/export/starexec/sandbox/solver/bin/starexec_run_Certifiable /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


YES
<?xml version="1.0"?>
<?xml-stylesheet type="text/xsl" href="cpfHTML.xsl"?>
<certificationProblem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="cpf.xsd">
 <input>
  <trsInput>
   <trs>
    <rules>
     <rule>
      <lhs>
       <funapp>
        <name>filter</name>
        <arg>
         <funapp>
          <name>cons</name>
          <arg>
           <var>X</var>
          </arg>
         </funapp>
        </arg>
        <arg>
         <funapp>
          <name>0</name>
         </funapp>
        </arg>
        <arg>
         <var>M</var>
        </arg>
       </funapp>
      </lhs>
      <rhs>
       <funapp>
        <name>cons</name>
        <arg>
         <funapp>
          <name>0</name>
         </funapp>
        </arg>
       </funapp>
      </rhs>
     </rule>
     <rule>
      <lhs>
       <funapp>
        <name>filter</name>
        <arg>
         <funapp>
          <name>cons</name>
          <arg>
           <var>X</var>
          </arg>
         </funapp>
        </arg>
        <arg>
         <funapp>
          <name>s</name>
          <arg>
           <var>N</var>
          </arg>
         </funapp>
        </arg>
        <arg>
         <var>M</var>
        </arg>
       </funapp>
      </lhs>
      <rhs>
       <funapp>
        <name>cons</name>
        <arg>
         <var>X</var>
        </arg>
       </funapp>
      </rhs>
     </rule>
     <rule>
      <lhs>
       <funapp>
        <name>sieve</name>
        <arg>
         <funapp>
          <name>cons</name>
          <arg>
           <funapp>
            <name>0</name>
           </funapp>
          </arg>
         </funapp>
        </arg>
       </funapp>
      </lhs>
      <rhs>
       <funapp>
        <name>cons</name>
        <arg>
         <funapp>
          <name>0</name>
         </funapp>
        </arg>
       </funapp>
      </rhs>
     </rule>
     <rule>
      <lhs>
       <funapp>
        <name>sieve</name>
        <arg>
         <funapp>
          <name>cons</name>
          <arg>
           <funapp>
            <name>s</name>
            <arg>
             <var>N</var>
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       </funapp>
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        <name>cons</name>
        <arg>
         <funapp>
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          <arg>
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         </funapp>
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       </funapp>
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     </rule>
     <rule>
      <lhs>
       <funapp>
        <name>nats</name>
        <arg>
         <var>N</var>
        </arg>
       </funapp>
      </lhs>
      <rhs>
       <funapp>
        <name>cons</name>
        <arg>
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       </funapp>
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     <rule>
      <lhs>
       <funapp>
        <name>zprimes</name>
       </funapp>
      </lhs>
      <rhs>
       <funapp>
        <name>sieve</name>
        <arg>
         <funapp>
          <name>nats</name>
          <arg>
           <funapp>
            <name>s</name>
            <arg>
             <funapp>
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              <arg>
               <funapp>
                <name>0</name>
               </funapp>
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             </funapp>
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           </funapp>
          </arg>
         </funapp>
        </arg>
       </funapp>
      </rhs>
     </rule>
    </rules>
   </trs>
  </trsInput>
 </input>
 <cpfVersion>2.2</cpfVersion>
 <proof>
  <trsTerminationProof>
   <dpTrans>
    <dps>
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      <rule>
       <lhs>
        <funapp>
         <sharp>
         <name>zprimes</name></sharp>
        </funapp>
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       <rhs>
        <funapp>
         <sharp>
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         <arg>
          <funapp>
           <name>s</name>
           <arg>
            <funapp>
             <name>s</name>
             <arg>
              <funapp>
               <name>0</name>
              </funapp>
             </arg>
            </funapp>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <sharp>
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        </funapp>
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       <rhs>
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         <sharp>
         <name>sieve</name></sharp>
         <arg>
          <funapp>
           <name>nats</name>
           <arg>
            <funapp>
             <name>s</name>
             <arg>
              <funapp>
               <name>s</name>
               <arg>
                <funapp>
                 <name>0</name>
                </funapp>
               </arg>
              </funapp>
             </arg>
            </funapp>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </rhs>
      </rule>
     </rules>
    </dps>
    <markedSymbols>true</markedSymbols>
    <dpProof>
     <depGraphProc>
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           <funapp>
            <sharp>
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           </funapp>
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          <rhs>
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            <sharp>
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                <arg>
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               </funapp>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </rhs>
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       <realScc>false</realScc>
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      <component>
       <dps>
        <rules>
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          <lhs>
           <funapp>
            <sharp>
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           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>nats</name></sharp>
            <arg>
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              <name>s</name>
              <arg>
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                <name>s</name>
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              </arg>
             </funapp>
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      </component>
     </depGraphProc>
    </dpProof>
   </dpTrans>
  </trsTerminationProof>
 </proof>
 <origin>
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   <tool>
    <name>NaTT</name>
    <version>certifiable-1.6</version>
   </tool>
  </proofOrigin>
 </origin>
</certificationProblem>