/export/starexec/sandbox2/solver/bin/starexec_run_Certifiable /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES
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          <lhs>
           <funapp>
            <sharp>
            <name>times</name></sharp>
            <arg>
             <var>x</var>
            </arg>
            <arg>
             <funapp>
              <name>i</name>
              <arg>
               <var>y</var>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>times</name></sharp>
            <arg>
             <var>x</var>
            </arg>
            <arg>
             <var>y</var>
            </arg>
           </funapp>
          </rhs>
         </rule>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>times</name></sharp>
            <arg>
             <var>x</var>
            </arg>
            <arg>
             <var>y</var>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>times</name></sharp>
            <arg>
             <var>y</var>
            </arg>
            <arg>
             <var>x</var>
            </arg>
           </funapp>
          </rhs>
         </rule>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>times</name></sharp>
            <arg>
             <var>x</var>
            </arg>
            <arg>
             <funapp>
              <name>plus</name>
              <arg>
               <var>y</var>
              </arg>
              <arg>
               <var>z</var>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>times</name></sharp>
            <arg>
             <var>x</var>
            </arg>
            <arg>
             <var>z</var>
            </arg>
           </funapp>
          </rhs>
         </rule>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>times</name></sharp>
            <arg>
             <var>x</var>
            </arg>
            <arg>
             <funapp>
              <name>times</name>
              <arg>
               <var>y</var>
              </arg>
              <arg>
               <var>z</var>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>times</name></sharp>
            <arg>
             <funapp>
              <name>times</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>times</name></sharp>
            <arg>
             <var>x</var>
            </arg>
            <arg>
             <funapp>
              <name>times</name>
              <arg>
               <var>y</var>
              </arg>
              <arg>
               <var>z</var>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>times</name></sharp>
            <arg>
             <var>x</var>
            </arg>
            <arg>
             <var>y</var>
            </arg>
           </funapp>
          </rhs>
         </rule>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>times</name></sharp>
            <arg>
             <var>x</var>
            </arg>
            <arg>
             <funapp>
              <name>plus</name>
              <arg>
               <var>y</var>
              </arg>
              <arg>
               <var>z</var>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>times</name></sharp>
            <arg>
             <var>x</var>
            </arg>
            <arg>
             <var>y</var>
            </arg>
           </funapp>
          </rhs>
         </rule>
        </rules>
       </dps>
       <realScc>true</realScc>
       <acDPTerminationProof>
        <acRedPairProc>
         <orderingConstraintProof>
          <redPair>
           <filteredRedPair>
            <argumentFilter>
            </argumentFilter>
            <weightedPathOrder>
             <precedenceStatus>
              <precedenceStatusEntry>
               <sharp>
               <name>plus</name></sharp>
               <arity>2</arity>
               <precedence>1
               </precedence>
               <status>
               </status>
              </precedenceStatusEntry>
              <precedenceStatusEntry>
               <sharp>
               <name>times</name></sharp>
               <arity>2</arity>
               <precedence>3
               </precedence>
               <status>
                <position>1</position>
                <position>2</position>
               </status>
              </precedenceStatusEntry>
              <precedenceStatusEntry>
               <name>0</name>
               <arity>0</arity>
               <precedence>0
               </precedence>
               <status>
               </status>
              </precedenceStatusEntry>
              <precedenceStatusEntry>
               <name>times</name>
               <arity>2</arity>
               <precedence>3
               </precedence>
               <status>
                <position>1</position>
                <position>2</position>
               </status>
              </precedenceStatusEntry>
              <precedenceStatusEntry>
               <name>i</name>
               <arity>1</arity>
               <precedence>2
               </precedence>
               <status>
                <position>1</position>
               </status>
              </precedenceStatusEntry>
              <precedenceStatusEntry>
               <name>plus</name>
               <arity>2</arity>
               <precedence>1
               </precedence>
               <status>
                <position>1</position>
                <position>2</position>
               </status>
              </precedenceStatusEntry>
              <precedenceStatusEntry>
               <sharp>
               <name>i</name></sharp>
               <arity>1</arity>
               <precedence>0
               </precedence>
               <status>
               </status>
              </precedenceStatusEntry>
             </precedenceStatus>
             <maxPoly>
              <interpret>
               <sharp>
               <name>plus</name></sharp>
               <arity>2</arity>
               <max>
                <constant>0</constant>
               </max>
              </interpret>
              <interpret>
               <sharp>
               <name>times</name></sharp>
               <arity>2</arity>
               <max>
                <sum>
                 <variable>1</variable>
                 <constant>0</constant>
                </sum>
                <sum>
                 <variable>2</variable>
                 <constant>0</constant>
                </sum>
                <constant>0</constant>
               </max>
              </interpret>
              <interpret>
               <name>0</name>
               <arity>0</arity>
               <sum>
                <constant>0</constant>
               </sum>
              </interpret>
              <interpret>
               <name>times</name>
               <arity>2</arity>
               <max>
                <sum>
                 <variable>1</variable>
                 <constant>0</constant>
                </sum>
                <sum>
                 <variable>2</variable>
                 <constant>0</constant>
                </sum>
                <constant>0</constant>
               </max>
              </interpret>
              <interpret>
               <name>i</name>
               <arity>1</arity>
               <sum>
                <variable>1</variable>
                <constant>0</constant>
               </sum>
              </interpret>
              <interpret>
               <name>plus</name>
               <arity>2</arity>
               <max>
                <sum>
                 <variable>1</variable>
                 <constant>0</constant>
                </sum>
                <sum>
                 <variable>2</variable>
                 <constant>0</constant>
                </sum>
                <constant>0</constant>
               </max>
              </interpret>
              <interpret>
               <sharp>
               <name>i</name></sharp>
               <arity>1</arity>
               <sum>
                <constant>0</constant>
               </sum>
              </interpret>
             </maxPoly>
            </weightedPathOrder>
           </filteredRedPair>
          </redPair>
         </orderingConstraintProof>
         <dps>
          <rules>
           <rule>
            <lhs>
             <funapp>
              <sharp>
              <name>times</name></sharp>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>plus</name>
                <arg>
                 <var>y</var>
                </arg>
                <arg>
                 <var>z</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <sharp>
              <name>times</name></sharp>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <var>y</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <sharp>
              <name>times</name></sharp>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>times</name>
                <arg>
                 <var>y</var>
                </arg>
                <arg>
                 <var>z</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <sharp>
              <name>times</name></sharp>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <var>y</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <sharp>
              <name>times</name></sharp>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>plus</name>
                <arg>
                 <var>y</var>
                </arg>
                <arg>
                 <var>z</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <sharp>
              <name>times</name></sharp>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <var>z</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <sharp>
              <name>times</name></sharp>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>i</name>
                <arg>
                 <var>y</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <sharp>
              <name>times</name></sharp>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <var>y</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
          </rules>
         </dps>
         <usableRules>
          <rules>
           <rule>
            <lhs>
             <funapp>
              <name>i</name>
              <arg>
               <funapp>
                <name>i</name>
                <arg>
                 <var>x</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <var>x</var>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>times</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>i</name>
                <arg>
                 <var>y</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>i</name>
              <arg>
               <funapp>
                <name>times</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <var>y</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>plus</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>0</name>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <var>x</var>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>i</name>
              <arg>
               <funapp>
                <name>0</name>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>0</name>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>i</name>
              <arg>
               <funapp>
                <name>plus</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <var>y</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>plus</name>
              <arg>
               <funapp>
                <name>i</name>
                <arg>
                 <var>x</var>
                </arg>
               </funapp>
              </arg>
              <arg>
               <funapp>
                <name>i</name>
                <arg>
                 <var>y</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>plus</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <var>y</var>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>plus</name>
              <arg>
               <var>y</var>
              </arg>
              <arg>
               <var>x</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>times</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>0</name>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>0</name>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>times</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <var>y</var>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>times</name>
              <arg>
               <var>y</var>
              </arg>
              <arg>
               <var>x</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>times</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>times</name>
                <arg>
                 <var>y</var>
                </arg>
                <arg>
                 <var>z</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>times</name>
              <arg>
               <funapp>
                <name>times</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>plus</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>plus</name>
                <arg>
                 <var>y</var>
                </arg>
                <arg>
                 <var>z</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>plus</name>
              <arg>
               <funapp>
                <name>plus</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>times</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>plus</name>
                <arg>
                 <var>y</var>
                </arg>
                <arg>
                 <var>z</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>plus</name>
              <arg>
               <funapp>
                <name>times</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <var>y</var>
                </arg>
               </funapp>
              </arg>
              <arg>
               <funapp>
                <name>times</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <var>z</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>plus</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>i</name>
                <arg>
                 <var>x</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>0</name>
             </funapp>
            </rhs>
           </rule>
          </rules>
         </usableRules>
         <acDPTerminationProof>
          <acDepGraphProc>
           <component>
            <dps>
             <rules>
              <rule>
               <lhs>
                <funapp>
                 <sharp>
                 <name>times</name></sharp>
                 <arg>
                  <var>x</var>
                 </arg>
                 <arg>
                  <var>y</var>
                 </arg>
                </funapp>
               </lhs>
               <rhs>
                <funapp>
                 <sharp>
                 <name>times</name></sharp>
                 <arg>
                  <var>y</var>
                 </arg>
                 <arg>
                  <var>x</var>
                 </arg>
                </funapp>
               </rhs>
              </rule>
              <rule>
               <lhs>
                <funapp>
                 <sharp>
                 <name>times</name></sharp>
                 <arg>
                  <var>x</var>
                 </arg>
                 <arg>
                  <funapp>
                   <name>times</name>
                   <arg>
                    <var>y</var>
                   </arg>
                   <arg>
                    <var>z</var>
                   </arg>
                  </funapp>
                 </arg>
                </funapp>
               </lhs>
               <rhs>
                <funapp>
                 <sharp>
                 <name>times</name></sharp>
                 <arg>
                  <funapp>
                   <name>times</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>
      <component>
       <dps>
        <rules>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>times</name></sharp>
            <arg>
             <var>x</var>
            </arg>
            <arg>
             <funapp>
              <name>plus</name>
              <arg>
               <var>y</var>
              </arg>
              <arg>
               <var>z</var>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>plus</name></sharp>
            <arg>
             <funapp>
              <name>times</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <var>y</var>
              </arg>
             </funapp>
            </arg>
            <arg>
             <funapp>
              <name>times</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <var>z</var>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </rhs>
         </rule>
        </rules>
       </dps>
       <realScc>false</realScc>
      </component>
      <component>
       <dps>
        <rules>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>times</name></sharp>
            <arg>
             <var>x</var>
            </arg>
            <arg>
             <funapp>
              <name>i</name>
              <arg>
               <var>y</var>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>i</name></sharp>
            <arg>
             <funapp>
              <name>times</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <var>y</var>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </rhs>
         </rule>
        </rules>
       </dps>
       <realScc>false</realScc>
      </component>
      <component>
       <dps>
        <rules>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>i</name></sharp>
            <arg>
             <funapp>
              <name>plus</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <var>y</var>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>i</name></sharp>
            <arg>
             <var>y</var>
            </arg>
           </funapp>
          </rhs>
         </rule>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>i</name></sharp>
            <arg>
             <funapp>
              <name>plus</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <var>y</var>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>i</name></sharp>
            <arg>
             <var>x</var>
            </arg>
           </funapp>
          </rhs>
         </rule>
        </rules>
       </dps>
       <realScc>true</realScc>
       <acDPTerminationProof>
        <acRedPairProc>
         <orderingConstraintProof>
          <redPair>
           <maxPoly>
            <interpret>
             <sharp>
             <name>plus</name></sharp>
             <arity>2</arity>
             <sum>
              <constant>0</constant>
             </sum>
            </interpret>
            <interpret>
             <sharp>
             <name>times</name></sharp>
             <arity>2</arity>
             <sum>
              <constant>0</constant>
             </sum>
            </interpret>
            <interpret>
             <name>0</name>
             <arity>0</arity>
             <sum>
              <constant>10197</constant>
             </sum>
            </interpret>
            <interpret>
             <name>times</name>
             <arity>2</arity>
             <sum>
              <variable>1</variable>
              <variable>2</variable>
              <constant>21239</constant>
             </sum>
            </interpret>
            <interpret>
             <name>i</name>
             <arity>1</arity>
             <sum>
              <variable>1</variable>
              <constant>2476</constant>
             </sum>
            </interpret>
            <interpret>
             <name>plus</name>
             <arity>2</arity>
             <sum>
              <variable>1</variable>
              <variable>2</variable>
              <constant>7720</constant>
             </sum>
            </interpret>
            <interpret>
             <sharp>
             <name>i</name></sharp>
             <arity>1</arity>
             <sum>
              <variable>1</variable>
              <constant>0</constant>
             </sum>
            </interpret>
           </maxPoly>
          </redPair>
         </orderingConstraintProof>
         <dps>
          <rules>
           <rule>
            <lhs>
             <funapp>
              <sharp>
              <name>i</name></sharp>
              <arg>
               <funapp>
                <name>plus</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <var>y</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <sharp>
              <name>i</name></sharp>
              <arg>
               <var>x</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <sharp>
              <name>i</name></sharp>
              <arg>
               <funapp>
                <name>plus</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <var>y</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <sharp>
              <name>i</name></sharp>
              <arg>
               <var>y</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
          </rules>
         </dps>
         <usableRules>
          <rules>
          </rules>
         </usableRules>
         <acDPTerminationProof>
          <acDepGraphProc>
          </acDepGraphProc>
         </acDPTerminationProof>
        </acRedPairProc>
       </acDPTerminationProof>
      </component>
      <component>
       <dps>
        <rules>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>i</name></sharp>
            <arg>
             <funapp>
              <name>plus</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <var>y</var>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>plus</name></sharp>
            <arg>
             <funapp>
              <name>i</name>
              <arg>
               <var>x</var>
              </arg>
             </funapp>
            </arg>
            <arg>
             <funapp>
              <name>i</name>
              <arg>
               <var>y</var>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </rhs>
         </rule>
        </rules>
       </dps>
       <realScc>false</realScc>
      </component>
      <component>
       <dps>
        <rules>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>plus</name></sharp>
            <arg>
             <var>x</var>
            </arg>
            <arg>
             <funapp>
              <name>plus</name>
              <arg>
               <var>y</var>
              </arg>
              <arg>
               <var>z</var>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>plus</name></sharp>
            <arg>
             <funapp>
              <name>plus</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>plus</name></sharp>
            <arg>
             <var>x</var>
            </arg>
            <arg>
             <var>y</var>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>plus</name></sharp>
            <arg>
             <var>y</var>
            </arg>
            <arg>
             <var>x</var>
            </arg>
           </funapp>
          </rhs>
         </rule>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>plus</name></sharp>
            <arg>
             <var>x</var>
            </arg>
            <arg>
             <funapp>
              <name>plus</name>
              <arg>
               <var>y</var>
              </arg>
              <arg>
               <var>z</var>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>plus</name></sharp>
            <arg>
             <var>x</var>
            </arg>
            <arg>
             <var>y</var>
            </arg>
           </funapp>
          </rhs>
         </rule>
        </rules>
       </dps>
       <realScc>true</realScc>
       <acDPTerminationProof><acTrivialProc/>
       </acDPTerminationProof>
      </component>
     </acDepGraphProc>
    </acDPTerminationProof>
    <acDPTerminationProof>
     <acDepGraphProc>
      <component>
       <dps>
        <rules>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>plus</name></sharp>
            <arg>
             <var>x</var>
            </arg>
            <arg>
             <funapp>
              <name>plus</name>
              <arg>
               <var>y</var>
              </arg>
              <arg>
               <var>z</var>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>plus</name></sharp>
            <arg>
             <var>x</var>
            </arg>
            <arg>
             <var>y</var>
            </arg>
           </funapp>
          </rhs>
         </rule>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>plus</name></sharp>
            <arg>
             <funapp>
              <name>plus</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>i</name>
                <arg>
                 <var>x</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </arg>
            <arg>
             <var>_1</var>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>plus</name></sharp>
            <arg>
             <funapp>
              <name>0</name>
             </funapp>
            </arg>
            <arg>
             <var>_1</var>
            </arg>
           </funapp>
          </rhs>
         </rule>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>plus</name></sharp>
            <arg>
             <var>x</var>
            </arg>
            <arg>
             <var>y</var>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>plus</name></sharp>
            <arg>
             <var>y</var>
            </arg>
            <arg>
             <var>x</var>
            </arg>
           </funapp>
          </rhs>
         </rule>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>plus</name></sharp>
            <arg>
             <funapp>
              <name>plus</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>0</name>
               </funapp>
              </arg>
             </funapp>
            </arg>
            <arg>
             <var>_1</var>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>plus</name></sharp>
            <arg>
             <var>x</var>
            </arg>
            <arg>
             <var>_1</var>
            </arg>
           </funapp>
          </rhs>
         </rule>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>plus</name></sharp>
            <arg>
             <var>x</var>
            </arg>
            <arg>
             <funapp>
              <name>plus</name>
              <arg>
               <var>y</var>
              </arg>
              <arg>
               <var>z</var>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>plus</name></sharp>
            <arg>
             <funapp>
              <name>plus</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>
           <maxPoly>
            <interpret>
             <sharp>
             <name>plus</name></sharp>
             <arity>2</arity>
             <sum>
              <variable>1</variable>
              <variable>2</variable>
              <constant>0</constant>
             </sum>
            </interpret>
            <interpret>
             <sharp>
             <name>times</name></sharp>
             <arity>2</arity>
             <sum>
              <constant>0</constant>
             </sum>
            </interpret>
            <interpret>
             <name>0</name>
             <arity>0</arity>
             <sum>
              <constant>1</constant>
             </sum>
            </interpret>
            <interpret>
             <name>times</name>
             <arity>2</arity>
             <sum>
              <variable>1</variable>
              <variable>2</variable>
              <constant>21239</constant>
             </sum>
            </interpret>
            <interpret>
             <name>i</name>
             <arity>1</arity>
             <sum>
              <variable>1</variable>
              <constant>11798</constant>
             </sum>
            </interpret>
            <interpret>
             <name>plus</name>
             <arity>2</arity>
             <sum>
              <variable>1</variable>
              <variable>2</variable>
              <constant>8366</constant>
             </sum>
            </interpret>
            <interpret>
             <sharp>
             <name>i</name></sharp>
             <arity>1</arity>
             <sum>
              <constant>0</constant>
             </sum>
            </interpret>
           </maxPoly>
          </redPair>
         </orderingConstraintProof>
         <dps>
          <rules>
           <rule>
            <lhs>
             <funapp>
              <sharp>
              <name>plus</name></sharp>
              <arg>
               <funapp>
                <name>plus</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <funapp>
                  <name>0</name>
                 </funapp>
                </arg>
               </funapp>
              </arg>
              <arg>
               <var>_1</var>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <sharp>
              <name>plus</name></sharp>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <var>_1</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <sharp>
              <name>plus</name></sharp>
              <arg>
               <funapp>
                <name>plus</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <funapp>
                  <name>i</name>
                  <arg>
                   <var>x</var>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
              <arg>
               <var>_1</var>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <sharp>
              <name>plus</name></sharp>
              <arg>
               <funapp>
                <name>0</name>
               </funapp>
              </arg>
              <arg>
               <var>_1</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <sharp>
              <name>plus</name></sharp>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>plus</name>
                <arg>
                 <var>y</var>
                </arg>
                <arg>
                 <var>z</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <sharp>
              <name>plus</name></sharp>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <var>y</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
          </rules>
         </dps>
         <usableRules>
          <rules>
           <rule>
            <lhs>
             <funapp>
              <name>plus</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>0</name>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <var>x</var>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>plus</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <var>y</var>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>plus</name>
              <arg>
               <var>y</var>
              </arg>
              <arg>
               <var>x</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>plus</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>plus</name>
                <arg>
                 <var>y</var>
                </arg>
                <arg>
                 <var>z</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>plus</name>
              <arg>
               <funapp>
                <name>plus</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>plus</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>i</name>
                <arg>
                 <var>x</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>0</name>
             </funapp>
            </rhs>
           </rule>
          </rules>
         </usableRules>
         <acDPTerminationProof>
          <acDepGraphProc>
           <component>
            <dps>
             <rules>
              <rule>
               <lhs>
                <funapp>
                 <sharp>
                 <name>plus</name></sharp>
                 <arg>
                  <var>x</var>
                 </arg>
                 <arg>
                  <var>y</var>
                 </arg>
                </funapp>
               </lhs>
               <rhs>
                <funapp>
                 <sharp>
                 <name>plus</name></sharp>
                 <arg>
                  <var>y</var>
                 </arg>
                 <arg>
                  <var>x</var>
                 </arg>
                </funapp>
               </rhs>
              </rule>
              <rule>
               <lhs>
                <funapp>
                 <sharp>
                 <name>plus</name></sharp>
                 <arg>
                  <var>x</var>
                 </arg>
                 <arg>
                  <funapp>
                   <name>plus</name>
                   <arg>
                    <var>y</var>
                   </arg>
                   <arg>
                    <var>z</var>
                   </arg>
                  </funapp>
                 </arg>
                </funapp>
               </lhs>
               <rhs>
                <funapp>
                 <sharp>
                 <name>plus</name></sharp>
                 <arg>
                  <funapp>
                   <name>plus</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>
      <component>
       <dps>
        <rules>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>times</name></sharp>
            <arg>
             <funapp>
              <name>times</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>i</name>
                <arg>
                 <var>y</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </arg>
            <arg>
             <var>_1</var>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>times</name></sharp>
            <arg>
             <funapp>
              <name>i</name>
              <arg>
               <funapp>
                <name>times</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <var>y</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </arg>
            <arg>
             <var>_1</var>
            </arg>
           </funapp>
          </rhs>
         </rule>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>times</name></sharp>
            <arg>
             <funapp>
              <name>times</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>plus</name>
                <arg>
                 <var>y</var>
                </arg>
                <arg>
                 <var>z</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </arg>
            <arg>
             <var>_1</var>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>times</name></sharp>
            <arg>
             <funapp>
              <name>plus</name>
              <arg>
               <funapp>
                <name>times</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <var>y</var>
                </arg>
               </funapp>
              </arg>
              <arg>
               <funapp>
                <name>times</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <var>z</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </arg>
            <arg>
             <var>_1</var>
            </arg>
           </funapp>
          </rhs>
         </rule>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>times</name></sharp>
            <arg>
             <var>x</var>
            </arg>
            <arg>
             <var>y</var>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>times</name></sharp>
            <arg>
             <var>y</var>
            </arg>
            <arg>
             <var>x</var>
            </arg>
           </funapp>
          </rhs>
         </rule>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>times</name></sharp>
            <arg>
             <var>x</var>
            </arg>
            <arg>
             <funapp>
              <name>times</name>
              <arg>
               <var>y</var>
              </arg>
              <arg>
               <var>z</var>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>times</name></sharp>
            <arg>
             <funapp>
              <name>times</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>times</name></sharp>
            <arg>
             <funapp>
              <name>times</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>0</name>
               </funapp>
              </arg>
             </funapp>
            </arg>
            <arg>
             <var>_1</var>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>times</name></sharp>
            <arg>
             <funapp>
              <name>0</name>
             </funapp>
            </arg>
            <arg>
             <var>_1</var>
            </arg>
           </funapp>
          </rhs>
         </rule>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>times</name></sharp>
            <arg>
             <var>x</var>
            </arg>
            <arg>
             <funapp>
              <name>times</name>
              <arg>
               <var>y</var>
              </arg>
              <arg>
               <var>z</var>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>times</name></sharp>
            <arg>
             <var>x</var>
            </arg>
            <arg>
             <var>y</var>
            </arg>
           </funapp>
          </rhs>
         </rule>
        </rules>
       </dps>
       <realScc>true</realScc>
       <acDPTerminationProof>
        <acRedPairProc>
         <orderingConstraintProof>
          <redPair>
           <filteredRedPair>
            <argumentFilter>
             <argumentFilterEntry>
              <name>i</name>
              <arity>1</arity>
              <collapsing>1</collapsing>
             </argumentFilterEntry>
            </argumentFilter>
            <weightedPathOrder>
             <precedenceStatus>
              <precedenceStatusEntry>
               <sharp>
               <name>plus</name></sharp>
               <arity>2</arity>
               <precedence>1
               </precedence>
               <status>
               </status>
              </precedenceStatusEntry>
              <precedenceStatusEntry>
               <sharp>
               <name>times</name></sharp>
               <arity>2</arity>
               <precedence>2
               </precedence>
               <status>
                <position>1</position>
                <position>2</position>
               </status>
              </precedenceStatusEntry>
              <precedenceStatusEntry>
               <name>0</name>
               <arity>0</arity>
               <precedence>0
               </precedence>
               <status>
               </status>
              </precedenceStatusEntry>
              <precedenceStatusEntry>
               <name>times</name>
               <arity>2</arity>
               <precedence>2
               </precedence>
               <status>
                <position>1</position>
                <position>2</position>
               </status>
              </precedenceStatusEntry>
              <precedenceStatusEntry>
               <name>plus</name>
               <arity>2</arity>
               <precedence>1
               </precedence>
               <status>
                <position>1</position>
                <position>2</position>
               </status>
              </precedenceStatusEntry>
              <precedenceStatusEntry>
               <sharp>
               <name>i</name></sharp>
               <arity>1</arity>
               <precedence>0
               </precedence>
               <status>
               </status>
              </precedenceStatusEntry>
             </precedenceStatus>
             <maxPoly>
              <interpret>
               <sharp>
               <name>plus</name></sharp>
               <arity>2</arity>
               <max>
                <constant>0</constant>
               </max>
              </interpret>
              <interpret>
               <sharp>
               <name>times</name></sharp>
               <arity>2</arity>
               <max>
                <sum>
                 <variable>1</variable>
                 <constant>0</constant>
                </sum>
                <sum>
                 <variable>2</variable>
                 <constant>0</constant>
                </sum>
                <constant>0</constant>
               </max>
              </interpret>
              <interpret>
               <name>0</name>
               <arity>0</arity>
               <sum>
                <constant>0</constant>
               </sum>
              </interpret>
              <interpret>
               <name>times</name>
               <arity>2</arity>
               <max>
                <sum>
                 <variable>1</variable>
                 <constant>0</constant>
                </sum>
                <sum>
                 <variable>2</variable>
                 <constant>0</constant>
                </sum>
                <constant>0</constant>
               </max>
              </interpret>
              <interpret>
               <name>plus</name>
               <arity>2</arity>
               <max>
                <sum>
                 <variable>1</variable>
                 <constant>0</constant>
                </sum>
                <sum>
                 <variable>2</variable>
                 <constant>0</constant>
                </sum>
                <constant>0</constant>
               </max>
              </interpret>
              <interpret>
               <sharp>
               <name>i</name></sharp>
               <arity>1</arity>
               <sum>
                <constant>0</constant>
               </sum>
              </interpret>
             </maxPoly>
            </weightedPathOrder>
           </filteredRedPair>
          </redPair>
         </orderingConstraintProof>
         <dps>
          <rules>
           <rule>
            <lhs>
             <funapp>
              <sharp>
              <name>times</name></sharp>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>times</name>
                <arg>
                 <var>y</var>
                </arg>
                <arg>
                 <var>z</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <sharp>
              <name>times</name></sharp>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <var>y</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <sharp>
              <name>times</name></sharp>
              <arg>
               <funapp>
                <name>times</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <funapp>
                  <name>0</name>
                 </funapp>
                </arg>
               </funapp>
              </arg>
              <arg>
               <var>_1</var>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <sharp>
              <name>times</name></sharp>
              <arg>
               <funapp>
                <name>0</name>
               </funapp>
              </arg>
              <arg>
               <var>_1</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <sharp>
              <name>times</name></sharp>
              <arg>
               <funapp>
                <name>times</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <funapp>
                  <name>plus</name>
                  <arg>
                   <var>y</var>
                  </arg>
                  <arg>
                   <var>z</var>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
              <arg>
               <var>_1</var>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <sharp>
              <name>times</name></sharp>
              <arg>
               <funapp>
                <name>plus</name>
                <arg>
                 <funapp>
                  <name>times</name>
                  <arg>
                   <var>x</var>
                  </arg>
                  <arg>
                   <var>y</var>
                  </arg>
                 </funapp>
                </arg>
                <arg>
                 <funapp>
                  <name>times</name>
                  <arg>
                   <var>x</var>
                  </arg>
                  <arg>
                   <var>z</var>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
              <arg>
               <var>_1</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <sharp>
              <name>times</name></sharp>
              <arg>
               <funapp>
                <name>times</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <funapp>
                  <name>i</name>
                  <arg>
                   <var>y</var>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
              <arg>
               <var>_1</var>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <sharp>
              <name>times</name></sharp>
              <arg>
               <funapp>
                <name>i</name>
                <arg>
                 <funapp>
                  <name>times</name>
                  <arg>
                   <var>x</var>
                  </arg>
                  <arg>
                   <var>y</var>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
              <arg>
               <var>_1</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
          </rules>
         </dps>
         <usableRules>
          <rules>
           <rule>
            <lhs>
             <funapp>
              <name>i</name>
              <arg>
               <funapp>
                <name>i</name>
                <arg>
                 <var>x</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <var>x</var>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>times</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>i</name>
                <arg>
                 <var>y</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>i</name>
              <arg>
               <funapp>
                <name>times</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <var>y</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>plus</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>0</name>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <var>x</var>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>i</name>
              <arg>
               <funapp>
                <name>0</name>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>0</name>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>i</name>
              <arg>
               <funapp>
                <name>plus</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <var>y</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>plus</name>
              <arg>
               <funapp>
                <name>i</name>
                <arg>
                 <var>x</var>
                </arg>
               </funapp>
              </arg>
              <arg>
               <funapp>
                <name>i</name>
                <arg>
                 <var>y</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>plus</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <var>y</var>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>plus</name>
              <arg>
               <var>y</var>
              </arg>
              <arg>
               <var>x</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>times</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>0</name>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>0</name>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>times</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <var>y</var>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>times</name>
              <arg>
               <var>y</var>
              </arg>
              <arg>
               <var>x</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>times</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>times</name>
                <arg>
                 <var>y</var>
                </arg>
                <arg>
                 <var>z</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>times</name>
              <arg>
               <funapp>
                <name>times</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>plus</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>plus</name>
                <arg>
                 <var>y</var>
                </arg>
                <arg>
                 <var>z</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>plus</name>
              <arg>
               <funapp>
                <name>plus</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>times</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>plus</name>
                <arg>
                 <var>y</var>
                </arg>
                <arg>
                 <var>z</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>plus</name>
              <arg>
               <funapp>
                <name>times</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <var>y</var>
                </arg>
               </funapp>
              </arg>
              <arg>
               <funapp>
                <name>times</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <var>z</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>plus</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>i</name>
                <arg>
                 <var>x</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>0</name>
             </funapp>
            </rhs>
           </rule>
          </rules>
         </usableRules>
         <acDPTerminationProof>
          <acDepGraphProc>
           <component>
            <dps>
             <rules>
              <rule>
               <lhs>
                <funapp>
                 <sharp>
                 <name>times</name></sharp>
                 <arg>
                  <var>x</var>
                 </arg>
                 <arg>
                  <var>y</var>
                 </arg>
                </funapp>
               </lhs>
               <rhs>
                <funapp>
                 <sharp>
                 <name>times</name></sharp>
                 <arg>
                  <var>y</var>
                 </arg>
                 <arg>
                  <var>x</var>
                 </arg>
                </funapp>
               </rhs>
              </rule>
              <rule>
               <lhs>
                <funapp>
                 <sharp>
                 <name>times</name></sharp>
                 <arg>
                  <var>x</var>
                 </arg>
                 <arg>
                  <funapp>
                   <name>times</name>
                   <arg>
                    <var>y</var>
                   </arg>
                   <arg>
                    <var>z</var>
                   </arg>
                  </funapp>
                 </arg>
                </funapp>
               </lhs>
               <rhs>
                <funapp>
                 <sharp>
                 <name>times</name></sharp>
                 <arg>
                  <funapp>
                   <name>times</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>
 </proof>
 <origin>
  <proofOrigin>
   <tool>
    <name>NaTT</name>
    <version>certifiable-1.6</version>
   </tool>
  </proofOrigin>
 </origin>
</certificationProblem>