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">
 <cpfVersion>2.2</cpfVersion>
 <proof>
  <acTerminationProof>
   <acRuleRemoval>
    <orderingConstraintProof>
     <redPair>
      <interpretation>
       <type>
        <polynomial>
         <domain><naturals/></domain>
         <degree>1</degree>
        </polynomial>
       </type>
       <interpret>
        <name>h</name>
        <arity>1</arity>
        <polynomial>
         <sum>
          <polynomial>
           <variable>1</variable>
          </polynomial>
          <polynomial>
           <coefficient>
           <integer>0</integer></coefficient>
          </polynomial>
         </sum>
        </polynomial>
       </interpret>
       <interpret>
        <name>a</name>
        <arity>0</arity>
        <polynomial>
         <sum>
          <polynomial>
           <coefficient>
           <integer>1</integer></coefficient>
          </polynomial>
         </sum>
        </polynomial>
       </interpret>
       <interpret>
        <name>b</name>
        <arity>0</arity>
        <polynomial>
         <sum>
          <polynomial>
           <coefficient>
           <integer>0</integer></coefficient>
          </polynomial>
         </sum>
        </polynomial>
       </interpret>
       <interpret>
        <name>f</name>
        <arity>2</arity>
        <polynomial>
         <sum>
          <polynomial>
           <variable>1</variable>
          </polynomial>
          <polynomial>
           <variable>2</variable>
          </polynomial>
          <polynomial>
           <coefficient>
           <integer>1</integer></coefficient>
          </polynomial>
         </sum>
        </polynomial>
       </interpret>
       <interpret>
        <name>i</name>
        <arity>2</arity>
        <polynomial>
         <sum>
          <polynomial>
           <variable>1</variable>
          </polynomial>
          <polynomial>
           <variable>2</variable>
          </polynomial>
          <polynomial>
           <coefficient>
           <integer>0</integer></coefficient>
          </polynomial>
         </sum>
        </polynomial>
       </interpret>
       <interpret>
        <name>g</name>
        <arity>1</arity>
        <polynomial>
         <sum>
          <polynomial>
           <variable>1</variable>
          </polynomial>
          <polynomial>
           <coefficient>
           <integer>1</integer></coefficient>
          </polynomial>
         </sum>
        </polynomial>
       </interpret>
      </interpretation>
     </redPair>
    </orderingConstraintProof>
    <trs>
     <rules>
      <rule>
       <lhs>
        <funapp>
         <name>f</name>
         <arg>
          <funapp>
           <name>h</name>
           <arg>
            <funapp>
             <name>a</name>
            </funapp>
           </arg>
          </funapp>
         </arg>
         <arg>
          <funapp>
           <name>a</name>
          </funapp>
         </arg>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <name>f</name>
         <arg>
          <funapp>
           <name>h</name>
           <arg>
            <funapp>
             <name>a</name>
            </funapp>
           </arg>
          </funapp>
         </arg>
         <arg>
          <funapp>
           <name>b</name>
          </funapp>
         </arg>
        </funapp>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <name>f</name>
         <arg>
          <funapp>
           <name>g</name>
           <arg>
            <funapp>
             <name>f</name>
             <arg>
              <funapp>
               <name>h</name>
               <arg>
                <funapp>
                 <name>a</name>
                </funapp>
               </arg>
              </funapp>
             </arg>
             <arg>
              <funapp>
               <name>a</name>
              </funapp>
             </arg>
            </funapp>
           </arg>
          </funapp>
         </arg>
         <arg>
          <funapp>
           <name>a</name>
          </funapp>
         </arg>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <name>f</name>
         <arg>
          <funapp>
           <name>h</name>
           <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>
      <rule>
       <lhs>
        <funapp>
         <name>f</name>
         <arg>
          <funapp>
           <name>g</name>
           <arg>
            <funapp>
             <name>h</name>
             <arg>
              <funapp>
               <name>a</name>
              </funapp>
             </arg>
            </funapp>
           </arg>
          </funapp>
         </arg>
         <arg>
          <funapp>
           <name>f</name>
           <arg>
            <funapp>
             <name>f</name>
             <arg>
              <funapp>
               <name>a</name>
              </funapp>
             </arg>
             <arg>
              <funapp>
               <name>a</name>
              </funapp>
             </arg>
            </funapp>
           </arg>
           <arg>
            <funapp>
             <name>a</name>
            </funapp>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <name>f</name>
         <arg>
          <funapp>
           <name>g</name>
           <arg>
            <funapp>
             <name>f</name>
             <arg>
              <funapp>
               <name>h</name>
               <arg>
                <funapp>
                 <name>a</name>
                </funapp>
               </arg>
              </funapp>
             </arg>
             <arg>
              <funapp>
               <name>a</name>
              </funapp>
             </arg>
            </funapp>
           </arg>
          </funapp>
         </arg>
         <arg>
          <funapp>
           <name>a</name>
          </funapp>
         </arg>
        </funapp>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <name>f</name>
         <arg>
          <funapp>
           <name>i</name>
           <arg>
            <var>x</var>
           </arg>
           <arg>
            <var>y</var>
           </arg>
          </funapp>
         </arg>
         <arg>
          <funapp>
           <name>f</name>
           <arg>
            <funapp>
             <name>a</name>
            </funapp>
           </arg>
           <arg>
            <var>y</var>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <name>f</name>
         <arg>
          <funapp>
           <name>g</name>
           <arg>
            <funapp>
             <name>i</name>
             <arg>
              <var>x</var>
             </arg>
             <arg>
              <var>y</var>
             </arg>
            </funapp>
           </arg>
          </funapp>
         </arg>
         <arg>
          <var>y</var>
         </arg>
        </funapp>
       </rhs>
      </rule>
     </rules>
    </trs>
    <acTerminationProof>
     <acDependencyPairs>
      <equations>
       <rules>
        <rule>
         <lhs>
          <funapp>
           <name>f</name>
           <arg>
            <var>x</var>
           </arg>
           <arg>
            <funapp>
             <name>f</name>
             <arg>
              <var>y</var>
             </arg>
             <arg>
              <var>z</var>
             </arg>
            </funapp>
           </arg>
          </funapp>
         </lhs>
         <rhs>
          <funapp>
           <name>f</name>
           <arg>
            <funapp>
             <name>f</name>
             <arg>
              <var>x</var>
             </arg>
             <arg>
              <var>y</var>
             </arg>
            </funapp>
           </arg>
           <arg>
            <var>z</var>
           </arg>
          </funapp>
         </rhs>
        </rule>
        <rule>
         <lhs>
          <funapp>
           <name>f</name>
           <arg>
            <var>x</var>
           </arg>
           <arg>
            <var>y</var>
           </arg>
          </funapp>
         </lhs>
         <rhs>
          <funapp>
           <name>f</name>
           <arg>
            <var>y</var>
           </arg>
           <arg>
            <var>x</var>
           </arg>
          </funapp>
         </rhs>
        </rule>
       </rules>
      </equations>
      <dpEquations>
       <rules>
        <rule>
         <lhs>
          <funapp>
           <sharp>
           <name>f</name></sharp>
           <arg>
            <var>x</var>
           </arg>
           <arg>
            <funapp>
             <name>f</name>
             <arg>
              <var>y</var>
             </arg>
             <arg>
              <var>z</var>
             </arg>
            </funapp>
           </arg>
          </funapp>
         </lhs>
         <rhs>
          <funapp>
           <sharp>
           <name>f</name></sharp>
           <arg>
            <funapp>
             <name>f</name>
             <arg>
              <var>x</var>
             </arg>
             <arg>
              <var>y</var>
             </arg>
            </funapp>
           </arg>
           <arg>
            <var>z</var>
           </arg>
          </funapp>
         </rhs>
        </rule>
        <rule>
         <lhs>
          <funapp>
           <sharp>
           <name>f</name></sharp>
           <arg>
            <var>x</var>
           </arg>
           <arg>
            <funapp>
             <name>f</name>
             <arg>
              <var>y</var>
             </arg>
             <arg>
              <var>z</var>
             </arg>
            </funapp>
           </arg>
          </funapp>
         </lhs>
         <rhs>
          <funapp>
           <sharp>
           <name>f</name></sharp>
           <arg>
            <var>x</var>
           </arg>
           <arg>
            <var>y</var>
           </arg>
          </funapp>
         </rhs>
        </rule>
        <rule>
         <lhs>
          <funapp>
           <sharp>
           <name>f</name></sharp>
           <arg>
            <var>x</var>
           </arg>
           <arg>
            <var>y</var>
           </arg>
          </funapp>
         </lhs>
         <rhs>
          <funapp>
           <sharp>
           <name>f</name></sharp>
           <arg>
            <var>y</var>
           </arg>
           <arg>
            <var>x</var>
           </arg>
          </funapp>
         </rhs>
        </rule>
       </rules>
      </dpEquations>
      <dps>
       <rules>
        <rule>
         <lhs>
          <funapp>
           <sharp>
           <name>f</name></sharp>
           <arg>
            <funapp>
             <name>h</name>
             <arg>
              <funapp>
               <name>a</name>
              </funapp>
             </arg>
            </funapp>
           </arg>
           <arg>
            <funapp>
             <name>g</name>
             <arg>
              <funapp>
               <name>a</name>
              </funapp>
             </arg>
            </funapp>
           </arg>
          </funapp>
         </lhs>
         <rhs>
          <funapp>
           <sharp>
           <name>f</name></sharp>
           <arg>
            <funapp>
             <name>g</name>
             <arg>
              <funapp>
               <name>h</name>
               <arg>
                <funapp>
                 <name>a</name>
                </funapp>
               </arg>
              </funapp>
             </arg>
            </funapp>
           </arg>
           <arg>
            <funapp>
             <name>a</name>
            </funapp>
           </arg>
          </funapp>
         </rhs>
        </rule>
       </rules>
      </dps>
      <extensions>
       <rules>
        <rule>
         <lhs>
          <funapp>
           <name>f</name>
           <arg>
            <funapp>
             <name>f</name>
             <arg>
              <funapp>
               <name>h</name>
               <arg>
                <funapp>
                 <name>a</name>
                </funapp>
               </arg>
              </funapp>
             </arg>
             <arg>
              <funapp>
               <name>g</name>
               <arg>
                <funapp>
                 <name>a</name>
                </funapp>
               </arg>
              </funapp>
             </arg>
            </funapp>
           </arg>
           <arg>
            <var>_1</var>
           </arg>
          </funapp>
         </lhs>
         <rhs>
          <funapp>
           <name>f</name>
           <arg>
            <funapp>
             <name>f</name>
             <arg>
              <funapp>
               <name>g</name>
               <arg>
                <funapp>
                 <name>h</name>
                 <arg>
                  <funapp>
                   <name>a</name>
                  </funapp>
                 </arg>
                </funapp>
               </arg>
              </funapp>
             </arg>
             <arg>
              <funapp>
               <name>a</name>
              </funapp>
             </arg>
            </funapp>
           </arg>
           <arg>
            <var>_1</var>
           </arg>
          </funapp>
         </rhs>
        </rule>
       </rules>
      </extensions>
      <acDPTerminationProof>
       <acDepGraphProc>
        <component>
         <dps>
          <rules>
           <rule>
            <lhs>
             <funapp>
              <sharp>
              <name>f</name></sharp>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <var>y</var>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <sharp>
              <name>f</name></sharp>
              <arg>
               <var>y</var>
              </arg>
              <arg>
               <var>x</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <sharp>
              <name>f</name></sharp>
              <arg>
               <funapp>
                <name>h</name>
                <arg>
                 <funapp>
                  <name>a</name>
                 </funapp>
                </arg>
               </funapp>
              </arg>
              <arg>
               <funapp>
                <name>g</name>
                <arg>
                 <funapp>
                  <name>a</name>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <sharp>
              <name>f</name></sharp>
              <arg>
               <funapp>
                <name>g</name>
                <arg>
                 <funapp>
                  <name>h</name>
                  <arg>
                   <funapp>
                    <name>a</name>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
              <arg>
               <funapp>
                <name>a</name>
               </funapp>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <sharp>
              <name>f</name></sharp>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>f</name>
                <arg>
                 <var>y</var>
                </arg>
                <arg>
                 <var>z</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <sharp>
              <name>f</name></sharp>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <var>y</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <sharp>
              <name>f</name></sharp>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>f</name>
                <arg>
                 <var>y</var>
                </arg>
                <arg>
                 <var>z</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <sharp>
              <name>f</name></sharp>
              <arg>
               <funapp>
                <name>f</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <var>y</var>
                </arg>
               </funapp>
              </arg>
              <arg>
               <var>z</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
          </rules>
         </dps>
         <realScc>true</realScc>
         <acDPTerminationProof>
          <acRedPairProc>
           <orderingConstraintProof>
            <redPair>
             <interpretation>
              <type>
               <polynomial>
                <domain><naturals/></domain>
                <degree>1</degree>
               </polynomial>
              </type>
              <interpret>
               <name>h</name>
               <arity>1</arity>
               <polynomial>
                <sum>
                 <polynomial>
                  <coefficient>
                  <integer>2</integer></coefficient>
                 </polynomial>
                </sum>
               </polynomial>
              </interpret>
              <interpret>
               <name>a</name>
               <arity>0</arity>
               <polynomial>
                <sum>
                 <polynomial>
                  <coefficient>
                  <integer>1</integer></coefficient>
                 </polynomial>
                </sum>
               </polynomial>
              </interpret>
              <interpret>
               <name>b</name>
               <arity>0</arity>
               <polynomial>
                <sum>
                 <polynomial>
                  <coefficient>
                  <integer>0</integer></coefficient>
                 </polynomial>
                </sum>
               </polynomial>
              </interpret>
              <interpret>
               <name>f</name>
               <arity>2</arity>
               <polynomial>
                <sum>
                 <polynomial>
                  <variable>1</variable>
                 </polynomial>
                 <polynomial>
                  <variable>2</variable>
                 </polynomial>
                 <polynomial>
                  <coefficient>
                  <integer>1</integer></coefficient>
                 </polynomial>
                </sum>
               </polynomial>
              </interpret>
              <interpret>
               <sharp>
               <name>f</name></sharp>
               <arity>2</arity>
               <polynomial>
                <sum>
                 <polynomial>
                  <variable>1</variable>
                 </polynomial>
                 <polynomial>
                  <variable>2</variable>
                 </polynomial>
                 <polynomial>
                  <coefficient>
                  <integer>0</integer></coefficient>
                 </polynomial>
                </sum>
               </polynomial>
              </interpret>
              <interpret>
               <name>i</name>
               <arity>2</arity>
               <polynomial>
                <sum>
                 <polynomial>
                  <coefficient>
                  <integer>0</integer></coefficient>
                 </polynomial>
                </sum>
               </polynomial>
              </interpret>
              <interpret>
               <name>g</name>
               <arity>1</arity>
               <polynomial>
                <sum>
                 <polynomial>
                  <coefficient>
                  <integer>0</integer></coefficient>
                 </polynomial>
                </sum>
               </polynomial>
              </interpret>
             </interpretation>
            </redPair>
           </orderingConstraintProof>
           <dps>
            <rules>
             <rule>
              <lhs>
               <funapp>
                <sharp>
                <name>f</name></sharp>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <funapp>
                  <name>f</name>
                  <arg>
                   <var>y</var>
                  </arg>
                  <arg>
                   <var>z</var>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </lhs>
              <rhs>
               <funapp>
                <sharp>
                <name>f</name></sharp>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <var>y</var>
                </arg>
               </funapp>
              </rhs>
             </rule>
             <rule>
              <lhs>
               <funapp>
                <sharp>
                <name>f</name></sharp>
                <arg>
                 <funapp>
                  <name>h</name>
                  <arg>
                   <funapp>
                    <name>a</name>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
                <arg>
                 <funapp>
                  <name>g</name>
                  <arg>
                   <funapp>
                    <name>a</name>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </lhs>
              <rhs>
               <funapp>
                <sharp>
                <name>f</name></sharp>
                <arg>
                 <funapp>
                  <name>g</name>
                  <arg>
                   <funapp>
                    <name>h</name>
                    <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>
                 <var>x</var>
                </arg>
                <arg>
                 <var>y</var>
                </arg>
               </funapp>
              </lhs>
              <rhs>
               <funapp>
                <name>f</name>
                <arg>
                 <var>y</var>
                </arg>
                <arg>
                 <var>x</var>
                </arg>
               </funapp>
              </rhs>
             </rule>
             <rule>
              <lhs>
               <funapp>
                <name>f</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <funapp>
                  <name>f</name>
                  <arg>
                   <var>y</var>
                  </arg>
                  <arg>
                   <var>z</var>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </lhs>
              <rhs>
               <funapp>
                <name>f</name>
                <arg>
                 <funapp>
                  <name>f</name>
                  <arg>
                   <var>x</var>
                  </arg>
                  <arg>
                   <var>y</var>
                  </arg>
                 </funapp>
                </arg>
                <arg>
                 <var>z</var>
                </arg>
               </funapp>
              </rhs>
             </rule>
             <rule>
              <lhs>
               <funapp>
                <name>f</name>
                <arg>
                 <funapp>
                  <name>h</name>
                  <arg>
                   <funapp>
                    <name>a</name>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
                <arg>
                 <funapp>
                  <name>g</name>
                  <arg>
                   <funapp>
                    <name>a</name>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </lhs>
              <rhs>
               <funapp>
                <name>f</name>
                <arg>
                 <funapp>
                  <name>g</name>
                  <arg>
                   <funapp>
                    <name>h</name>
                    <arg>
                     <funapp>
                      <name>a</name>
                     </funapp>
                    </arg>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
                <arg>
                 <funapp>
                  <name>a</name>
                 </funapp>
                </arg>
               </funapp>
              </rhs>
             </rule>
            </rules>
           </usableRules>
           <acDPTerminationProof>
            <acDepGraphProc>
             <component>
              <dps>
               <rules>
                <rule>
                 <lhs>
                  <funapp>
                   <sharp>
                   <name>f</name></sharp>
                   <arg>
                    <var>x</var>
                   </arg>
                   <arg>
                    <var>y</var>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <sharp>
                   <name>f</name></sharp>
                   <arg>
                    <var>y</var>
                   </arg>
                   <arg>
                    <var>x</var>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <sharp>
                   <name>f</name></sharp>
                   <arg>
                    <var>x</var>
                   </arg>
                   <arg>
                    <funapp>
                     <name>f</name>
                     <arg>
                      <var>y</var>
                     </arg>
                     <arg>
                      <var>z</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <sharp>
                   <name>f</name></sharp>
                   <arg>
                    <funapp>
                     <name>f</name>
                     <arg>
                      <var>x</var>
                     </arg>
                     <arg>
                      <var>y</var>
                     </arg>
                    </funapp>
                   </arg>
                   <arg>
                    <var>z</var>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
               </rules>
              </dps>
              <realScc>true</realScc>
              <acDPTerminationProof><acTrivialProc/>
              </acDPTerminationProof>
             </component>
            </acDepGraphProc>
           </acDPTerminationProof>
          </acRedPairProc>
         </acDPTerminationProof>
        </component>
       </acDepGraphProc>
      </acDPTerminationProof>
      <acDPTerminationProof>
       <acDepGraphProc>
        <component>
         <dps>
          <rules>
           <rule>
            <lhs>
             <funapp>
              <sharp>
              <name>f</name></sharp>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <var>y</var>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <sharp>
              <name>f</name></sharp>
              <arg>
               <var>y</var>
              </arg>
              <arg>
               <var>x</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <sharp>
              <name>f</name></sharp>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>f</name>
                <arg>
                 <var>y</var>
                </arg>
                <arg>
                 <var>z</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <sharp>
              <name>f</name></sharp>
              <arg>
               <funapp>
                <name>f</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <var>y</var>
                </arg>
               </funapp>
              </arg>
              <arg>
               <var>z</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <sharp>
              <name>f</name></sharp>
              <arg>
               <funapp>
                <name>f</name>
                <arg>
                 <funapp>
                  <name>h</name>
                  <arg>
                   <funapp>
                    <name>a</name>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
                <arg>
                 <funapp>
                  <name>g</name>
                  <arg>
                   <funapp>
                    <name>a</name>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
              <arg>
               <var>_1</var>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <sharp>
              <name>f</name></sharp>
              <arg>
               <funapp>
                <name>f</name>
                <arg>
                 <funapp>
                  <name>g</name>
                  <arg>
                   <funapp>
                    <name>h</name>
                    <arg>
                     <funapp>
                      <name>a</name>
                     </funapp>
                    </arg>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
                <arg>
                 <funapp>
                  <name>a</name>
                 </funapp>
                </arg>
               </funapp>
              </arg>
              <arg>
               <var>_1</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <sharp>
              <name>f</name></sharp>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>f</name>
                <arg>
                 <var>y</var>
                </arg>
                <arg>
                 <var>z</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <sharp>
              <name>f</name></sharp>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <var>y</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
          </rules>
         </dps>
         <realScc>true</realScc>
         <acDPTerminationProof>
          <acRedPairProc>
           <orderingConstraintProof>
            <redPair>
             <interpretation>
              <type>
               <polynomial>
                <domain><naturals/></domain>
                <degree>1</degree>
               </polynomial>
              </type>
              <interpret>
               <name>h</name>
               <arity>1</arity>
               <polynomial>
                <sum>
                 <polynomial>
                  <coefficient>
                  <integer>2</integer></coefficient>
                 </polynomial>
                </sum>
               </polynomial>
              </interpret>
              <interpret>
               <name>a</name>
               <arity>0</arity>
               <polynomial>
                <sum>
                 <polynomial>
                  <coefficient>
                  <integer>1</integer></coefficient>
                 </polynomial>
                </sum>
               </polynomial>
              </interpret>
              <interpret>
               <name>b</name>
               <arity>0</arity>
               <polynomial>
                <sum>
                 <polynomial>
                  <coefficient>
                  <integer>0</integer></coefficient>
                 </polynomial>
                </sum>
               </polynomial>
              </interpret>
              <interpret>
               <name>f</name>
               <arity>2</arity>
               <polynomial>
                <sum>
                 <polynomial>
                  <variable>1</variable>
                 </polynomial>
                 <polynomial>
                  <variable>2</variable>
                 </polynomial>
                 <polynomial>
                  <coefficient>
                  <integer>1</integer></coefficient>
                 </polynomial>
                </sum>
               </polynomial>
              </interpret>
              <interpret>
               <sharp>
               <name>f</name></sharp>
               <arity>2</arity>
               <polynomial>
                <sum>
                 <polynomial>
                  <variable>1</variable>
                 </polynomial>
                 <polynomial>
                  <variable>2</variable>
                 </polynomial>
                 <polynomial>
                  <coefficient>
                  <integer>0</integer></coefficient>
                 </polynomial>
                </sum>
               </polynomial>
              </interpret>
              <interpret>
               <name>i</name>
               <arity>2</arity>
               <polynomial>
                <sum>
                 <polynomial>
                  <coefficient>
                  <integer>0</integer></coefficient>
                 </polynomial>
                </sum>
               </polynomial>
              </interpret>
              <interpret>
               <name>g</name>
               <arity>1</arity>
               <polynomial>
                <sum>
                 <polynomial>
                  <coefficient>
                  <integer>0</integer></coefficient>
                 </polynomial>
                </sum>
               </polynomial>
              </interpret>
             </interpretation>
            </redPair>
           </orderingConstraintProof>
           <dps>
            <rules>
             <rule>
              <lhs>
               <funapp>
                <sharp>
                <name>f</name></sharp>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <funapp>
                  <name>f</name>
                  <arg>
                   <var>y</var>
                  </arg>
                  <arg>
                   <var>z</var>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </lhs>
              <rhs>
               <funapp>
                <sharp>
                <name>f</name></sharp>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <var>y</var>
                </arg>
               </funapp>
              </rhs>
             </rule>
             <rule>
              <lhs>
               <funapp>
                <sharp>
                <name>f</name></sharp>
                <arg>
                 <funapp>
                  <name>f</name>
                  <arg>
                   <funapp>
                    <name>h</name>
                    <arg>
                     <funapp>
                      <name>a</name>
                     </funapp>
                    </arg>
                   </funapp>
                  </arg>
                  <arg>
                   <funapp>
                    <name>g</name>
                    <arg>
                     <funapp>
                      <name>a</name>
                     </funapp>
                    </arg>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
                <arg>
                 <var>_1</var>
                </arg>
               </funapp>
              </lhs>
              <rhs>
               <funapp>
                <sharp>
                <name>f</name></sharp>
                <arg>
                 <funapp>
                  <name>f</name>
                  <arg>
                   <funapp>
                    <name>g</name>
                    <arg>
                     <funapp>
                      <name>h</name>
                      <arg>
                       <funapp>
                        <name>a</name>
                       </funapp>
                      </arg>
                     </funapp>
                    </arg>
                   </funapp>
                  </arg>
                  <arg>
                   <funapp>
                    <name>a</name>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
                <arg>
                 <var>_1</var>
                </arg>
               </funapp>
              </rhs>
             </rule>
            </rules>
           </dps>
           <usableRules>
            <rules>
             <rule>
              <lhs>
               <funapp>
                <name>f</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <var>y</var>
                </arg>
               </funapp>
              </lhs>
              <rhs>
               <funapp>
                <name>f</name>
                <arg>
                 <var>y</var>
                </arg>
                <arg>
                 <var>x</var>
                </arg>
               </funapp>
              </rhs>
             </rule>
             <rule>
              <lhs>
               <funapp>
                <name>f</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <funapp>
                  <name>f</name>
                  <arg>
                   <var>y</var>
                  </arg>
                  <arg>
                   <var>z</var>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </lhs>
              <rhs>
               <funapp>
                <name>f</name>
                <arg>
                 <funapp>
                  <name>f</name>
                  <arg>
                   <var>x</var>
                  </arg>
                  <arg>
                   <var>y</var>
                  </arg>
                 </funapp>
                </arg>
                <arg>
                 <var>z</var>
                </arg>
               </funapp>
              </rhs>
             </rule>
             <rule>
              <lhs>
               <funapp>
                <name>f</name>
                <arg>
                 <funapp>
                  <name>h</name>
                  <arg>
                   <funapp>
                    <name>a</name>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
                <arg>
                 <funapp>
                  <name>g</name>
                  <arg>
                   <funapp>
                    <name>a</name>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </lhs>
              <rhs>
               <funapp>
                <name>f</name>
                <arg>
                 <funapp>
                  <name>g</name>
                  <arg>
                   <funapp>
                    <name>h</name>
                    <arg>
                     <funapp>
                      <name>a</name>
                     </funapp>
                    </arg>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
                <arg>
                 <funapp>
                  <name>a</name>
                 </funapp>
                </arg>
               </funapp>
              </rhs>
             </rule>
            </rules>
           </usableRules>
           <acDPTerminationProof>
            <acDepGraphProc>
             <component>
              <dps>
               <rules>
                <rule>
                 <lhs>
                  <funapp>
                   <sharp>
                   <name>f</name></sharp>
                   <arg>
                    <var>x</var>
                   </arg>
                   <arg>
                    <var>y</var>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <sharp>
                   <name>f</name></sharp>
                   <arg>
                    <var>y</var>
                   </arg>
                   <arg>
                    <var>x</var>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <sharp>
                   <name>f</name></sharp>
                   <arg>
                    <var>x</var>
                   </arg>
                   <arg>
                    <funapp>
                     <name>f</name>
                     <arg>
                      <var>y</var>
                     </arg>
                     <arg>
                      <var>z</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <sharp>
                   <name>f</name></sharp>
                   <arg>
                    <funapp>
                     <name>f</name>
                     <arg>
                      <var>x</var>
                     </arg>
                     <arg>
                      <var>y</var>
                     </arg>
                    </funapp>
                   </arg>
                   <arg>
                    <var>z</var>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
               </rules>
              </dps>
              <realScc>true</realScc>
              <acDPTerminationProof><acTrivialProc/>
              </acDPTerminationProof>
             </component>
            </acDepGraphProc>
           </acDPTerminationProof>
          </acRedPairProc>
         </acDPTerminationProof>
        </component>
       </acDepGraphProc>
      </acDPTerminationProof>
     </acDependencyPairs>
    </acTerminationProof>
   </acRuleRemoval>
  </acTerminationProof>
 </proof>
 <origin>
  <proofOrigin>
   <tool>
    <name>NaTT</name>
    <version>1.7</version>
   </tool>
  </proofOrigin>
 </origin>
</certificationProblem>