP_parameter convolution_rec"
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    locfile="../there_and_back_again.mlw"
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    loclnum="23" loccnumb="10" loccnume="25" expl="VC for convolution_rec"
    sum="22faf431ac140b8b7d34f3293b8a62bc" proved="true"
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    shape="Cainfix =aNilacombineV0areverseV2Aainfix =alengthV2alengthV0Aainfix =V1ainfix ++V2V1EaNilCainfix =aConsaTuple2V3V7V5acombineV0areverseV9Aainfix =alengthV9alengthV0Aainfix =V1ainfix ++V9V8EaConsVVfwV6Iainfix =V5acombineV4areverseV10Aainfix =alengthV10alengthV4Aainfix =V1ainfix ++V10V6EFAainfix &lt;=alengthV4alengthV1ACfaNilainfix =V11V4aConswVV0aConsVVV0Iainfix &lt;=alengthV0alengthV1F">
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    <label name="expl:VC for convolution_rec"/>
    <transf name="split_goal_wp"
     proved="true">
     <goal name="WP_parameter convolution_rec.1"
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      locfile="../there_and_back_again.mlw"
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      loclnum="23" loccnumb="10" loccnume="25" expl="1. postcondition"
      sum="2578338d236d385b43ab4fc5e13ecc2a" proved="true"
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      shape="postconditionCainfix =aNilacombineV0areverseV2Aainfix =alengthV2alengthV0Aainfix =V1ainfix ++V2V1EaNiltaConsVVV0Iainfix &lt;=alengthV0alengthV1F">
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      <label name="expl:VC for convolution_rec"/>
      <proof prover="1" timelimit="120"
       memlimit="1000">
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       <result status="valid" time="0.09"/>
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      </proof>
     </goal>
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     <goal name="WP_parameter convolution_rec.2"
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      locfile="../there_and_back_again.mlw"
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      loclnum="23" loccnumb="10" loccnume="25" expl="2. variant decrease"
      sum="58fe9655e71712006c4d108961ab8235" proved="true"
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      shape="variant decreaseCtaNilCfaNilainfix =V4V3aConswVV0aConsVVV0Iainfix &lt;=alengthV0alengthV1F">
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      <label name="expl:VC for convolution_rec"/>
      <proof prover="0" timelimit="5"
       memlimit="1000">
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       <result status="valid" time="0.02"/>
      </proof>
     </goal>
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     <goal name="WP_parameter convolution_rec.3"
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      locfile="../there_and_back_again.mlw"
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      loclnum="23" loccnumb="10" loccnume="25" expl="3. precondition"
      sum="f5a1ff8c6e6ca528baf5fd2645aa4871" proved="true"
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      shape="preconditionCtaNilainfix &lt;=alengthV3alengthV1aConsVVV0Iainfix &lt;=alengthV0alengthV1F">
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      <label name="expl:VC for convolution_rec"/>
      <proof prover="0" timelimit="5"
       memlimit="1000">
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       <result status="valid" time="0.01"/>
      </proof>
     </goal>
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     <goal name="WP_parameter convolution_rec.4"
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      locfile="../there_and_back_again.mlw"
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      loclnum="23" loccnumb="10" loccnume="25" expl="4. postcondition"
      sum="30ca916d2de77d7836e6edaf4aa59226" proved="true"
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      shape="postconditionCtaNilCainfix =aConsaTuple2V2V6V4acombineV0areverseV8Aainfix =alengthV8alengthV0Aainfix =V1ainfix ++V8V7EaConsVVtwV5Iainfix =V4acombineV3areverseV9Aainfix =alengthV9alengthV3Aainfix =V1ainfix ++V9V5EFIainfix &lt;=alengthV3alengthV1aConsVVV0Iainfix &lt;=alengthV0alengthV1F">
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      <label name="expl:VC for convolution_rec"/>
      <proof prover="2" timelimit="5"
       memlimit="1000">
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       <result status="valid" time="0.10"/>
      </proof>
     </goal>
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     <goal name="WP_parameter convolution_rec.5"
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      locfile="../there_and_back_again.mlw"
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      loclnum="23" loccnumb="10" loccnume="25" expl="5. unreachable point"
      sum="bcd1a3f4e8c1f94806b0a1a2efe8e0c7" proved="true"
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      shape="unreachable pointCtaNilCtaConsVVfwV5Iainfix =V4acombineV3areverseV8Aainfix =alengthV8alengthV3Aainfix =V1ainfix ++V8V5EFIainfix &lt;=alengthV3alengthV1aConsVVV0Iainfix &lt;=alengthV0alengthV1F">
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      <label name="expl:VC for convolution_rec"/>
      <proof prover="0" timelimit="5"
       memlimit="1000">
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       <result status="valid" time="0.01"/>
      </proof>
     </goal>
    </transf>
   </goal>
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   <goal name="WP_parameter convolution"
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    locfile="../there_and_back_again.mlw"
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    loclnum="38" loccnumb="6" loccnume="17" expl="VC for convolution"
    sum="47bd5f6ce3b3a33fcb639be1178401ea" proved="true"
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    shape="ainfix =V2acombineV0areverseV1Iainfix =V2acombineV0areverseV4Aainfix =alengthV4alengthV0Aainfix =V1ainfix ++V4V3EFAainfix &lt;=alengthV0alengthV1Iainfix =alengthV0alengthV1F">
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    <label name="expl:VC for convolution"/>
    <transf name="split_goal_wp"
     proved="true">
     <goal name="WP_parameter convolution.1"
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      locfile="../there_and_back_again.mlw"
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      loclnum="38" loccnumb="6" loccnume="17" expl="1. precondition"
      sum="33b7e3fa21baef1f5528850d357347ea" proved="true"
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      shape="preconditionainfix &lt;=alengthV0alengthV1Iainfix =alengthV0alengthV1F">
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      <label name="expl:VC for convolution"/>
      <proof prover="0" timelimit="5"
       memlimit="1000">
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       <result status="valid" time="0.01"/>
      </proof>
     </goal>
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     <goal name="WP_parameter convolution.2"
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      locfile="../there_and_back_again.mlw"
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      loclnum="38" loccnumb="6" loccnume="17" expl="2. postcondition"
      sum="585a01daf53e72da42746dc842ae0114" proved="true"
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      shape="postconditionainfix =V2acombineV0areverseV1Iainfix =V2acombineV0areverseV4Aainfix =alengthV4alengthV0Aainfix =V1ainfix ++V4V3EFIainfix &lt;=alengthV0alengthV1Iainfix =alengthV0alengthV1F">
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      <label name="expl:VC for convolution"/>
      <proof prover="0" timelimit="5"
       memlimit="1000">
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       <result status="valid" time="0.02"/>
      </proof>
     </goal>
    </transf>
   </goal>
  </theory>
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  <theory name="Palindrome" locfile="../there_and_back_again.mlw"
   loclnum="51" loccnumb="7" loccnume="17" verified="true"
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   expanded="true">
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   <goal name="WP_parameter palindrome_rec"
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    locfile="../there_and_back_again.mlw"
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    loclnum="66" loccnumb="10" loccnume="24" expl="VC for palindrome_rec"
    sum="dd552eb4487b09f2fb5cb966f1a1ba03" proved="true" expanded="true"
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    shape="CCCNainfix =anthV8V0anthainfix -ainfix -alengthV1c1V8V0Aainfix &lt;V8alengthV1Aainfix &lt;=c0V8EINainfix =anthV9V7anthainfix -ainfix -alengthV5c1V9V7Aainfix &lt;V9alengthV5Aainfix &lt;=c0V9EACiNainfix =anthV13V0anthainfix -ainfix -alengthV1c1V13V0Aainfix &lt;V13alengthV1Aainfix &lt;=c0V13EapalV0alengthV1Aainfix =V0ainfix ++V14V12Aainfix =alengthV14alengthV1Eainfix =V6V11Aainfix =anthainfix -alengthV1c1V0aSomeV11aConsVVfaNilV10IapalV7alengthV5Aainfix =V7ainfix ++V15V10Aainfix =alengthV15alengthV5EFAainfix &gt;=alengthV7alengthV5ACfaNilainfix =V16V7aConswVV0aConsVVfwV0aConsVVCapalV0alengthV1Aainfix =V0ainfix ++V19V18Aainfix =alengthV19alengthV1EaConsVVfwV0aNilV3aConsVVapalV0alengthV1Aainfix =V0ainfix ++V20V0Aainfix =alengthV20alengthV1EaNilV1Iainfix &gt;=alengthV0alengthV1F">
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    <label name="expl:VC for palindrome_rec"/>
    <transf name="split_goal_wp" proved="true"
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     expanded="true">
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     <goal name="WP_parameter palindrome_rec.1"
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      locfile="../there_and_back_again.mlw"
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      loclnum="66" loccnumb="10" loccnume="24" expl="1. variant decrease"
      sum="1a7a77a2b71d12a8f29292c7c0032432" proved="true" expanded="true"
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      shape="variant decreaseCCCCfaNilainfix =V8V7aConswVV0aConsVVtwV0aConsVVtaNilV3aConsVVtaNilV1Iainfix &gt;=alengthV0alengthV1F">
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      <label name="expl:VC for palindrome_rec"/>
      <proof prover="0" timelimit="5"
       memlimit="1000">
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       <result status="valid" time="0.01"/>
      </proof>
     </goal>
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     <goal name="WP_parameter palindrome_rec.2"
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      locfile="../there_and_back_again.mlw"
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      loclnum="66" loccnumb="10" loccnume="24" expl="2. precondition"
      sum="ac9e85b375c6e7c6dbdffa8d13088ce7" proved="true" expanded="true"
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      shape="preconditionCCCainfix &gt;=alengthV7alengthV5aConsVVtwV0aConsVVtaNilV3aConsVVtaNilV1Iainfix &gt;=alengthV0alengthV1F">
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      <label name="expl:VC for palindrome_rec"/>
      <proof prover="0" timelimit="5"
       memlimit="1000">
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       <result status="valid" time="0.01"/>
      </proof>
     </goal>
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     <goal name="WP_parameter palindrome_rec.3"
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      locfile="../there_and_back_again.mlw"
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      loclnum="66" loccnumb="10" loccnume="24" expl="3. assertion"
      sum="8e5acc27f24c3c888305d7da4a95b51e" proved="true" expanded="true"
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      shape="assertionCCCCainfix =anthainfix -alengthV1c1V0aSomeV9aConsVVtaNilV8IapalV7alengthV5Aainfix =V7ainfix ++V11V8Aainfix =alengthV11alengthV5EFIainfix &gt;=alengthV7alengthV5aConsVVtwV0aConsVVtaNilV3aConsVVtaNilV1Iainfix &gt;=alengthV0alengthV1F">
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      <label name="expl:VC for palindrome_rec"/>
      <proof prover="0" timelimit="5"
       memlimit="1000">
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       <result status="valid" time="0.05"/>
      </proof>
     </goal>
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     <goal name="WP_parameter palindrome_rec.4"
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      locfile="../there_and_back_again.mlw"
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      loclnum="66" loccnumb="10" loccnume="24" expl="4. postcondition"
      sum="47b001718e81143a66d2ce685428f062" proved="true" expanded="true"
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      shape="postconditionCCCCainfix =V0ainfix ++V11V10Aainfix =alengthV11alengthV1EIainfix =V6V9Iainfix =anthainfix -alengthV1c1V0aSomeV9aConsVVtaNilV8IapalV7alengthV5Aainfix =V7ainfix ++V12V8Aainfix =alengthV12alengthV5EFIainfix &gt;=alengthV7alengthV5aConsVVtwV0aConsVVtaNilV3aConsVVtaNilV1Iainfix &gt;=alengthV0alengthV1F">
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      <label name="expl:VC for palindrome_rec"/>
      <proof prover="2" timelimit="5"
       memlimit="1000">
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       <result status="valid" time="0.30"/>
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      </proof>
     </goal>
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     <goal name="WP_parameter palindrome_rec.5"
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      locfile="../there_and_back_again.mlw"
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      loclnum="66" loccnumb="10" loccnume="24" expl="5. postcondition"
      sum="32fc2bfbe40ce7a16a80e9b8afee640b" proved="true" expanded="true"
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      shape="postconditionCCCCapalV0alengthV1Iainfix =V6V9Iainfix =anthainfix -alengthV1c1V0aSomeV9aConsVVtaNilV8IapalV7alengthV5Aainfix =V7ainfix ++V11V8Aainfix =alengthV11alengthV5EFIainfix &gt;=alengthV7alengthV5aConsVVtwV0aConsVVtaNilV3aConsVVtaNilV1Iainfix &gt;=alengthV0alengthV1F">
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      <label name="expl:VC for palindrome_rec"/>
      <proof prover="0" timelimit="5"
       memlimit="1000">
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       <result status="valid" time="0.13"/>
      </proof>
     </goal>
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     <goal name="WP_parameter palindrome_rec.6"
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      locfile="../there_and_back_again.mlw"
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      loclnum="66" loccnumb="10" loccnume="24"
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      expl="6. exceptional postcondition"
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      sum="73ad5639e6af1dc25f1f797b6efaf5ce" proved="true" expanded="true"
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      shape="exceptional postconditionCCCCNainfix =anthV11V0anthainfix -ainfix -alengthV1c1V11V0Aainfix &lt;V11alengthV1Aainfix &lt;=c0V11EINainfix =V6V9Iainfix =anthainfix -alengthV1c1V0aSomeV9aConsVVtaNilV8IapalV7alengthV5Aainfix =V7ainfix ++V12V8Aainfix =alengthV12alengthV5EFIainfix &gt;=alengthV7alengthV5aConsVVtwV0aConsVVtaNilV3aConsVVtaNilV1Iainfix &gt;=alengthV0alengthV1F">
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      <label name="expl:VC for palindrome_rec"/>
      <proof prover="0" timelimit="5"
       memlimit="1000">
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       <result status="valid" time="0.06"/>
      </proof>
     </goal>
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     <goal name="WP_parameter palindrome_rec.7"
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      locfile="../there_and_back_again.mlw"
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      loclnum="66" loccnumb="10" loccnume="24" expl="7. unreachable point"
      sum="ea9ceb9e47703654db4620edd54076c5" proved="true" expanded="true"
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      shape="unreachable pointCCCCtaConsVVfaNilV8IapalV7alengthV5Aainfix =V7ainfix ++V11V8Aainfix =alengthV11alengthV5EFIainfix &gt;=alengthV7alengthV5aConsVVtwV0aConsVVtaNilV3aConsVVtaNilV1Iainfix &gt;=alengthV0alengthV1F">
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      <label name="expl:VC for palindrome_rec"/>
      <proof prover="0" timelimit="5"
       memlimit="1000">
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       <result status="valid" time="0.01"/>
      </proof>
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      <proof prover="1" timelimit="5"
       memlimit="1000">
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       <result status="valid" time="0.03"/>
      </proof>
     </goal>
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     <goal name="WP_parameter palindrome_rec.8"
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      locfile="../there_and_back_again.mlw"
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      loclnum="66" loccnumb="10" loccnume="24"
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      expl="8. exceptional postcondition"
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      sum="7b8665c0759287816f2d21516d87252d" proved="true" expanded="true"
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      shape="exceptional postconditionCCCNainfix =anthV8V0anthainfix -ainfix -alengthV1c1V8V0Aainfix &lt;V8alengthV1Aainfix &lt;=c0V8EINainfix =anthV9V7anthainfix -ainfix -alengthV5c1V9V7Aainfix &lt;V9alengthV5Aainfix &lt;=c0V9EIainfix &gt;=alengthV7alengthV5aConsVVtwV0aConsVVtaNilV3aConsVVtaNilV1Iainfix &gt;=alengthV0alengthV1F">
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      <label name="expl:VC for palindrome_rec"/>
      <proof prover="3" timelimit="20" memlimit="1000"
       edited="there_and_back_again_Palindrome_WP_parameter_palindrome_rec_1.v">
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       <result status="valid" time="1.32"/>
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      </proof>
     </goal>
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     <goal name="WP_parameter palindrome_rec.9"
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      locfile="../there_and_back_again.mlw"
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      loclnum="66" loccnumb="10" loccnume="24" expl="9. unreachable point"
      sum="102f622c5f6b32ba86e1ae09910dd0c6" proved="true" expanded="true"
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      shape="unreachable pointCCCtaConsVVfwV0aConsVVtaNilV3aConsVVtaNilV1Iainfix &gt;=alengthV0alengthV1F">
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      <label name="expl:VC for palindrome_rec"/>
      <proof prover="0" timelimit="5"
       memlimit="1000">
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       <result status="valid" time="0.02"/>
      </proof>
     </goal>
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     <goal name="WP_parameter palindrome_rec.10"
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      locfile="../there_and_back_again.mlw"
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      loclnum="66" loccnumb="10" loccnume="24" expl="10. postcondition"
      sum="8903219d760c8ddd560216ed8097a389" proved="true" expanded="true"
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      shape="postconditionCCtaConsVVCainfix =V0ainfix ++V8V7Aainfix =alengthV8alengthV1EaConsVVtwV0aNilV3aConsVVtaNilV1Iainfix &gt;=alengthV0alengthV1F">
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      <label name="expl:VC for palindrome_rec"/>
      <proof prover="0" timelimit="5"
       memlimit="1000">
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       <result status="valid" time="3.08"/>
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      </proof>
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      <proof prover="2" timelimit="5"
       memlimit="1000">
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       <result status="valid" time="0.02"/>
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      </proof>
     </goal>
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     <goal name="WP_parameter palindrome_rec.11"
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      locfile="../there_and_back_again.mlw"
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      loclnum="66" loccnumb="10" loccnume="24" expl="11. postcondition"
      sum="1f8372a46e1c3a17ca4823c821af42a6" proved="true" expanded="true"
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      shape="postconditionCCtaConsVVCapalV0alengthV1aConsVVtwV0aNilV3aConsVVtaNilV1Iainfix &gt;=alengthV0alengthV1F">
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      <label name="expl:VC for palindrome_rec"/>
      <proof prover="0" timelimit="5"
       memlimit="1000">
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       <result status="valid" time="0.01"/>
      </proof>
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      <proof prover="1" timelimit="5"
       memlimit="1000">
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       <result status="valid" time="0.02"/>
      </proof>
     </goal>
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     <goal name="WP_parameter palindrome_rec.12"
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      locfile="../there_and_back_again.mlw"
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      loclnum="66" loccnumb="10" loccnume="24" expl="12. unreachable point"
      sum="60fca71367765252f9ba31446a6115e9" proved="true" expanded="true"
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      shape="unreachable pointCCtaConsVVCtaConsVVfwV0aNilV3aConsVVtaNilV1Iainfix &gt;=alengthV0alengthV1F">
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      <label name="expl:VC for palindrome_rec"/>
      <proof prover="0" timelimit="5"
       memlimit="1000">
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       <result status="valid" time="0.02"/>
      </proof>
     </goal>
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     <goal name="WP_parameter palindrome_rec.13"
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      locfile="../there_and_back_again.mlw"
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      loclnum="66" loccnumb="10" loccnume="24" expl="13. postcondition"
      sum="f1095cdb88e521e35e8f8144a884e437" proved="true" expanded="true"
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      shape="postconditionCtaConsVVainfix =V0ainfix ++V4V0Aainfix =alengthV4alengthV1EaNilV1Iainfix &gt;=alengthV0alengthV1F">
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      <label name="expl:VC for palindrome_rec"/>
      <proof prover="0" timelimit="5"
       memlimit="1000">
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       <result status="valid" time="0.01"/>
      </proof>
     </goal>
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     <goal name="WP_parameter palindrome_rec.14"
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      locfile="../there_and_back_again.mlw"
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      loclnum="66" loccnumb="10" loccnume="24" expl="14. postcondition"
      sum="98fb188919fbeafd2b93e7e5acaaf262" proved="true" expanded="true"
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      shape="postconditionCtaConsVVapalV0alengthV1aNilV1Iainfix &gt;=alengthV0alengthV1F">
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      <label name="expl:VC for palindrome_rec"/>
      <proof prover="0" timelimit="5"
       memlimit="1000">
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       <result status="valid" time="0.01"/>
      </proof>
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      <proof prover="1" timelimit="5"
       memlimit="1000">
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       <result status="valid" time="0.00"/>
      </proof>
     </goal>
    </transf>
   </goal>
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   <goal name="WP_parameter palindrome" locfile="../there_and_back_again.mlw"
    loclnum="88" loccnumb="6" loccnume="16" expl="VC for palindrome"
    sum="ce72ff80fecefc0803403b1a085ff159" proved="true" expanded="true"
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    shape="NapalV0alengthV0INainfix =anthV1V0anthainfix -ainfix -alengthV0c1V1V0Aainfix &lt;V1alengthV0Aainfix &lt;=c0V1EAapalV0alengthV0IapalV0alengthV0Aainfix =V0ainfix ++V3V2Aainfix =alengthV3alengthV0EFAainfix &gt;=alengthV0alengthV0F">
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    <label name="expl:VC for palindrome"/>
    <transf name="split_goal_wp" proved="true"
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     expanded="true">
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     <goal name="WP_parameter palindrome.1"
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      locfile="../there_and_back_again.mlw"
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      loclnum="88" loccnumb="6" loccnume="16" expl="1. precondition"
      sum="5667369f374fab825af928fae9143a6b" proved="true" expanded="true"
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      shape="preconditionainfix &gt;=alengthV0alengthV0F">
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      <label name="expl:VC for palindrome"/>
      <proof prover="0" timelimit="5"
       memlimit="1000">
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       <result status="valid" time="0.00"/>
      </proof>
     </goal>
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     <goal name="WP_parameter palindrome.2"
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      locfile="../there_and_back_again.mlw"
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      loclnum="88" loccnumb="6" loccnume="16" expl="2. postcondition"
      sum="cee6be324cc4a5f00b2ae34f1915510e" proved="true" expanded="true"
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      shape="postconditionapalV0alengthV0IapalV0alengthV0Aainfix =V0ainfix ++V2V1Aainfix =alengthV2alengthV0EFIainfix &gt;=alengthV0alengthV0F">
319 320 321
      <label name="expl:VC for palindrome"/>
      <proof prover="0" timelimit="5"
       memlimit="1000">
322 323 324
       <result status="valid" time="0.00"/>
      </proof>
     </goal>
325
     <goal name="WP_parameter palindrome.3"
326
      locfile="../there_and_back_again.mlw"
327 328
      loclnum="88" loccnumb="6" loccnume="16" expl="3. postcondition"
      sum="433d9c3cbbf49f33bf85b40fd469f835" proved="true" expanded="true"
329
      shape="postconditionNapalV0alengthV0INainfix =anthV1V0anthainfix -ainfix -alengthV0c1V1V0Aainfix &lt;V1alengthV0Aainfix &lt;=c0V1EIainfix &gt;=alengthV0alengthV0F">
330 331 332
      <label name="expl:VC for palindrome"/>
      <proof prover="0" timelimit="5"
       memlimit="1000">
333 334 335 336 337 338
       <result status="valid" time="0.01"/>
      </proof>
     </goal>
    </transf>
   </goal>
  </theory>
339 340
 </file>
</why3session>