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


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YES
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                <name>s</name>
                <arg>
                 <var>X</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>mark</name>
              <arg>
               <var>X</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>mark</name>
              <arg>
               <funapp>
                <name>p</name>
                <arg>
                 <var>X</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>a__p</name>
              <arg>
               <funapp>
                <name>mark</name>
                <arg>
                 <var>X</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>a__p</name>
              <arg>
               <var>X</var>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>p</name>
              <arg>
               <var>X</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>mark</name>
              <arg>
               <funapp>
                <name>cons</name>
                <arg>
                 <var>X1</var>
                </arg>
                <arg>
                 <var>X2</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>cons</name>
              <arg>
               <funapp>
                <name>mark</name>
                <arg>
                 <var>X1</var>
                </arg>
               </funapp>
              </arg>
              <arg>
               <var>X2</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>a__f</name>
              <arg>
               <var>X</var>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>f</name>
              <arg>
               <var>X</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>mark</name>
              <arg>
               <funapp>
                <name>0</name>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>0</name>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>a__f</name>
              <arg>
               <funapp>
                <name>s</name>
                <arg>
                 <funapp>
                  <name>0</name>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>a__f</name>
              <arg>
               <funapp>
                <name>a__p</name>
                <arg>
                 <funapp>
                  <name>s</name>
                  <arg>
                   <funapp>
                    <name>0</name>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </rhs>
           </rule>
          </rules>
         </usableRules>
         <dpProof>
          <depGraphProc>
           <component>
            <dps>
             <rules>
              <rule>
               <lhs>
                <funapp>
                 <sharp>
                 <name>mark</name></sharp>
                 <arg>
                  <funapp>
                   <name>p</name>
                   <arg>
                    <var>X</var>
                   </arg>
                  </funapp>
                 </arg>
                </funapp>
               </lhs>
               <rhs>
                <funapp>
                 <sharp>
                 <name>mark</name></sharp>
                 <arg>
                  <var>X</var>
                 </arg>
                </funapp>
               </rhs>
              </rule>
             </rules>
            </dps>
            <realScc>true</realScc>
            <dpProof>
             <redPairUrProc>
              <orderingConstraintProof>
               <redPair>
                <maxPoly>
                 <interpret>
                  <name>s</name>
                  <arity>1</arity>
                  <sum>
                   <variable>1</variable>
                   <constant>29480</constant>
                  </sum>
                 </interpret>
                 <interpret>
                  <name>a__f</name>
                  <arity>1</arity>
                  <sum>
                   <constant>4</constant>
                  </sum>
                 </interpret>
                 <interpret>
                  <name>a__p</name>
                  <arity>1</arity>
                  <sum>
                   <variable>1</variable>
                   <constant>1</constant>
                  </sum>
                 </interpret>
                 <interpret>
                  <name>f</name>
                  <arity>1</arity>
                  <sum>
                   <constant>4</constant>
                  </sum>
                 </interpret>
                 <interpret>
                  <name>p</name>
                  <arity>1</arity>
                  <sum>
                   <variable>1</variable>
                   <constant>1</constant>
                  </sum>
                 </interpret>
                 <interpret>
                  <sharp>
                  <name>mark</name></sharp>
                  <arity>1</arity>
                  <sum>
                   <variable>1</variable>
                   <constant>29484</constant>
                  </sum>
                 </interpret>
                 <interpret>
                  <name>0</name>
                  <arity>0</arity>
                  <sum>
                   <constant>3</constant>
                  </sum>
                 </interpret>
                 <interpret>
                  <name>mark</name>
                  <arity>1</arity>
                  <sum>
                   <variable>1</variable>
                   <constant>2241</constant>
                  </sum>
                 </interpret>
                 <interpret>
                  <sharp>
                  <name>a__p</name></sharp>
                  <arity>1</arity>
                  <sum>
                   <variable>1</variable>
                   <constant>0</constant>
                  </sum>
                 </interpret>
                 <interpret>
                  <name>cons</name>
                  <arity>2</arity>
                  <sum>
                   <variable>1</variable>
                   <constant>1</constant>
                  </sum>
                 </interpret>
                 <interpret>
                  <sharp>
                  <name>a__f</name></sharp>
                  <arity>1</arity>
                  <sum>
                   <constant>29487</constant>
                  </sum>
                 </interpret>
                </maxPoly>
               </redPair>
              </orderingConstraintProof>
              <dps>
               <rules>
               </rules>
              </dps>
              <usableRules>
               <rules>
                <rule>
                 <lhs>
                  <funapp>
                   <name>mark</name>
                   <arg>
                    <funapp>
                     <name>f</name>
                     <arg>
                      <var>X</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <name>a__f</name>
                   <arg>
                    <funapp>
                     <name>mark</name>
                     <arg>
                      <var>X</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <name>mark</name>
                   <arg>
                    <funapp>
                     <name>s</name>
                     <arg>
                      <var>X</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <name>s</name>
                   <arg>
                    <funapp>
                     <name>mark</name>
                     <arg>
                      <var>X</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <name>a__f</name>
                   <arg>
                    <funapp>
                     <name>0</name>
                    </funapp>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <name>cons</name>
                   <arg>
                    <funapp>
                     <name>0</name>
                    </funapp>
                   </arg>
                   <arg>
                    <funapp>
                     <name>f</name>
                     <arg>
                      <funapp>
                       <name>s</name>
                       <arg>
                        <funapp>
                         <name>0</name>
                        </funapp>
                       </arg>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <name>a__p</name>
                   <arg>
                    <funapp>
                     <name>s</name>
                     <arg>
                      <var>X</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <name>mark</name>
                   <arg>
                    <var>X</var>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <name>mark</name>
                   <arg>
                    <funapp>
                     <name>p</name>
                     <arg>
                      <var>X</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <name>a__p</name>
                   <arg>
                    <funapp>
                     <name>mark</name>
                     <arg>
                      <var>X</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <name>a__p</name>
                   <arg>
                    <var>X</var>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <name>p</name>
                   <arg>
                    <var>X</var>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <name>mark</name>
                   <arg>
                    <funapp>
                     <name>cons</name>
                     <arg>
                      <var>X1</var>
                     </arg>
                     <arg>
                      <var>X2</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <name>cons</name>
                   <arg>
                    <funapp>
                     <name>mark</name>
                     <arg>
                      <var>X1</var>
                     </arg>
                    </funapp>
                   </arg>
                   <arg>
                    <var>X2</var>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <name>a__f</name>
                   <arg>
                    <var>X</var>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <name>f</name>
                   <arg>
                    <var>X</var>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <name>mark</name>
                   <arg>
                    <funapp>
                     <name>0</name>
                    </funapp>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <name>0</name>
                  </funapp>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <name>a__f</name>
                   <arg>
                    <funapp>
                     <name>s</name>
                     <arg>
                      <funapp>
                       <name>0</name>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <name>a__f</name>
                   <arg>
                    <funapp>
                     <name>a__p</name>
                     <arg>
                      <funapp>
                       <name>s</name>
                       <arg>
                        <funapp>
                         <name>0</name>
                        </funapp>
                       </arg>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
               </rules>
              </usableRules>
              <dpProof>
               <depGraphProc>
               </depGraphProc>
              </dpProof>
             </redPairUrProc>
            </dpProof>
           </component>
           <component>
            <dps>
             <rules>
              <rule>
               <lhs>
                <funapp>
                 <sharp>
                 <name>a__f</name></sharp>
                 <arg>
                  <funapp>
                   <name>s</name>
                   <arg>
                    <funapp>
                     <name>0</name>
                    </funapp>
                   </arg>
                  </funapp>
                 </arg>
                </funapp>
               </lhs>
               <rhs>
                <funapp>
                 <sharp>
                 <name>a__f</name></sharp>
                 <arg>
                  <funapp>
                   <name>a__p</name>
                   <arg>
                    <funapp>
                     <name>s</name>
                     <arg>
                      <funapp>
                       <name>0</name>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </arg>
                </funapp>
               </rhs>
              </rule>
             </rules>
            </dps>
            <realScc>true</realScc>
            <dpProof>
             <redPairUrProc>
              <orderingConstraintProof>
               <redPair>
                <filteredRedPair>
                 <argumentFilter>
                  <argumentFilterEntry>
                   <name>mark</name>
                   <arity>1</arity>
                   <collapsing>1</collapsing>
                  </argumentFilterEntry>
                  <argumentFilterEntry>
                   <sharp>
                   <name>a__p</name></sharp>
                   <arity>1</arity>
                   <collapsing>1</collapsing>
                  </argumentFilterEntry>
                 </argumentFilter>
                 <weightedPathOrder>
                  <precedenceStatus>
                   <precedenceStatusEntry>
                    <name>s</name>
                    <arity>1</arity>
                    <precedence>2
                    </precedence>
                    <status>
                    </status>
                   </precedenceStatusEntry>
                   <precedenceStatusEntry>
                    <name>a__f</name>
                    <arity>1</arity>
                    <precedence>1
                    </precedence>
                    <status>
                    </status>
                   </precedenceStatusEntry>
                   <precedenceStatusEntry>
                    <name>a__p</name>
                    <arity>1</arity>
                    <precedence>0
                    </precedence>
                    <status>
                    </status>
                   </precedenceStatusEntry>
                   <precedenceStatusEntry>
                    <name>f</name>
                    <arity>1</arity>
                    <precedence>1
                    </precedence>
                    <status>
                    </status>
                   </precedenceStatusEntry>
                   <precedenceStatusEntry>
                    <name>p</name>
                    <arity>1</arity>
                    <precedence>0
                    </precedence>
                    <status>
                    </status>
                   </precedenceStatusEntry>
                   <precedenceStatusEntry>
                    <sharp>
                    <name>mark</name></sharp>
                    <arity>1</arity>
                    <precedence>0
                    </precedence>
                    <status>
                    </status>
                   </precedenceStatusEntry>
                   <precedenceStatusEntry>
                    <name>0</name>
                    <arity>0</arity>
                    <precedence>1
                    </precedence>
                    <status>
                    </status>
                   </precedenceStatusEntry>
                   <precedenceStatusEntry>
                    <name>cons</name>
                    <arity>2</arity>
                    <precedence>1
                    </precedence>
                    <status>
                    </status>
                   </precedenceStatusEntry>
                   <precedenceStatusEntry>
                    <sharp>
                    <name>a__f</name></sharp>
                    <arity>1</arity>
                    <precedence>0
                    </precedence>
                    <status>
                     <position>1</position>
                    </status>
                   </precedenceStatusEntry>
                  </precedenceStatus>
                  <maxPoly>
                   <interpret>
                    <name>s</name>
                    <arity>1</arity>
                    <sum>
                     <variable>1</variable>
                     <constant>1</constant>
                    </sum>
                   </interpret>
                   <interpret>
                    <name>a__f</name>
                    <arity>1</arity>
                    <sum>
                     <constant>32286</constant>
                    </sum>
                   </interpret>
                   <interpret>
                    <name>a__p</name>
                    <arity>1</arity>
                    <sum>
                     <variable>1</variable>
                     <constant>0</constant>
                    </sum>
                   </interpret>
                   <interpret>
                    <name>f</name>
                    <arity>1</arity>
                    <sum>
                     <constant>32286</constant>
                    </sum>
                   </interpret>
                   <interpret>
                    <name>p</name>
                    <arity>1</arity>
                    <sum>
                     <variable>1</variable>
                     <constant>0</constant>
                    </sum>
                   </interpret>
                   <interpret>
                    <sharp>
                    <name>mark</name></sharp>
                    <arity>1</arity>
                    <sum>
                     <constant>1</constant>
                    </sum>
                   </interpret>
                   <interpret>
                    <name>0</name>
                    <arity>0</arity>
                    <sum>
                     <constant>32287</constant>
                    </sum>
                   </interpret>
                   <interpret>
                    <name>cons</name>
                    <arity>2</arity>
                    <sum>
                     <constant>32286</constant>
                    </sum>
                   </interpret>
                   <interpret>
                    <sharp>
                    <name>a__f</name></sharp>
                    <arity>1</arity>
                    <sum>
                     <variable>1</variable>
                     <constant>1</constant>
                    </sum>
                   </interpret>
                  </maxPoly>
                 </weightedPathOrder>
                </filteredRedPair>
               </redPair>
              </orderingConstraintProof>
              <dps>
               <rules>
               </rules>
              </dps>
              <usableRules>
               <rules>
                <rule>
                 <lhs>
                  <funapp>
                   <name>mark</name>
                   <arg>
                    <funapp>
                     <name>f</name>
                     <arg>
                      <var>X</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <name>a__f</name>
                   <arg>
                    <funapp>
                     <name>mark</name>
                     <arg>
                      <var>X</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <name>mark</name>
                   <arg>
                    <funapp>
                     <name>s</name>
                     <arg>
                      <var>X</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <name>s</name>
                   <arg>
                    <funapp>
                     <name>mark</name>
                     <arg>
                      <var>X</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <name>a__f</name>
                   <arg>
                    <funapp>
                     <name>0</name>
                    </funapp>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <name>cons</name>
                   <arg>
                    <funapp>
                     <name>0</name>
                    </funapp>
                   </arg>
                   <arg>
                    <funapp>
                     <name>f</name>
                     <arg>
                      <funapp>
                       <name>s</name>
                       <arg>
                        <funapp>
                         <name>0</name>
                        </funapp>
                       </arg>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <name>a__p</name>
                   <arg>
                    <funapp>
                     <name>s</name>
                     <arg>
                      <var>X</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <name>mark</name>
                   <arg>
                    <var>X</var>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <name>mark</name>
                   <arg>
                    <funapp>
                     <name>p</name>
                     <arg>
                      <var>X</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <name>a__p</name>
                   <arg>
                    <funapp>
                     <name>mark</name>
                     <arg>
                      <var>X</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <name>a__p</name>
                   <arg>
                    <var>X</var>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <name>p</name>
                   <arg>
                    <var>X</var>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <name>mark</name>
                   <arg>
                    <funapp>
                     <name>cons</name>
                     <arg>
                      <var>X1</var>
                     </arg>
                     <arg>
                      <var>X2</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <name>cons</name>
                   <arg>
                    <funapp>
                     <name>mark</name>
                     <arg>
                      <var>X1</var>
                     </arg>
                    </funapp>
                   </arg>
                   <arg>
                    <var>X2</var>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <name>a__f</name>
                   <arg>
                    <var>X</var>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <name>f</name>
                   <arg>
                    <var>X</var>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <name>mark</name>
                   <arg>
                    <funapp>
                     <name>0</name>
                    </funapp>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <name>0</name>
                  </funapp>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <name>a__f</name>
                   <arg>
                    <funapp>
                     <name>s</name>
                     <arg>
                      <funapp>
                       <name>0</name>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <name>a__f</name>
                   <arg>
                    <funapp>
                     <name>a__p</name>
                     <arg>
                      <funapp>
                       <name>s</name>
                       <arg>
                        <funapp>
                         <name>0</name>
                        </funapp>
                       </arg>
                      </funapp>
                     </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>