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>7</name>
        <arity>0</arity>
        <polynomial>
         <sum>
          <polynomial>
           <coefficient>
           <integer>14</integer></coefficient>
          </polynomial>
         </sum>
        </polynomial>
       </interpret>
       <interpret>
        <name>1</name>
        <arity>0</arity>
        <polynomial>
         <sum>
          <polynomial>
           <coefficient>
           <integer>2</integer></coefficient>
          </polynomial>
         </sum>
        </polynomial>
       </interpret>
       <interpret>
        <name>4</name>
        <arity>0</arity>
        <polynomial>
         <sum>
          <polynomial>
           <coefficient>
           <integer>8</integer></coefficient>
          </polynomial>
         </sum>
        </polynomial>
       </interpret>
       <interpret>
        <name>s</name>
        <arity>1</arity>
        <polynomial>
         <sum>
          <polynomial>
           <variable>1</variable>
          </polynomial>
          <polynomial>
           <coefficient>
           <integer>1</integer></coefficient>
          </polynomial>
         </sum>
        </polynomial>
       </interpret>
       <interpret>
        <name>max2</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>max'</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>5</name>
        <arity>0</arity>
        <polynomial>
         <sum>
          <polynomial>
           <coefficient>
           <integer>10</integer></coefficient>
          </polynomial>
         </sum>
        </polynomial>
       </interpret>
       <interpret>
        <name>3</name>
        <arity>0</arity>
        <polynomial>
         <sum>
          <polynomial>
           <coefficient>
           <integer>6</integer></coefficient>
          </polynomial>
         </sum>
        </polynomial>
       </interpret>
       <interpret>
        <name>9</name>
        <arity>0</arity>
        <polynomial>
         <sum>
          <polynomial>
           <coefficient>
           <integer>18</integer></coefficient>
          </polynomial>
         </sum>
        </polynomial>
       </interpret>
       <interpret>
        <name>8</name>
        <arity>0</arity>
        <polynomial>
         <sum>
          <polynomial>
           <coefficient>
           <integer>16</integer></coefficient>
          </polynomial>
         </sum>
        </polynomial>
       </interpret>
       <interpret>
        <name>0</name>
        <arity>0</arity>
        <polynomial>
         <sum>
          <polynomial>
           <coefficient>
           <integer>0</integer></coefficient>
          </polynomial>
         </sum>
        </polynomial>
       </interpret>
       <interpret>
        <name>max</name>
        <arity>1</arity>
        <polynomial>
         <sum>
          <polynomial>
           <variable>1</variable>
          </polynomial>
          <polynomial>
           <coefficient>
           <integer>0</integer></coefficient>
          </polynomial>
         </sum>
        </polynomial>
       </interpret>
       <interpret>
        <name>singl</name>
        <arity>1</arity>
        <polynomial>
         <sum>
          <polynomial>
           <variable>1</variable>
          </polynomial>
          <polynomial>
           <coefficient>
           <integer>2</integer></coefficient>
          </polynomial>
         </sum>
        </polynomial>
       </interpret>
       <interpret>
        <name>2</name>
        <arity>0</arity>
        <polynomial>
         <sum>
          <polynomial>
           <coefficient>
           <integer>4</integer></coefficient>
          </polynomial>
         </sum>
        </polynomial>
       </interpret>
       <interpret>
        <name>empty</name>
        <arity>0</arity>
        <polynomial>
         <sum>
          <polynomial>
           <coefficient>
           <integer>1</integer></coefficient>
          </polynomial>
         </sum>
        </polynomial>
       </interpret>
       <interpret>
        <name>6</name>
        <arity>0</arity>
        <polynomial>
         <sum>
          <polynomial>
           <coefficient>
           <integer>12</integer></coefficient>
          </polynomial>
         </sum>
        </polynomial>
       </interpret>
       <interpret>
        <name>app</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>
      </interpretation>
     </redPair>
    </orderingConstraintProof>
    <trs>
     <rules>
      <rule>
       <lhs>
        <funapp>
         <name>4</name>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <name>s</name>
         <arg>
          <funapp>
           <name>3</name>
          </funapp>
         </arg>
        </funapp>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <name>max2</name>
         <arg>
          <var>x</var>
         </arg>
         <arg>
          <funapp>
           <name>empty</name>
          </funapp>
         </arg>
        </funapp>
       </lhs>
       <rhs>
        <var>x</var>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <name>8</name>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <name>s</name>
         <arg>
          <funapp>
           <name>7</name>
          </funapp>
         </arg>
        </funapp>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <name>1</name>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <name>s</name>
         <arg>
          <funapp>
           <name>0</name>
          </funapp>
         </arg>
        </funapp>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <name>3</name>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <name>s</name>
         <arg>
          <funapp>
           <name>2</name>
          </funapp>
         </arg>
        </funapp>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <name>max2</name>
         <arg>
          <var>x</var>
         </arg>
         <arg>
          <funapp>
           <name>singl</name>
           <arg>
            <var>y</var>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <name>max'</name>
         <arg>
          <var>x</var>
         </arg>
         <arg>
          <var>y</var>
         </arg>
        </funapp>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <name>max2</name>
         <arg>
          <var>x</var>
         </arg>
         <arg>
          <funapp>
           <name>app</name>
           <arg>
            <funapp>
             <name>singl</name>
             <arg>
              <var>y</var>
             </arg>
            </funapp>
           </arg>
           <arg>
            <var>Z</var>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <name>max2</name>
         <arg>
          <funapp>
           <name>max'</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>5</name>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <name>s</name>
         <arg>
          <funapp>
           <name>4</name>
          </funapp>
         </arg>
        </funapp>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <name>max'</name>
         <arg>
          <funapp>
           <name>0</name>
          </funapp>
         </arg>
         <arg>
          <var>x</var>
         </arg>
        </funapp>
       </lhs>
       <rhs>
        <var>x</var>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <name>7</name>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <name>s</name>
         <arg>
          <funapp>
           <name>6</name>
          </funapp>
         </arg>
        </funapp>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <name>max</name>
         <arg>
          <funapp>
           <name>app</name>
           <arg>
            <funapp>
             <name>singl</name>
             <arg>
              <var>x</var>
             </arg>
            </funapp>
           </arg>
           <arg>
            <var>Y</var>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <name>max2</name>
         <arg>
          <var>x</var>
         </arg>
         <arg>
          <var>Y</var>
         </arg>
        </funapp>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <name>app</name>
         <arg>
          <funapp>
           <name>empty</name>
          </funapp>
         </arg>
         <arg>
          <var>X</var>
         </arg>
        </funapp>
       </lhs>
       <rhs>
        <var>X</var>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <name>max'</name>
         <arg>
          <funapp>
           <name>s</name>
           <arg>
            <var>x</var>
           </arg>
          </funapp>
         </arg>
         <arg>
          <funapp>
           <name>s</name>
           <arg>
            <var>y</var>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <name>s</name>
         <arg>
          <funapp>
           <name>max'</name>
           <arg>
            <var>x</var>
           </arg>
           <arg>
            <var>y</var>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <name>9</name>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <name>s</name>
         <arg>
          <funapp>
           <name>8</name>
          </funapp>
         </arg>
        </funapp>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <name>max</name>
         <arg>
          <funapp>
           <name>singl</name>
           <arg>
            <var>x</var>
           </arg>
          </funapp>
         </arg>
        </funapp>
       </lhs>
       <rhs>
        <var>x</var>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <name>6</name>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <name>s</name>
         <arg>
          <funapp>
           <name>5</name>
          </funapp>
         </arg>
        </funapp>
       </rhs>
      </rule>
      <rule>
       <lhs>
        <funapp>
         <name>2</name>
        </funapp>
       </lhs>
       <rhs>
        <funapp>
         <name>s</name>
         <arg>
          <funapp>
           <name>1</name>
          </funapp>
         </arg>
        </funapp>
       </rhs>
      </rule>
     </rules>
    </trs>
    <acTerminationProof><acRIsEmpty/>
    </acTerminationProof>
   </acRuleRemoval>
  </acTerminationProof>
 </proof>
 <origin>
  <proofOrigin>
   <tool>
    <name>NaTT</name>
    <version>1.7</version>
   </tool>
  </proofOrigin>
 </origin>
</certificationProblem>