/export/starexec/sandbox2/solver/bin/starexec_run_Certifiable /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/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>f</name>
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         <funapp>
          <name>f</name>
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           <funapp>
            <name>a</name>
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         </funapp>
        </arg>
        <arg>
         <funapp>
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       <funapp>
        <name>f</name>
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         <funapp>
          <name>f</name>
          <arg>
           <funapp>
            <name>f</name>
            <arg>
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            <arg>
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              <name>a</name>
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          <arg>
           <funapp>
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       </funapp>
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     </rule>
    </rules>
   </trs>
  </trsInput>
 </input>
 <cpfVersion>2.2</cpfVersion>
 <proof>
  <trsTerminationProof>
   <dpTrans>
    <dps>
     <rules>
      <rule>
       <lhs>
        <funapp>
         <sharp>
         <name>f</name></sharp>
         <arg>
          <funapp>
           <name>f</name>
           <arg>
            <funapp>
             <name>a</name>
            </funapp>
           </arg>
           <arg>
            <var>x</var>
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         <arg>
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        <funapp>
         <sharp>
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           <arg>
            <var>x</var>
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           <arg>
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         <arg>
          <funapp>
           <name>f</name>
           <arg>
            <funapp>
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           <arg>
            <funapp>
             <name>a</name>
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        </funapp>
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       <lhs>
        <funapp>
         <sharp>
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         <arg>
          <funapp>
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           <arg>
            <funapp>
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           <arg>
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         <arg>
          <funapp>
           <name>a</name>
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       </lhs>
       <rhs>
        <funapp>
         <sharp>
         <name>f</name></sharp>
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          <var>x</var>
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         <arg>
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           <name>a</name>
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        </funapp>
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      <rule>
       <lhs>
        <funapp>
         <sharp>
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         <arg>
          <funapp>
           <name>f</name>
           <arg>
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             <name>a</name>
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            <var>x</var>
           </arg>
          </funapp>
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         <arg>
          <funapp>
           <name>a</name>
          </funapp>
         </arg>
        </funapp>
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       <rhs>
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         <sharp>
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          <funapp>
           <name>f</name>
           <arg>
            <funapp>
             <name>f</name>
             <arg>
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             </arg>
             <arg>
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           <arg>
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             <arg>
              <funapp>
               <name>a</name>
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             </arg>
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         </arg>
         <arg>
          <funapp>
           <name>a</name>
          </funapp>
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      </rule>
      <rule>
       <lhs>
        <funapp>
         <sharp>
         <name>f</name></sharp>
         <arg>
          <funapp>
           <name>f</name>
           <arg>
            <funapp>
             <name>a</name>
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           <name>a</name>
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        </funapp>
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      </rule>
     </rules>
    </dps>
    <markedSymbols>true</markedSymbols>
    <dpProof>
     <depGraphProc>
      <component>
       <dps>
        <rules>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>f</name></sharp>
            <arg>
             <funapp>
              <name>f</name>
              <arg>
               <funapp>
                <name>a</name>
               </funapp>
              </arg>
              <arg>
               <var>x</var>
              </arg>
             </funapp>
            </arg>
            <arg>
             <funapp>
              <name>a</name>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>f</name></sharp>
            <arg>
             <funapp>
              <name>f</name>
              <arg>
               <funapp>
                <name>f</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <funapp>
                  <name>a</name>
                 </funapp>
                </arg>
               </funapp>
              </arg>
              <arg>
               <funapp>
                <name>f</name>
                <arg>
                 <funapp>
                  <name>a</name>
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                </arg>
                <arg>
                 <funapp>
                  <name>a</name>
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                </arg>
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             </funapp>
            </arg>
            <arg>
             <funapp>
              <name>a</name>
             </funapp>
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          </rhs>
         </rule>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>f</name></sharp>
            <arg>
             <funapp>
              <name>f</name>
              <arg>
               <funapp>
                <name>a</name>
               </funapp>
              </arg>
              <arg>
               <var>x</var>
              </arg>
             </funapp>
            </arg>
            <arg>
             <funapp>
              <name>a</name>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>f</name></sharp>
            <arg>
             <var>x</var>
            </arg>
            <arg>
             <funapp>
              <name>a</name>
             </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>
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            <interpret>
             <name>a</name>
             <arity>0</arity>
             <polynomial>
              <sum>
               <polynomial>
                <coefficient>
                 <vector>
                  <coefficient>
                  <integer>1</integer></coefficient>
                  <coefficient>
                  <integer>0</integer></coefficient>
                 </vector>
                </coefficient>
               </polynomial>
              </sum>
             </polynomial>
            </interpret>
            <interpret>
             <name>f</name>
             <arity>2</arity>
             <polynomial>
              <sum>
               <polynomial>
                <product>
                 <polynomial>
                  <coefficient>
                   <matrix>
                    <vector>
                     <coefficient>
                     <integer>0</integer></coefficient>
                     <coefficient>
                     <integer>1</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>
                <product>
                 <polynomial>
                  <coefficient>
                   <matrix>
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                     <coefficient>
                     <integer>0</integer></coefficient>
                     <coefficient>
                     <integer>0</integer></coefficient>
                    </vector>
                    <vector>
                     <coefficient>
                     <integer>0</integer></coefficient>
                     <coefficient>
                     <integer>1</integer></coefficient>
                    </vector>
                   </matrix>
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                 <polynomial>
                  <variable>2</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>f</name></sharp>
             <arity>2</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>
           </interpretation>
          </redPair>
         </orderingConstraintProof>
         <dps>
          <rules>
           <rule>
            <lhs>
             <funapp>
              <sharp>
              <name>f</name></sharp>
              <arg>
               <funapp>
                <name>f</name>
                <arg>
                 <funapp>
                  <name>a</name>
                 </funapp>
                </arg>
                <arg>
                 <var>x</var>
                </arg>
               </funapp>
              </arg>
              <arg>
               <funapp>
                <name>a</name>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <sharp>
              <name>f</name></sharp>
              <arg>
               <funapp>
                <name>f</name>
                <arg>
                 <funapp>
                  <name>f</name>
                  <arg>
                   <var>x</var>
                  </arg>
                  <arg>
                   <funapp>
                    <name>a</name>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
                <arg>
                 <funapp>
                  <name>f</name>
                  <arg>
                   <funapp>
                    <name>a</name>
                   </funapp>
                  </arg>
                  <arg>
                   <funapp>
                    <name>a</name>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
              <arg>
               <funapp>
                <name>a</name>
               </funapp>
              </arg>
             </funapp>
            </rhs>
           </rule>
          </rules>
         </dps>
         <usableRules>
          <rules>
           <rule>
            <lhs>
             <funapp>
              <name>f</name>
              <arg>
               <funapp>
                <name>f</name>
                <arg>
                 <funapp>
                  <name>a</name>
                 </funapp>
                </arg>
                <arg>
                 <var>x</var>
                </arg>
               </funapp>
              </arg>
              <arg>
               <funapp>
                <name>a</name>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>f</name>
              <arg>
               <funapp>
                <name>f</name>
                <arg>
                 <funapp>
                  <name>f</name>
                  <arg>
                   <var>x</var>
                  </arg>
                  <arg>
                   <funapp>
                    <name>a</name>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
                <arg>
                 <funapp>
                  <name>f</name>
                  <arg>
                   <funapp>
                    <name>a</name>
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                  </arg>
                  <arg>
                   <funapp>
                    <name>a</name>
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                  </arg>
                 </funapp>
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               </funapp>
              </arg>
              <arg>
               <funapp>
                <name>a</name>
               </funapp>
              </arg>
             </funapp>
            </rhs>
           </rule>
          </rules>
         </usableRules>
         <dpProof>
          <depGraphProc>
           <component>
            <dps>
             <rules>
              <rule>
               <lhs>
                <funapp>
                 <sharp>
                 <name>f</name></sharp>
                 <arg>
                  <funapp>
                   <name>f</name>
                   <arg>
                    <funapp>
                     <name>a</name>
                    </funapp>
                   </arg>
                   <arg>
                    <var>x</var>
                   </arg>
                  </funapp>
                 </arg>
                 <arg>
                  <funapp>
                   <name>a</name>
                  </funapp>
                 </arg>
                </funapp>
               </lhs>
               <rhs>
                <funapp>
                 <sharp>
                 <name>f</name></sharp>
                 <arg>
                  <funapp>
                   <name>f</name>
                   <arg>
                    <funapp>
                     <name>f</name>
                     <arg>
                      <var>x</var>
                     </arg>
                     <arg>
                      <funapp>
                       <name>a</name>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                   <arg>
                    <funapp>
                     <name>f</name>
                     <arg>
                      <funapp>
                       <name>a</name>
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                     </arg>
                     <arg>
                      <funapp>
                       <name>a</name>
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                     </arg>
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                   </arg>
                  </funapp>
                 </arg>
                 <arg>
                  <funapp>
                   <name>a</name>
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                 </arg>
                </funapp>
               </rhs>
              </rule>
             </rules>
            </dps>
            <realScc>true</realScc>
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             <redPairUrProc>
              <orderingConstraintProof>
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                <interpretation>
                 <type>
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                   <domain><naturals/>
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                   <dimension>2
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                   <strictDimension>1
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                 <interpret>
                  <name>a</name>
                  <arity>0</arity>
                  <polynomial>
                   <sum>
                    <polynomial>
                     <coefficient>
                      <vector>
                       <coefficient>
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                       <coefficient>
                       <integer>1</integer></coefficient>
                      </vector>
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                 <interpret>
                  <name>f</name>
                  <arity>2</arity>
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                   <sum>
                    <polynomial>
                     <product>
                      <polynomial>
                       <coefficient>
                        <matrix>
                         <vector>
                          <coefficient>
                          <integer>0</integer></coefficient>
                          <coefficient>
                          <integer>1</integer></coefficient>
                         </vector>
                         <vector>
                          <coefficient>
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                          <coefficient>
                          <integer>0</integer></coefficient>
                         </vector>
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                      <polynomial>
                       <variable>1</variable>
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                    <polynomial>
                     <coefficient>
                      <vector>
                       <coefficient>
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                       <coefficient>
                       <integer>1</integer></coefficient>
                      </vector>
                     </coefficient>
                    </polynomial>
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                 </interpret>
                 <interpret>
                  <sharp>
                  <name>f</name></sharp>
                  <arity>2</arity>
                  <polynomial>
                   <sum>
                    <polynomial>
                     <product>
                      <polynomial>
                       <coefficient>
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                         <vector>
                          <coefficient>
                          <integer>0</integer></coefficient>
                          <coefficient>
                          <integer>0</integer></coefficient>
                         </vector>
                         <vector>
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                          <coefficient>
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                      <polynomial>
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                       <coefficient>
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              <dps>
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                 <lhs>
                  <funapp>
                   <name>f</name>
                   <arg>
                    <funapp>
                     <name>f</name>
                     <arg>
                      <funapp>
                       <name>a</name>
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                     <arg>
                      <var>x</var>
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                    </funapp>
                   </arg>
                   <arg>
                    <funapp>
                     <name>a</name>
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                   </arg>
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                 <rhs>
                  <funapp>
                   <name>f</name>
                   <arg>
                    <funapp>
                     <name>f</name>
                     <arg>
                      <funapp>
                       <name>f</name>
                       <arg>
                        <var>x</var>
                       </arg>
                       <arg>
                        <funapp>
                         <name>a</name>
                        </funapp>
                       </arg>
                      </funapp>
                     </arg>
                     <arg>
                      <funapp>
                       <name>f</name>
                       <arg>
                        <funapp>
                         <name>a</name>
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                       </arg>
                       <arg>
                        <funapp>
                         <name>a</name>
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                   <arg>
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           </component>
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          <lhs>
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            <sharp>
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             <funapp>
              <name>f</name>
              <arg>
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              <arg>
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              <arg>
               <var>x</var>
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            <name>f</name></sharp>
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             <funapp>
              <name>f</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>a</name>
               </funapp>
              </arg>
             </funapp>
            </arg>
            <arg>
             <funapp>
              <name>f</name>
              <arg>
               <funapp>
                <name>a</name>
               </funapp>
              </arg>
              <arg>
               <funapp>
                <name>a</name>
               </funapp>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </rhs>
         </rule>
        </rules>
       </dps>
       <realScc>false</realScc>
      </component>
     </depGraphProc>
    </dpProof>
   </dpTrans>
  </trsTerminationProof>
 </proof>
 <origin>
  <proofOrigin>
   <tool>
    <name>NaTT</name>
    <version>certifiable-1.6</version>
   </tool>
  </proofOrigin>
 </origin>
</certificationProblem>