/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>P</name>
        <arg>
         <var>x1</var>
        </arg>
       </funapp>
      </lhs>
      <rhs>
       <funapp>
        <name>Q</name>
        <arg>
         <funapp>
          <name>Q</name>
          <arg>
           <funapp>
            <name>p</name>
            <arg>
             <var>x1</var>
            </arg>
           </funapp>
          </arg>
         </funapp>
        </arg>
       </funapp>
      </rhs>
     </rule>
     <rule>
      <lhs>
       <funapp>
        <name>p</name>
        <arg>
         <funapp>
          <name>p</name>
          <arg>
           <var>x1</var>
          </arg>
         </funapp>
        </arg>
       </funapp>
      </lhs>
      <rhs>
       <funapp>
        <name>q</name>
        <arg>
         <funapp>
          <name>q</name>
          <arg>
           <var>x1</var>
          </arg>
         </funapp>
        </arg>
       </funapp>
      </rhs>
     </rule>
     <rule>
      <lhs>
       <funapp>
        <name>p</name>
        <arg>
         <funapp>
          <name>Q</name>
          <arg>
           <funapp>
            <name>Q</name>
            <arg>
             <var>x1</var>
            </arg>
           </funapp>
          </arg>
         </funapp>
        </arg>
       </funapp>
      </lhs>
      <rhs>
       <funapp>
        <name>Q</name>
        <arg>
         <funapp>
          <name>Q</name>
          <arg>
           <funapp>
            <name>p</name>
            <arg>
             <var>x1</var>
            </arg>
           </funapp>
          </arg>
         </funapp>
        </arg>
       </funapp>
      </rhs>
     </rule>
     <rule>
      <lhs>
       <funapp>
        <name>Q</name>
        <arg>
         <funapp>
          <name>p</name>
          <arg>
           <funapp>
            <name>q</name>
            <arg>
             <var>x1</var>
            </arg>
           </funapp>
          </arg>
         </funapp>
        </arg>
       </funapp>
      </lhs>
      <rhs>
       <funapp>
        <name>q</name>
        <arg>
         <funapp>
          <name>p</name>
          <arg>
           <funapp>
            <name>Q</name>
            <arg>
             <var>x1</var>
            </arg>
           </funapp>
          </arg>
         </funapp>
        </arg>
       </funapp>
      </rhs>
     </rule>
     <rule>
      <lhs>
       <funapp>
        <name>q</name>
        <arg>
         <funapp>
          <name>q</name>
          <arg>
           <funapp>
            <name>p</name>
            <arg>
             <var>x1</var>
            </arg>
           </funapp>
          </arg>
         </funapp>
        </arg>
       </funapp>
      </lhs>
      <rhs>
       <funapp>
        <name>p</name>
        <arg>
         <funapp>
          <name>q</name>
          <arg>
           <funapp>
            <name>q</name>
            <arg>
             <var>x1</var>
            </arg>
           </funapp>
          </arg>
         </funapp>
        </arg>
       </funapp>
      </rhs>
     </rule>
     <rule>
      <lhs>
       <funapp>
        <name>q</name>
        <arg>
         <funapp>
          <name>Q</name>
          <arg>
           <var>x1</var>
          </arg>
         </funapp>
        </arg>
       </funapp>
      </lhs>
      <rhs>
       <var>x1</var>
      </rhs>
     </rule>
     <rule>
      <lhs>
       <funapp>
        <name>Q</name>
        <arg>
         <funapp>
          <name>q</name>
          <arg>
           <var>x1</var>
          </arg>
         </funapp>
        </arg>
       </funapp>
      </lhs>
      <rhs>
       <var>x1</var>
      </rhs>
     </rule>
     <rule>
      <lhs>
       <funapp>
        <name>p</name>
        <arg>
         <funapp>
          <name>P</name>
          <arg>
           <var>x1</var>
          </arg>
         </funapp>
        </arg>
       </funapp>
      </lhs>
      <rhs>
       <var>x1</var>
      </rhs>
     </rule>
     <rule>
      <lhs>
       <funapp>
        <name>P</name>
        <arg>
         <funapp>
          <name>p</name>
          <arg>
           <var>x1</var>
          </arg>
         </funapp>
        </arg>
       </funapp>
      </lhs>
      <rhs>
       <var>x1</var>
      </rhs>
     </rule>
    </rules>
   </trs>
  </trsInput>
 </input>
 <cpfVersion>2.2</cpfVersion>
 <proof>
  <trsTerminationProof>
   <dpTrans>
    <dps>
     <rules>
      <rule>
       <lhs>
        <funapp>
         <sharp>
         <name>p</name></sharp>
         <arg>
          <funapp>
           <name>p</name>
           <arg>
            <var>x1</var>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <sharp>
         <name>q</name></sharp>
         <arg>
          <var>x1</var>
         </arg>
        </funapp>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <sharp>
         <name>p</name></sharp>
         <arg>
          <funapp>
           <name>Q</name>
           <arg>
            <funapp>
             <name>Q</name>
             <arg>
              <var>x1</var>
             </arg>
            </funapp>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <sharp>
         <name>Q</name></sharp>
         <arg>
          <funapp>
           <name>Q</name>
           <arg>
            <funapp>
             <name>p</name>
             <arg>
              <var>x1</var>
             </arg>
            </funapp>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <sharp>
         <name>Q</name></sharp>
         <arg>
          <funapp>
           <name>p</name>
           <arg>
            <funapp>
             <name>q</name>
             <arg>
              <var>x1</var>
             </arg>
            </funapp>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <sharp>
         <name>p</name></sharp>
         <arg>
          <funapp>
           <name>Q</name>
           <arg>
            <var>x1</var>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <sharp>
         <name>P</name></sharp>
         <arg>
          <var>x1</var>
         </arg>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <sharp>
         <name>Q</name></sharp>
         <arg>
          <funapp>
           <name>Q</name>
           <arg>
            <funapp>
             <name>p</name>
             <arg>
              <var>x1</var>
             </arg>
            </funapp>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <sharp>
         <name>P</name></sharp>
         <arg>
          <var>x1</var>
         </arg>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <sharp>
         <name>p</name></sharp>
         <arg>
          <var>x1</var>
         </arg>
        </funapp>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <sharp>
         <name>Q</name></sharp>
         <arg>
          <funapp>
           <name>p</name>
           <arg>
            <funapp>
             <name>q</name>
             <arg>
              <var>x1</var>
             </arg>
            </funapp>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <sharp>
         <name>q</name></sharp>
         <arg>
          <funapp>
           <name>p</name>
           <arg>
            <funapp>
             <name>Q</name>
             <arg>
              <var>x1</var>
             </arg>
            </funapp>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <sharp>
         <name>Q</name></sharp>
         <arg>
          <funapp>
           <name>p</name>
           <arg>
            <funapp>
             <name>q</name>
             <arg>
              <var>x1</var>
             </arg>
            </funapp>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <sharp>
         <name>Q</name></sharp>
         <arg>
          <var>x1</var>
         </arg>
        </funapp>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <sharp>
         <name>p</name></sharp>
         <arg>
          <funapp>
           <name>Q</name>
           <arg>
            <funapp>
             <name>Q</name>
             <arg>
              <var>x1</var>
             </arg>
            </funapp>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <sharp>
         <name>Q</name></sharp>
         <arg>
          <funapp>
           <name>p</name>
           <arg>
            <var>x1</var>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <sharp>
         <name>P</name></sharp>
         <arg>
          <var>x1</var>
         </arg>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <sharp>
         <name>Q</name></sharp>
         <arg>
          <funapp>
           <name>p</name>
           <arg>
            <var>x1</var>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <sharp>
         <name>q</name></sharp>
         <arg>
          <funapp>
           <name>q</name>
           <arg>
            <funapp>
             <name>p</name>
             <arg>
              <var>x1</var>
             </arg>
            </funapp>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <sharp>
         <name>q</name></sharp>
         <arg>
          <var>x1</var>
         </arg>
        </funapp>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <sharp>
         <name>q</name></sharp>
         <arg>
          <funapp>
           <name>q</name>
           <arg>
            <funapp>
             <name>p</name>
             <arg>
              <var>x1</var>
             </arg>
            </funapp>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <sharp>
         <name>p</name></sharp>
         <arg>
          <funapp>
           <name>q</name>
           <arg>
            <funapp>
             <name>q</name>
             <arg>
              <var>x1</var>
             </arg>
            </funapp>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <sharp>
         <name>p</name></sharp>
         <arg>
          <funapp>
           <name>p</name>
           <arg>
            <var>x1</var>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <sharp>
         <name>q</name></sharp>
         <arg>
          <funapp>
           <name>q</name>
           <arg>
            <var>x1</var>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <sharp>
         <name>p</name></sharp>
         <arg>
          <funapp>
           <name>Q</name>
           <arg>
            <funapp>
             <name>Q</name>
             <arg>
              <var>x1</var>
             </arg>
            </funapp>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <sharp>
         <name>p</name></sharp>
         <arg>
          <var>x1</var>
         </arg>
        </funapp>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <sharp>
         <name>q</name></sharp>
         <arg>
          <funapp>
           <name>q</name>
           <arg>
            <funapp>
             <name>p</name>
             <arg>
              <var>x1</var>
             </arg>
            </funapp>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <sharp>
         <name>q</name></sharp>
         <arg>
          <funapp>
           <name>q</name>
           <arg>
            <var>x1</var>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </rhs>
      </rule>
     </rules>
    </dps>
    <markedSymbols>true</markedSymbols>
    <dpProof>
     <depGraphProc>
      <component>
       <dps>
        <rules>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>P</name></sharp>
            <arg>
             <var>x1</var>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>p</name></sharp>
            <arg>
             <var>x1</var>
            </arg>
           </funapp>
          </rhs>
         </rule>
        </rules>
       </dps>
       <realScc>false</realScc>
      </component>
      <component>
       <dps>
        <rules>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>P</name></sharp>
            <arg>
             <var>x1</var>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>Q</name></sharp>
            <arg>
             <funapp>
              <name>Q</name>
              <arg>
               <funapp>
                <name>p</name>
                <arg>
                 <var>x1</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </rhs>
         </rule>
        </rules>
       </dps>
       <realScc>false</realScc>
      </component>
      <component>
       <dps>
        <rules>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>P</name></sharp>
            <arg>
             <var>x1</var>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>Q</name></sharp>
            <arg>
             <funapp>
              <name>p</name>
              <arg>
               <var>x1</var>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </rhs>
         </rule>
        </rules>
       </dps>
       <realScc>false</realScc>
      </component>
      <component>
       <dps>
        <rules>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>q</name></sharp>
            <arg>
             <funapp>
              <name>q</name>
              <arg>
               <funapp>
                <name>p</name>
                <arg>
                 <var>x1</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>q</name></sharp>
            <arg>
             <funapp>
              <name>q</name>
              <arg>
               <var>x1</var>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </rhs>
         </rule>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>Q</name></sharp>
            <arg>
             <funapp>
              <name>p</name>
              <arg>
               <funapp>
                <name>q</name>
                <arg>
                 <var>x1</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>Q</name></sharp>
            <arg>
             <var>x1</var>
            </arg>
           </funapp>
          </rhs>
         </rule>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>Q</name></sharp>
            <arg>
             <funapp>
              <name>p</name>
              <arg>
               <funapp>
                <name>q</name>
                <arg>
                 <var>x1</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>q</name></sharp>
            <arg>
             <funapp>
              <name>p</name>
              <arg>
               <funapp>
                <name>Q</name>
                <arg>
                 <var>x1</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </rhs>
         </rule>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>p</name></sharp>
            <arg>
             <funapp>
              <name>Q</name>
              <arg>
               <funapp>
                <name>Q</name>
                <arg>
                 <var>x1</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>p</name></sharp>
            <arg>
             <var>x1</var>
            </arg>
           </funapp>
          </rhs>
         </rule>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>p</name></sharp>
            <arg>
             <funapp>
              <name>p</name>
              <arg>
               <var>x1</var>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>q</name></sharp>
            <arg>
             <funapp>
              <name>q</name>
              <arg>
               <var>x1</var>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </rhs>
         </rule>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>q</name></sharp>
            <arg>
             <funapp>
              <name>q</name>
              <arg>
               <funapp>
                <name>p</name>
                <arg>
                 <var>x1</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>p</name></sharp>
            <arg>
             <funapp>
              <name>q</name>
              <arg>
               <funapp>
                <name>q</name>
                <arg>
                 <var>x1</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </rhs>
         </rule>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>Q</name></sharp>
            <arg>
             <funapp>
              <name>p</name>
              <arg>
               <funapp>
                <name>q</name>
                <arg>
                 <var>x1</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>p</name></sharp>
            <arg>
             <funapp>
              <name>Q</name>
              <arg>
               <var>x1</var>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </rhs>
         </rule>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>p</name></sharp>
            <arg>
             <funapp>
              <name>Q</name>
              <arg>
               <funapp>
                <name>Q</name>
                <arg>
                 <var>x1</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>Q</name></sharp>
            <arg>
             <funapp>
              <name>Q</name>
              <arg>
               <funapp>
                <name>p</name>
                <arg>
                 <var>x1</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </rhs>
         </rule>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>q</name></sharp>
            <arg>
             <funapp>
              <name>q</name>
              <arg>
               <funapp>
                <name>p</name>
                <arg>
                 <var>x1</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>q</name></sharp>
            <arg>
             <var>x1</var>
            </arg>
           </funapp>
          </rhs>
         </rule>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>p</name></sharp>
            <arg>
             <funapp>
              <name>Q</name>
              <arg>
               <funapp>
                <name>Q</name>
                <arg>
                 <var>x1</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>Q</name></sharp>
            <arg>
             <funapp>
              <name>p</name>
              <arg>
               <var>x1</var>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </rhs>
         </rule>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>p</name></sharp>
            <arg>
             <funapp>
              <name>p</name>
              <arg>
               <var>x1</var>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>q</name></sharp>
            <arg>
             <var>x1</var>
            </arg>
           </funapp>
          </rhs>
         </rule>
        </rules>
       </dps>
       <realScc>true</realScc>
       <dpProof>
        <redPairUrProc>
         <orderingConstraintProof>
          <redPair>
           <maxPoly>
            <interpret>
             <sharp>
             <name>P</name></sharp>
             <arity>1</arity>
             <sum>
              <constant>0</constant>
             </sum>
            </interpret>
            <interpret>
             <name>Q</name>
             <arity>1</arity>
             <sum>
              <variable>1</variable>
              <constant>3253</constant>
             </sum>
            </interpret>
            <interpret>
             <name>q</name>
             <arity>1</arity>
             <sum>
              <variable>1</variable>
              <constant>10451</constant>
             </sum>
            </interpret>
            <interpret>
             <sharp>
             <name>Q</name></sharp>
             <arity>1</arity>
             <sum>
              <variable>1</variable>
              <constant>0</constant>
             </sum>
            </interpret>
            <interpret>
             <sharp>
             <name>p</name></sharp>
             <arity>1</arity>
             <sum>
              <variable>1</variable>
              <constant>7199</constant>
             </sum>
            </interpret>
            <interpret>
             <name>p</name>
             <arity>1</arity>
             <sum>
              <variable>1</variable>
              <constant>10452</constant>
             </sum>
            </interpret>
            <interpret>
             <name>P</name>
             <arity>1</arity>
             <sum>
              <variable>1</variable>
              <constant>36466</constant>
             </sum>
            </interpret>
            <interpret>
             <sharp>
             <name>q</name></sharp>
             <arity>1</arity>
             <sum>
              <variable>1</variable>
              <constant>7198</constant>
             </sum>
            </interpret>
           </maxPoly>
          </redPair>
         </orderingConstraintProof>
         <dps>
          <rules>
           <rule>
            <lhs>
             <funapp>
              <sharp>
              <name>p</name></sharp>
              <arg>
               <funapp>
                <name>Q</name>
                <arg>
                 <funapp>
                  <name>Q</name>
                  <arg>
                   <var>x1</var>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <sharp>
              <name>Q</name></sharp>
              <arg>
               <funapp>
                <name>Q</name>
                <arg>
                 <funapp>
                  <name>p</name>
                  <arg>
                   <var>x1</var>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <sharp>
              <name>q</name></sharp>
              <arg>
               <funapp>
                <name>q</name>
                <arg>
                 <funapp>
                  <name>p</name>
                  <arg>
                   <var>x1</var>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <sharp>
              <name>p</name></sharp>
              <arg>
               <funapp>
                <name>q</name>
                <arg>
                 <funapp>
                  <name>q</name>
                  <arg>
                   <var>x1</var>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <sharp>
              <name>Q</name></sharp>
              <arg>
               <funapp>
                <name>p</name>
                <arg>
                 <funapp>
                  <name>q</name>
                  <arg>
                   <var>x1</var>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <sharp>
              <name>q</name></sharp>
              <arg>
               <funapp>
                <name>p</name>
                <arg>
                 <funapp>
                  <name>Q</name>
                  <arg>
                   <var>x1</var>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </rhs>
           </rule>
          </rules>
         </dps>
         <usableRules>
          <rules>
           <rule>
            <lhs>
             <funapp>
              <name>Q</name>
              <arg>
               <funapp>
                <name>p</name>
                <arg>
                 <funapp>
                  <name>q</name>
                  <arg>
                   <var>x1</var>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>q</name>
              <arg>
               <funapp>
                <name>p</name>
                <arg>
                 <funapp>
                  <name>Q</name>
                  <arg>
                   <var>x1</var>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>p</name>
              <arg>
               <funapp>
                <name>P</name>
                <arg>
                 <var>x1</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <var>x1</var>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>p</name>
              <arg>
               <funapp>
                <name>Q</name>
                <arg>
                 <funapp>
                  <name>Q</name>
                  <arg>
                   <var>x1</var>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>Q</name>
              <arg>
               <funapp>
                <name>Q</name>
                <arg>
                 <funapp>
                  <name>p</name>
                  <arg>
                   <var>x1</var>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>q</name>
              <arg>
               <funapp>
                <name>q</name>
                <arg>
                 <funapp>
                  <name>p</name>
                  <arg>
                   <var>x1</var>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>p</name>
              <arg>
               <funapp>
                <name>q</name>
                <arg>
                 <funapp>
                  <name>q</name>
                  <arg>
                   <var>x1</var>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>Q</name>
              <arg>
               <funapp>
                <name>q</name>
                <arg>
                 <var>x1</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <var>x1</var>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>q</name>
              <arg>
               <funapp>
                <name>Q</name>
                <arg>
                 <var>x1</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <var>x1</var>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>p</name>
              <arg>
               <funapp>
                <name>p</name>
                <arg>
                 <var>x1</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>q</name>
              <arg>
               <funapp>
                <name>q</name>
                <arg>
                 <var>x1</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </rhs>
           </rule>
          </rules>
         </usableRules>
         <dpProof>
          <depGraphProc>
           <component>
            <dps>
             <rules>
              <rule>
               <lhs>
                <funapp>
                 <sharp>
                 <name>Q</name></sharp>
                 <arg>
                  <funapp>
                   <name>p</name>
                   <arg>
                    <funapp>
                     <name>q</name>
                     <arg>
                      <var>x1</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </arg>
                </funapp>
               </lhs>
               <rhs>
                <funapp>
                 <sharp>
                 <name>q</name></sharp>
                 <arg>
                  <funapp>
                   <name>p</name>
                   <arg>
                    <funapp>
                     <name>Q</name>
                     <arg>
                      <var>x1</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </arg>
                </funapp>
               </rhs>
              </rule>
              <rule>
               <lhs>
                <funapp>
                 <sharp>
                 <name>p</name></sharp>
                 <arg>
                  <funapp>
                   <name>Q</name>
                   <arg>
                    <funapp>
                     <name>Q</name>
                     <arg>
                      <var>x1</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </arg>
                </funapp>
               </lhs>
               <rhs>
                <funapp>
                 <sharp>
                 <name>Q</name></sharp>
                 <arg>
                  <funapp>
                   <name>Q</name>
                   <arg>
                    <funapp>
                     <name>p</name>
                     <arg>
                      <var>x1</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </arg>
                </funapp>
               </rhs>
              </rule>
              <rule>
               <lhs>
                <funapp>
                 <sharp>
                 <name>q</name></sharp>
                 <arg>
                  <funapp>
                   <name>q</name>
                   <arg>
                    <funapp>
                     <name>p</name>
                     <arg>
                      <var>x1</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </arg>
                </funapp>
               </lhs>
               <rhs>
                <funapp>
                 <sharp>
                 <name>p</name></sharp>
                 <arg>
                  <funapp>
                   <name>q</name>
                   <arg>
                    <funapp>
                     <name>q</name>
                     <arg>
                      <var>x1</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </arg>
                </funapp>
               </rhs>
              </rule>
             </rules>
            </dps>
            <realScc>true</realScc>
            <dpProof>
             <redPairUrProc>
              <orderingConstraintProof>
               <redPair>
                <interpretation>
                 <type>
                  <matrixInterpretation>
                   <domain><naturals/>
                   </domain>
                   <dimension>2
                   </dimension>
                   <strictDimension>1
                   </strictDimension>
                  </matrixInterpretation>
                 </type>
                 <interpret>
                  <sharp>
                  <name>P</name></sharp>
                  <arity>1</arity>
                  <polynomial>
                   <sum>
                    <polynomial>
                     <coefficient>
                      <vector>
                       <coefficient>
                       <integer>0</integer></coefficient>
                       <coefficient>
                       <integer>0</integer></coefficient>
                      </vector>
                     </coefficient>
                    </polynomial>
                   </sum>
                  </polynomial>
                 </interpret>
                 <interpret>
                  <name>Q</name>
                  <arity>1</arity>
                  <polynomial>
                   <sum>
                    <polynomial>
                     <product>
                      <polynomial>
                       <coefficient>
                        <matrix>
                         <vector>
                          <coefficient>
                          <integer>0</integer></coefficient>
                          <coefficient>
                          <integer>1</integer></coefficient>
                         </vector>
                         <vector>
                          <coefficient>
                          <integer>1</integer></coefficient>
                          <coefficient>
                          <integer>0</integer></coefficient>
                         </vector>
                        </matrix>
                       </coefficient>
                      </polynomial>
                      <polynomial>
                       <variable>1</variable>
                      </polynomial>
                     </product>
                    </polynomial>
                    <polynomial>
                     <coefficient>
                      <vector>
                       <coefficient>
                       <integer>0</integer></coefficient>
                       <coefficient>
                       <integer>0</integer></coefficient>
                      </vector>
                     </coefficient>
                    </polynomial>
                   </sum>
                  </polynomial>
                 </interpret>
                 <interpret>
                  <name>q</name>
                  <arity>1</arity>
                  <polynomial>
                   <sum>
                    <polynomial>
                     <product>
                      <polynomial>
                       <coefficient>
                        <matrix>
                         <vector>
                          <coefficient>
                          <integer>0</integer></coefficient>
                          <coefficient>
                          <integer>1</integer></coefficient>
                         </vector>
                         <vector>
                          <coefficient>
                          <integer>1</integer></coefficient>
                          <coefficient>
                          <integer>0</integer></coefficient>
                         </vector>
                        </matrix>
                       </coefficient>
                      </polynomial>
                      <polynomial>
                       <variable>1</variable>
                      </polynomial>
                     </product>
                    </polynomial>
                    <polynomial>
                     <coefficient>
                      <vector>
                       <coefficient>
                       <integer>0</integer></coefficient>
                       <coefficient>
                       <integer>0</integer></coefficient>
                      </vector>
                     </coefficient>
                    </polynomial>
                   </sum>
                  </polynomial>
                 </interpret>
                 <interpret>
                  <sharp>
                  <name>Q</name></sharp>
                  <arity>1</arity>
                  <polynomial>
                   <sum>
                    <polynomial>
                     <product>
                      <polynomial>
                       <coefficient>
                        <matrix>
                         <vector>
                          <coefficient>
                          <integer>0</integer></coefficient>
                          <coefficient>
                          <integer>0</integer></coefficient>
                         </vector>
                         <vector>
                          <coefficient>
                          <integer>1</integer></coefficient>
                          <coefficient>
                          <integer>0</integer></coefficient>
                         </vector>
                        </matrix>
                       </coefficient>
                      </polynomial>
                      <polynomial>
                       <variable>1</variable>
                      </polynomial>
                     </product>
                    </polynomial>
                    <polynomial>
                     <coefficient>
                      <vector>
                       <coefficient>
                       <integer>0</integer></coefficient>
                       <coefficient>
                       <integer>0</integer></coefficient>
                      </vector>
                     </coefficient>
                    </polynomial>
                   </sum>
                  </polynomial>
                 </interpret>
                 <interpret>
                  <sharp>
                  <name>p</name></sharp>
                  <arity>1</arity>
                  <polynomial>
                   <sum>
                    <polynomial>
                     <product>
                      <polynomial>
                       <coefficient>
                        <matrix>
                         <vector>
                          <coefficient>
                          <integer>1</integer></coefficient>
                          <coefficient>
                          <integer>0</integer></coefficient>
                         </vector>
                         <vector>
                          <coefficient>
                          <integer>1</integer></coefficient>
                          <coefficient>
                          <integer>0</integer></coefficient>
                         </vector>
                        </matrix>
                       </coefficient>
                      </polynomial>
                      <polynomial>
                       <variable>1</variable>
                      </polynomial>
                     </product>
                    </polynomial>
                    <polynomial>
                     <coefficient>
                      <vector>
                       <coefficient>
                       <integer>17625</integer></coefficient>
                       <coefficient>
                       <integer>0</integer></coefficient>
                      </vector>
                     </coefficient>
                    </polynomial>
                   </sum>
                  </polynomial>
                 </interpret>
                 <interpret>
                  <name>p</name>
                  <arity>1</arity>
                  <polynomial>
                   <sum>
                    <polynomial>
                     <product>
                      <polynomial>
                       <coefficient>
                        <matrix>
                         <vector>
                          <coefficient>
                          <integer>1</integer></coefficient>
                          <coefficient>
                          <integer>1</integer></coefficient>
                         </vector>
                         <vector>
                          <coefficient>
                          <integer>1</integer></coefficient>
                          <coefficient>
                          <integer>1</integer></coefficient>
                         </vector>
                        </matrix>
                       </coefficient>
                      </polynomial>
                      <polynomial>
                       <variable>1</variable>
                      </polynomial>
                     </product>
                    </polynomial>
                    <polynomial>
                     <coefficient>
                      <vector>
                       <coefficient>
                       <integer>17623</integer></coefficient>
                       <coefficient>
                       <integer>17627</integer></coefficient>
                      </vector>
                     </coefficient>
                    </polynomial>
                   </sum>
                  </polynomial>
                 </interpret>
                 <interpret>
                  <name>P</name>
                  <arity>1</arity>
                  <polynomial>
                   <sum>
                    <polynomial>
                     <product>
                      <polynomial>
                       <coefficient>
                        <matrix>
                         <vector>
                          <coefficient>
                          <integer>1</integer></coefficient>
                          <coefficient>
                          <integer>1</integer></coefficient>
                         </vector>
                         <vector>
                          <coefficient>
                          <integer>1</integer></coefficient>
                          <coefficient>
                          <integer>1</integer></coefficient>
                         </vector>
                        </matrix>
                       </coefficient>
                      </polynomial>
                      <polynomial>
                       <variable>1</variable>
                      </polynomial>
                     </product>
                    </polynomial>
                    <polynomial>
                     <coefficient>
                      <vector>
                       <coefficient>
                       <integer>26763</integer></coefficient>
                       <coefficient>
                       <integer>18345</integer></coefficient>
                      </vector>
                     </coefficient>
                    </polynomial>
                   </sum>
                  </polynomial>
                 </interpret>
                 <interpret>
                  <sharp>
                  <name>q</name></sharp>
                  <arity>1</arity>
                  <polynomial>
                   <sum>
                    <polynomial>
                     <product>
                      <polynomial>
                       <coefficient>
                        <matrix>
                         <vector>
                          <coefficient>
                          <integer>1</integer></coefficient>
                          <coefficient>
                          <integer>0</integer></coefficient>
                         </vector>
                         <vector>
                          <coefficient>
                          <integer>0</integer></coefficient>
                          <coefficient>
                          <integer>0</integer></coefficient>
                         </vector>
                        </matrix>
                       </coefficient>
                      </polynomial>
                      <polynomial>
                       <variable>1</variable>
                      </polynomial>
                     </product>
                    </polynomial>
                    <polynomial>
                     <coefficient>
                      <vector>
                       <coefficient>
                       <integer>0</integer></coefficient>
                       <coefficient>
                       <integer>0</integer></coefficient>
                      </vector>
                     </coefficient>
                    </polynomial>
                   </sum>
                  </polynomial>
                 </interpret>
                </interpretation>
               </redPair>
              </orderingConstraintProof>
              <dps>
               <rules>
               </rules>
              </dps>
              <usableRules>
               <rules>
                <rule>
                 <lhs>
                  <funapp>
                   <name>Q</name>
                   <arg>
                    <funapp>
                     <name>p</name>
                     <arg>
                      <funapp>
                       <name>q</name>
                       <arg>
                        <var>x1</var>
                       </arg>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <name>q</name>
                   <arg>
                    <funapp>
                     <name>p</name>
                     <arg>
                      <funapp>
                       <name>Q</name>
                       <arg>
                        <var>x1</var>
                       </arg>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <name>p</name>
                   <arg>
                    <funapp>
                     <name>P</name>
                     <arg>
                      <var>x1</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <var>x1</var>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <name>p</name>
                   <arg>
                    <funapp>
                     <name>Q</name>
                     <arg>
                      <funapp>
                       <name>Q</name>
                       <arg>
                        <var>x1</var>
                       </arg>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <name>Q</name>
                   <arg>
                    <funapp>
                     <name>Q</name>
                     <arg>
                      <funapp>
                       <name>p</name>
                       <arg>
                        <var>x1</var>
                       </arg>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <name>q</name>
                   <arg>
                    <funapp>
                     <name>q</name>
                     <arg>
                      <funapp>
                       <name>p</name>
                       <arg>
                        <var>x1</var>
                       </arg>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <name>p</name>
                   <arg>
                    <funapp>
                     <name>q</name>
                     <arg>
                      <funapp>
                       <name>q</name>
                       <arg>
                        <var>x1</var>
                       </arg>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <name>Q</name>
                   <arg>
                    <funapp>
                     <name>q</name>
                     <arg>
                      <var>x1</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <var>x1</var>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <name>q</name>
                   <arg>
                    <funapp>
                     <name>Q</name>
                     <arg>
                      <var>x1</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <var>x1</var>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <name>p</name>
                   <arg>
                    <funapp>
                     <name>p</name>
                     <arg>
                      <var>x1</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <name>q</name>
                   <arg>
                    <funapp>
                     <name>q</name>
                     <arg>
                      <var>x1</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
               </rules>
              </usableRules>
              <dpProof>
               <depGraphProc>
               </depGraphProc>
              </dpProof>
             </redPairUrProc>
            </dpProof>
           </component>
          </depGraphProc>
         </dpProof>
        </redPairUrProc>
       </dpProof>
      </component>
     </depGraphProc>
    </dpProof>
   </dpTrans>
  </trsTerminationProof>
 </proof>
 <origin>
  <proofOrigin>
   <tool>
    <name>NaTT</name>
    <version>certifiable-1.6</version>
   </tool>
  </proofOrigin>
 </origin>
</certificationProblem>