NO
<?xml version="1.0"?>
<?xml-stylesheet type="text/xsl" href="cpfHTML.xsl"?>
<certificationProblem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="../xml/cpf.xsd">
<input>
 <trsInput>
  <trs>
   <rules>
    <rule>
     <lhs>
      <funapp>
       <name>f</name>
       <arg>
        <funapp>
         <name>f</name>
         <arg>
          <var>x</var>
         </arg>
        </funapp>
       </arg>
      </funapp>
     </lhs>
     <rhs>
      <funapp>
       <name>f</name>
       <arg>
        <funapp>
         <name>g</name>
         <arg>
          <funapp>
           <name>f</name>
           <arg>
            <funapp>
             <name>f</name>
             <arg>
              <var>x</var>
             </arg>
            </funapp>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </arg>
      </funapp>
     </rhs>
    </rule>
    <rule>
     <lhs>
      <funapp>
       <name>f</name>
       <arg>
        <var>x</var>
       </arg>
      </funapp>
     </lhs>
     <rhs>
      <var>x</var>
     </rhs>
    </rule>
   </rules>
  </trs>
 </trsInput>
</input>
<cpfVersion>2.1</cpfVersion>
<proof>
 <crDisproof>
  <nonJoinableFork>
   <rewriteSequence>
    <startTerm>
     <funapp>
      <name>f</name>
      <arg>
       <funapp>
        <name>f</name>
        <arg>
         <funapp>
          <name>c_1</name>
         </funapp>
        </arg>
       </funapp>
      </arg>
     </funapp>
    </startTerm>
    <rewriteStep>
     <positionInTerm/>
     <rule>
      <lhs>
       <funapp>
        <name>f</name>
        <arg>
         <funapp>
          <name>f</name>
          <arg>
           <var>x</var>
          </arg>
         </funapp>
        </arg>
       </funapp>
      </lhs>
      <rhs>
       <funapp>
        <name>f</name>
        <arg>
         <funapp>
          <name>g</name>
          <arg>
           <funapp>
            <name>f</name>
            <arg>
             <funapp>
              <name>f</name>
              <arg>
               <var>x</var>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </arg>
         </funapp>
        </arg>
       </funapp>
      </rhs>
     </rule>
     <funapp>
      <name>f</name>
      <arg>
       <funapp>
        <name>g</name>
        <arg>
         <funapp>
          <name>f</name>
          <arg>
           <funapp>
            <name>f</name>
            <arg>
             <funapp>
              <name>c_1</name>
             </funapp>
            </arg>
           </funapp>
          </arg>
         </funapp>
        </arg>
       </funapp>
      </arg>
     </funapp>
    </rewriteStep>
    <rewriteStep>
     <positionInTerm/>
     <rule>
      <lhs>
       <funapp>
        <name>f</name>
        <arg>
         <var>x</var>
        </arg>
       </funapp>
      </lhs>
      <rhs>
       <var>x</var>
      </rhs>
     </rule>
     <funapp>
      <name>g</name>
      <arg>
       <funapp>
        <name>f</name>
        <arg>
         <funapp>
          <name>f</name>
          <arg>
           <funapp>
            <name>c_1</name>
           </funapp>
          </arg>
         </funapp>
        </arg>
       </funapp>
      </arg>
     </funapp>
    </rewriteStep>
    <rewriteStep>
     <positionInTerm>
      <position>1</position>
     </positionInTerm>
     <rule>
      <lhs>
       <funapp>
        <name>f</name>
        <arg>
         <var>x</var>
        </arg>
       </funapp>
      </lhs>
      <rhs>
       <var>x</var>
      </rhs>
     </rule>
     <funapp>
      <name>g</name>
      <arg>
       <funapp>
        <name>f</name>
        <arg>
         <funapp>
          <name>c_1</name>
         </funapp>
        </arg>
       </funapp>
      </arg>
     </funapp>
    </rewriteStep>
    <rewriteStep>
     <positionInTerm>
      <position>1</position>
     </positionInTerm>
     <rule>
      <lhs>
       <funapp>
        <name>f</name>
        <arg>
         <var>x</var>
        </arg>
       </funapp>
      </lhs>
      <rhs>
       <var>x</var>
      </rhs>
     </rule>
     <funapp>
      <name>g</name>
      <arg>
       <funapp>
        <name>c_1</name>
       </funapp>
      </arg>
     </funapp>
    </rewriteStep>
   </rewriteSequence>
   <rewriteSequence>
    <startTerm>
     <funapp>
      <name>f</name>
      <arg>
       <funapp>
        <name>f</name>
        <arg>
         <funapp>
          <name>c_1</name>
         </funapp>
        </arg>
       </funapp>
      </arg>
     </funapp>
    </startTerm>
    <rewriteStep>
     <positionInTerm/>
     <rule>
      <lhs>
       <funapp>
        <name>f</name>
        <arg>
         <var>x</var>
        </arg>
       </funapp>
      </lhs>
      <rhs>
       <var>x</var>
      </rhs>
     </rule>
     <funapp>
      <name>f</name>
      <arg>
       <funapp>
        <name>c_1</name>
       </funapp>
      </arg>
     </funapp>
    </rewriteStep>
    <rewriteStep>
     <positionInTerm/>
     <rule>
      <lhs>
       <funapp>
        <name>f</name>
        <arg>
         <var>x</var>
        </arg>
       </funapp>
      </lhs>
      <rhs>
       <var>x</var>
      </rhs>
     </rule>
     <funapp>
      <name>c_1</name>
     </funapp>
    </rewriteStep>
   </rewriteSequence>
   <usableRulesNonJoin>
    <argumentFilterNonJoin>
     <argumentFilter>
      <argumentFilterEntry>
       <name>g</name>
       <arity>1</arity>
       <nonCollapsing/>
      </argumentFilterEntry>
      <argumentFilterEntry>
       <name>c_1</name>
       <arity>0</arity>
       <nonCollapsing/>
      </argumentFilterEntry>
     </argumentFilter>
     <usableRulesNonJoin>
      <strictDecrease>
       <orderingConstraintProof>
        <redPair>
         <pathOrder>
          <statusPrecedence>
           <statusPrecedenceEntry>
            <name>g</name>
            <arity>0</arity>
            <precedence>2</precedence>
            <mul/>
           </statusPrecedenceEntry>
           <statusPrecedenceEntry>
            <name>c_1</name>
            <arity>0</arity>
            <precedence>1</precedence>
            <mul/>
           </statusPrecedenceEntry>
          </statusPrecedence>
         </pathOrder>
        </redPair>
       </orderingConstraintProof>
      </strictDecrease>
     </usableRulesNonJoin>
    </argumentFilterNonJoin>
   </usableRulesNonJoin>
  </nonJoinableFork>
 </crDisproof>
</proof>
<origin>
 <proofOrigin>
  <tool>
   <name>ACP</name>
   <version>0.72</version>
  </tool>
 </proofOrigin>
</origin>
</certificationProblem>