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


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MAYBE
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              <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>minus</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <var>y</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
          </rules>
         </usableRules>
         <dpProof>
          <depGraphProc>
          </depGraphProc>
         </dpProof>
        </redPairUrProc>
       </dpProof>
      </component>
      <component>
       <dps>
        <rules>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>plus</name></sharp>
            <arg>
             <funapp>
              <name>plus</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>s</name>
                <arg>
                 <funapp>
                  <name>0</name>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </arg>
            <arg>
             <funapp>
              <name>plus</name>
              <arg>
               <var>y</var>
              </arg>
              <arg>
               <funapp>
                <name>s</name>
                <arg>
                 <funapp>
                  <name>s</name>
                  <arg>
                   <var>z</var>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>plus</name></sharp>
            <arg>
             <funapp>
              <name>plus</name>
              <arg>
               <var>y</var>
              </arg>
              <arg>
               <funapp>
                <name>s</name>
                <arg>
                 <funapp>
                  <name>s</name>
                  <arg>
                   <var>z</var>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </arg>
            <arg>
             <funapp>
              <name>plus</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>s</name>
                <arg>
                 <funapp>
                  <name>0</name>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </rhs>
         </rule>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>plus</name></sharp>
            <arg>
             <funapp>
              <name>minus</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>s</name>
                <arg>
                 <funapp>
                  <name>0</name>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </arg>
            <arg>
             <funapp>
              <name>minus</name>
              <arg>
               <var>y</var>
              </arg>
              <arg>
               <funapp>
                <name>s</name>
                <arg>
                 <funapp>
                  <name>s</name>
                  <arg>
                   <var>z</var>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </lhs>
          <rhs>
           <funapp>
            <sharp>
            <name>plus</name></sharp>
            <arg>
             <funapp>
              <name>minus</name>
              <arg>
               <var>y</var>
              </arg>
              <arg>
               <funapp>
                <name>s</name>
                <arg>
                 <funapp>
                  <name>s</name>
                  <arg>
                   <var>z</var>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </arg>
            <arg>
             <funapp>
              <name>minus</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <funapp>
                <name>s</name>
                <arg>
                 <funapp>
                  <name>0</name>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </arg>
           </funapp>
          </rhs>
         </rule>
         <rule>
          <lhs>
           <funapp>
            <sharp>
            <name>plus</name></sharp>
            <arg>
             <funapp>
              <name>s</name>
              <arg>
               <var>x</var>
              </arg>
             </funapp>
            </arg>
            <arg>
             <var>y</var>
            </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>
       <dpProof>
        <redPairUrProc>
         <orderingConstraintProof>
          <redPair>
           <maxPoly>
            <interpret>
             <name>s</name>
             <arity>1</arity>
             <sum>
              <variable>1</variable>
              <constant>1</constant>
             </sum>
            </interpret>
            <interpret>
             <name>minus</name>
             <arity>2</arity>
             <sum>
              <variable>1</variable>
              <variable>2</variable>
              <constant>1</constant>
             </sum>
            </interpret>
            <interpret>
             <sharp>
             <name>plus</name></sharp>
             <arity>2</arity>
             <sum>
              <variable>1</variable>
              <variable>2</variable>
              <constant>0</constant>
             </sum>
            </interpret>
            <interpret>
             <name>0</name>
             <arity>0</arity>
             <sum>
              <constant>16203</constant>
             </sum>
            </interpret>
            <interpret>
             <name>quot</name>
             <arity>2</arity>
             <sum>
              <constant>0</constant>
             </sum>
            </interpret>
            <interpret>
             <sharp>
             <name>minus</name></sharp>
             <arity>2</arity>
             <sum>
              <constant>0</constant>
             </sum>
            </interpret>
            <interpret>
             <name>plus</name>
             <arity>2</arity>
             <sum>
              <variable>1</variable>
              <variable>2</variable>
              <constant>29483</constant>
             </sum>
            </interpret>
            <interpret>
             <sharp>
             <name>quot</name></sharp>
             <arity>2</arity>
             <sum>
              <variable>1</variable>
              <constant>0</constant>
             </sum>
            </interpret>
           </maxPoly>
          </redPair>
         </orderingConstraintProof>
         <dps>
          <rules>
           <rule>
            <lhs>
             <funapp>
              <sharp>
              <name>plus</name></sharp>
              <arg>
               <funapp>
                <name>minus</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <funapp>
                  <name>s</name>
                  <arg>
                   <funapp>
                    <name>0</name>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
              <arg>
               <funapp>
                <name>minus</name>
                <arg>
                 <var>y</var>
                </arg>
                <arg>
                 <funapp>
                  <name>s</name>
                  <arg>
                   <funapp>
                    <name>s</name>
                    <arg>
                     <var>z</var>
                    </arg>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <sharp>
              <name>plus</name></sharp>
              <arg>
               <funapp>
                <name>minus</name>
                <arg>
                 <var>y</var>
                </arg>
                <arg>
                 <funapp>
                  <name>s</name>
                  <arg>
                   <funapp>
                    <name>s</name>
                    <arg>
                     <var>z</var>
                    </arg>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
              <arg>
               <funapp>
                <name>minus</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <funapp>
                  <name>s</name>
                  <arg>
                   <funapp>
                    <name>0</name>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </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>s</name>
                  <arg>
                   <funapp>
                    <name>0</name>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
              <arg>
               <funapp>
                <name>plus</name>
                <arg>
                 <var>y</var>
                </arg>
                <arg>
                 <funapp>
                  <name>s</name>
                  <arg>
                   <funapp>
                    <name>s</name>
                    <arg>
                     <var>z</var>
                    </arg>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <sharp>
              <name>plus</name></sharp>
              <arg>
               <funapp>
                <name>plus</name>
                <arg>
                 <var>y</var>
                </arg>
                <arg>
                 <funapp>
                  <name>s</name>
                  <arg>
                   <funapp>
                    <name>s</name>
                    <arg>
                     <var>z</var>
                    </arg>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
              <arg>
               <funapp>
                <name>plus</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <funapp>
                  <name>s</name>
                  <arg>
                   <funapp>
                    <name>0</name>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </rhs>
           </rule>
          </rules>
         </dps>
         <usableRules>
          <rules>
           <rule>
            <lhs>
             <funapp>
              <name>plus</name>
              <arg>
               <funapp>
                <name>plus</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <funapp>
                  <name>s</name>
                  <arg>
                   <funapp>
                    <name>0</name>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
              <arg>
               <funapp>
                <name>plus</name>
                <arg>
                 <var>y</var>
                </arg>
                <arg>
                 <funapp>
                  <name>s</name>
                  <arg>
                   <funapp>
                    <name>s</name>
                    <arg>
                     <var>z</var>
                    </arg>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>plus</name>
              <arg>
               <funapp>
                <name>plus</name>
                <arg>
                 <var>y</var>
                </arg>
                <arg>
                 <funapp>
                  <name>s</name>
                  <arg>
                   <funapp>
                    <name>s</name>
                    <arg>
                     <var>z</var>
                    </arg>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
              <arg>
               <funapp>
                <name>plus</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <funapp>
                  <name>s</name>
                  <arg>
                   <funapp>
                    <name>0</name>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>minus</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>
               <funapp>
                <name>0</name>
               </funapp>
              </arg>
              <arg>
               <var>y</var>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <var>y</var>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>plus</name>
              <arg>
               <funapp>
                <name>minus</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <funapp>
                  <name>s</name>
                  <arg>
                   <funapp>
                    <name>0</name>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
              <arg>
               <funapp>
                <name>minus</name>
                <arg>
                 <var>y</var>
                </arg>
                <arg>
                 <funapp>
                  <name>s</name>
                  <arg>
                   <funapp>
                    <name>s</name>
                    <arg>
                     <var>z</var>
                    </arg>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>plus</name>
              <arg>
               <funapp>
                <name>minus</name>
                <arg>
                 <var>y</var>
                </arg>
                <arg>
                 <funapp>
                  <name>s</name>
                  <arg>
                   <funapp>
                    <name>s</name>
                    <arg>
                     <var>z</var>
                    </arg>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
              <arg>
               <funapp>
                <name>minus</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <funapp>
                  <name>s</name>
                  <arg>
                   <funapp>
                    <name>0</name>
                   </funapp>
                  </arg>
                 </funapp>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>plus</name>
              <arg>
               <funapp>
                <name>s</name>
                <arg>
                 <var>x</var>
                </arg>
               </funapp>
              </arg>
              <arg>
               <var>y</var>
              </arg>
             </funapp>
            </lhs>
            <rhs>
             <funapp>
              <name>s</name>
              <arg>
               <funapp>
                <name>plus</name>
                <arg>
                 <var>x</var>
                </arg>
                <arg>
                 <var>y</var>
                </arg>
               </funapp>
              </arg>
             </funapp>
            </rhs>
           </rule>
           <rule>
            <lhs>
             <funapp>
              <name>minus</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>minus</name>
              <arg>
               <var>x</var>
              </arg>
              <arg>
               <var>y</var>
              </arg>
             </funapp>
            </rhs>
           </rule>
          </rules>
         </usableRules>
         <dpProof>
          <depGraphProc>
           <component>
            <dps>
             <rules>
              <rule>
               <lhs>
                <funapp>
                 <sharp>
                 <name>plus</name></sharp>
                 <arg>
                  <funapp>
                   <name>plus</name>
                   <arg>
                    <var>x</var>
                   </arg>
                   <arg>
                    <funapp>
                     <name>s</name>
                     <arg>
                      <funapp>
                       <name>0</name>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </arg>
                 <arg>
                  <funapp>
                   <name>plus</name>
                   <arg>
                    <var>y</var>
                   </arg>
                   <arg>
                    <funapp>
                     <name>s</name>
                     <arg>
                      <funapp>
                       <name>s</name>
                       <arg>
                        <var>z</var>
                       </arg>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </arg>
                </funapp>
               </lhs>
               <rhs>
                <funapp>
                 <sharp>
                 <name>plus</name></sharp>
                 <arg>
                  <funapp>
                   <name>plus</name>
                   <arg>
                    <var>y</var>
                   </arg>
                   <arg>
                    <funapp>
                     <name>s</name>
                     <arg>
                      <funapp>
                       <name>s</name>
                       <arg>
                        <var>z</var>
                       </arg>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </arg>
                 <arg>
                  <funapp>
                   <name>plus</name>
                   <arg>
                    <var>x</var>
                   </arg>
                   <arg>
                    <funapp>
                     <name>s</name>
                     <arg>
                      <funapp>
                       <name>0</name>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </arg>
                </funapp>
               </rhs>
              </rule>
              <rule>
               <lhs>
                <funapp>
                 <sharp>
                 <name>plus</name></sharp>
                 <arg>
                  <funapp>
                   <name>minus</name>
                   <arg>
                    <var>x</var>
                   </arg>
                   <arg>
                    <funapp>
                     <name>s</name>
                     <arg>
                      <funapp>
                       <name>0</name>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </arg>
                 <arg>
                  <funapp>
                   <name>minus</name>
                   <arg>
                    <var>y</var>
                   </arg>
                   <arg>
                    <funapp>
                     <name>s</name>
                     <arg>
                      <funapp>
                       <name>s</name>
                       <arg>
                        <var>z</var>
                       </arg>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </arg>
                </funapp>
               </lhs>
               <rhs>
                <funapp>
                 <sharp>
                 <name>plus</name></sharp>
                 <arg>
                  <funapp>
                   <name>minus</name>
                   <arg>
                    <var>y</var>
                   </arg>
                   <arg>
                    <funapp>
                     <name>s</name>
                     <arg>
                      <funapp>
                       <name>s</name>
                       <arg>
                        <var>z</var>
                       </arg>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </arg>
                 <arg>
                  <funapp>
                   <name>minus</name>
                   <arg>
                    <var>x</var>
                   </arg>
                   <arg>
                    <funapp>
                     <name>s</name>
                     <arg>
                      <funapp>
                       <name>0</name>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </arg>
                </funapp>
               </rhs>
              </rule>
             </rules>
            </dps>
            <realScc>true</realScc>
            <dpProof>
             <redPairUrProc>
              <orderingConstraintProof>
               <redPair>
                <interpretation>
                 <type>
                  <matrixInterpretation>
                   <domain><naturals/>
                   </domain>
                   <dimension>2
                   </dimension>
                   <strictDimension>1
                   </strictDimension>
                  </matrixInterpretation>
                 </type>
                 <interpret>
                  <name>s</name>
                  <arity>1</arity>
                  <polynomial>
                   <sum>
                    <polynomial>
                     <variable>1</variable>
                    </polynomial>
                    <polynomial>
                     <coefficient>
                      <vector>
                       <coefficient>
                       <integer>1</integer></coefficient>
                       <coefficient>
                       <integer>2</integer></coefficient>
                      </vector>
                     </coefficient>
                    </polynomial>
                   </sum>
                  </polynomial>
                 </interpret>
                 <interpret>
                  <name>minus</name>
                  <arity>2</arity>
                  <polynomial>
                   <sum>
                    <polynomial>
                     <product>
                      <polynomial>
                       <coefficient>
                        <matrix>
                         <vector>
                          <coefficient>
                          <integer>1</integer></coefficient>
                          <coefficient>
                          <integer>1</integer></coefficient>
                         </vector>
                         <vector>
                          <coefficient>
                          <integer>1</integer></coefficient>
                          <coefficient>
                          <integer>1</integer></coefficient>
                         </vector>
                        </matrix>
                       </coefficient>
                      </polynomial>
                      <polynomial>
                       <variable>1</variable>
                      </polynomial>
                     </product>
                    </polynomial>
                    <polynomial>
                     <product>
                      <polynomial>
                       <coefficient>
                        <matrix>
                         <vector>
                          <coefficient>
                          <integer>0</integer></coefficient>
                          <coefficient>
                          <integer>0</integer></coefficient>
                         </vector>
                         <vector>
                          <coefficient>
                          <integer>1</integer></coefficient>
                          <coefficient>
                          <integer>0</integer></coefficient>
                         </vector>
                        </matrix>
                       </coefficient>
                      </polynomial>
                      <polynomial>
                       <variable>2</variable>
                      </polynomial>
                     </product>
                    </polynomial>
                    <polynomial>
                     <coefficient>
                      <vector>
                       <coefficient>
                       <integer>0</integer></coefficient>
                       <coefficient>
                       <integer>1</integer></coefficient>
                      </vector>
                     </coefficient>
                    </polynomial>
                   </sum>
                  </polynomial>
                 </interpret>
                 <interpret>
                  <sharp>
                  <name>plus</name></sharp>
                  <arity>2</arity>
                  <polynomial>
                   <sum>
                    <polynomial>
                     <product>
                      <polynomial>
                       <coefficient>
                        <matrix>
                         <vector>
                          <coefficient>
                          <integer>0</integer></coefficient>
                          <coefficient>
                          <integer>0</integer></coefficient>
                         </vector>
                         <vector>
                          <coefficient>
                          <integer>1</integer></coefficient>
                          <coefficient>
                          <integer>1</integer></coefficient>
                         </vector>
                        </matrix>
                       </coefficient>
                      </polynomial>
                      <polynomial>
                       <variable>1</variable>
                      </polynomial>
                     </product>
                    </polynomial>
                    <polynomial>
                     <product>
                      <polynomial>
                       <coefficient>
                        <matrix>
                         <vector>
                          <coefficient>
                          <integer>1</integer></coefficient>
                          <coefficient>
                          <integer>1</integer></coefficient>
                         </vector>
                         <vector>
                          <coefficient>
                          <integer>0</integer></coefficient>
                          <coefficient>
                          <integer>0</integer></coefficient>
                         </vector>
                        </matrix>
                       </coefficient>
                      </polynomial>
                      <polynomial>
                       <variable>2</variable>
                      </polynomial>
                     </product>
                    </polynomial>
                    <polynomial>
                     <coefficient>
                      <vector>
                       <coefficient>
                       <integer>0</integer></coefficient>
                       <coefficient>
                       <integer>0</integer></coefficient>
                      </vector>
                     </coefficient>
                    </polynomial>
                   </sum>
                  </polynomial>
                 </interpret>
                 <interpret>
                  <name>0</name>
                  <arity>0</arity>
                  <polynomial>
                   <sum>
                    <polynomial>
                     <coefficient>
                      <vector>
                       <coefficient>
                       <integer>1</integer></coefficient>
                       <coefficient>
                       <integer>1</integer></coefficient>
                      </vector>
                     </coefficient>
                    </polynomial>
                   </sum>
                  </polynomial>
                 </interpret>
                 <interpret>
                  <name>quot</name>
                  <arity>2</arity>
                  <polynomial>
                   <sum>
                    <polynomial>
                     <coefficient>
                      <vector>
                       <coefficient>
                       <integer>0</integer></coefficient>
                       <coefficient>
                       <integer>0</integer></coefficient>
                      </vector>
                     </coefficient>
                    </polynomial>
                   </sum>
                  </polynomial>
                 </interpret>
                 <interpret>
                  <sharp>
                  <name>minus</name></sharp>
                  <arity>2</arity>
                  <polynomial>
                   <sum>
                    <polynomial>
                     <coefficient>
                      <vector>
                       <coefficient>
                       <integer>0</integer></coefficient>
                       <coefficient>
                       <integer>0</integer></coefficient>
                      </vector>
                     </coefficient>
                    </polynomial>
                   </sum>
                  </polynomial>
                 </interpret>
                 <interpret>
                  <name>plus</name>
                  <arity>2</arity>
                  <polynomial>
                   <sum>
                    <polynomial>
                     <product>
                      <polynomial>
                       <coefficient>
                        <matrix>
                         <vector>
                          <coefficient>
                          <integer>1</integer></coefficient>
                          <coefficient>
                          <integer>1</integer></coefficient>
                         </vector>
                         <vector>
                          <coefficient>
                          <integer>1</integer></coefficient>
                          <coefficient>
                          <integer>1</integer></coefficient>
                         </vector>
                        </matrix>
                       </coefficient>
                      </polynomial>
                      <polynomial>
                       <variable>1</variable>
                      </polynomial>
                     </product>
                    </polynomial>
                    <polynomial>
                     <product>
                      <polynomial>
                       <coefficient>
                        <matrix>
                         <vector>
                          <coefficient>
                          <integer>1</integer></coefficient>
                          <coefficient>
                          <integer>1</integer></coefficient>
                         </vector>
                         <vector>
                          <coefficient>
                          <integer>1</integer></coefficient>
                          <coefficient>
                          <integer>1</integer></coefficient>
                         </vector>
                        </matrix>
                       </coefficient>
                      </polynomial>
                      <polynomial>
                       <variable>2</variable>
                      </polynomial>
                     </product>
                    </polynomial>
                    <polynomial>
                     <coefficient>
                      <vector>
                       <coefficient>
                       <integer>1</integer></coefficient>
                       <coefficient>
                       <integer>1</integer></coefficient>
                      </vector>
                     </coefficient>
                    </polynomial>
                   </sum>
                  </polynomial>
                 </interpret>
                 <interpret>
                  <sharp>
                  <name>quot</name></sharp>
                  <arity>2</arity>
                  <polynomial>
                   <sum>
                    <polynomial>
                     <coefficient>
                      <vector>
                       <coefficient>
                       <integer>0</integer></coefficient>
                       <coefficient>
                       <integer>0</integer></coefficient>
                      </vector>
                     </coefficient>
                    </polynomial>
                   </sum>
                  </polynomial>
                 </interpret>
                </interpretation>
               </redPair>
              </orderingConstraintProof>
              <dps>
               <rules>
                <rule>
                 <lhs>
                  <funapp>
                   <sharp>
                   <name>plus</name></sharp>
                   <arg>
                    <funapp>
                     <name>plus</name>
                     <arg>
                      <var>x</var>
                     </arg>
                     <arg>
                      <funapp>
                       <name>s</name>
                       <arg>
                        <funapp>
                         <name>0</name>
                        </funapp>
                       </arg>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                   <arg>
                    <funapp>
                     <name>plus</name>
                     <arg>
                      <var>y</var>
                     </arg>
                     <arg>
                      <funapp>
                       <name>s</name>
                       <arg>
                        <funapp>
                         <name>s</name>
                         <arg>
                          <var>z</var>
                         </arg>
                        </funapp>
                       </arg>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <sharp>
                   <name>plus</name></sharp>
                   <arg>
                    <funapp>
                     <name>plus</name>
                     <arg>
                      <var>y</var>
                     </arg>
                     <arg>
                      <funapp>
                       <name>s</name>
                       <arg>
                        <funapp>
                         <name>s</name>
                         <arg>
                          <var>z</var>
                         </arg>
                        </funapp>
                       </arg>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                   <arg>
                    <funapp>
                     <name>plus</name>
                     <arg>
                      <var>x</var>
                     </arg>
                     <arg>
                      <funapp>
                       <name>s</name>
                       <arg>
                        <funapp>
                         <name>0</name>
                        </funapp>
                       </arg>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
               </rules>
              </dps>
              <usableRules>
               <rules>
                <rule>
                 <lhs>
                  <funapp>
                   <name>plus</name>
                   <arg>
                    <funapp>
                     <name>plus</name>
                     <arg>
                      <var>x</var>
                     </arg>
                     <arg>
                      <funapp>
                       <name>s</name>
                       <arg>
                        <funapp>
                         <name>0</name>
                        </funapp>
                       </arg>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                   <arg>
                    <funapp>
                     <name>plus</name>
                     <arg>
                      <var>y</var>
                     </arg>
                     <arg>
                      <funapp>
                       <name>s</name>
                       <arg>
                        <funapp>
                         <name>s</name>
                         <arg>
                          <var>z</var>
                         </arg>
                        </funapp>
                       </arg>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <name>plus</name>
                   <arg>
                    <funapp>
                     <name>plus</name>
                     <arg>
                      <var>y</var>
                     </arg>
                     <arg>
                      <funapp>
                       <name>s</name>
                       <arg>
                        <funapp>
                         <name>s</name>
                         <arg>
                          <var>z</var>
                         </arg>
                        </funapp>
                       </arg>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                   <arg>
                    <funapp>
                     <name>plus</name>
                     <arg>
                      <var>x</var>
                     </arg>
                     <arg>
                      <funapp>
                       <name>s</name>
                       <arg>
                        <funapp>
                         <name>0</name>
                        </funapp>
                       </arg>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <name>minus</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>
                    <funapp>
                     <name>0</name>
                    </funapp>
                   </arg>
                   <arg>
                    <var>y</var>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <var>y</var>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <name>plus</name>
                   <arg>
                    <funapp>
                     <name>minus</name>
                     <arg>
                      <var>x</var>
                     </arg>
                     <arg>
                      <funapp>
                       <name>s</name>
                       <arg>
                        <funapp>
                         <name>0</name>
                        </funapp>
                       </arg>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                   <arg>
                    <funapp>
                     <name>minus</name>
                     <arg>
                      <var>y</var>
                     </arg>
                     <arg>
                      <funapp>
                       <name>s</name>
                       <arg>
                        <funapp>
                         <name>s</name>
                         <arg>
                          <var>z</var>
                         </arg>
                        </funapp>
                       </arg>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <name>plus</name>
                   <arg>
                    <funapp>
                     <name>minus</name>
                     <arg>
                      <var>y</var>
                     </arg>
                     <arg>
                      <funapp>
                       <name>s</name>
                       <arg>
                        <funapp>
                         <name>s</name>
                         <arg>
                          <var>z</var>
                         </arg>
                        </funapp>
                       </arg>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                   <arg>
                    <funapp>
                     <name>minus</name>
                     <arg>
                      <var>x</var>
                     </arg>
                     <arg>
                      <funapp>
                       <name>s</name>
                       <arg>
                        <funapp>
                         <name>0</name>
                        </funapp>
                       </arg>
                      </funapp>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <name>plus</name>
                   <arg>
                    <funapp>
                     <name>s</name>
                     <arg>
                      <var>x</var>
                     </arg>
                    </funapp>
                   </arg>
                   <arg>
                    <var>y</var>
                   </arg>
                  </funapp>
                 </lhs>
                 <rhs>
                  <funapp>
                   <name>s</name>
                   <arg>
                    <funapp>
                     <name>plus</name>
                     <arg>
                      <var>x</var>
                     </arg>
                     <arg>
                      <var>y</var>
                     </arg>
                    </funapp>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
                <rule>
                 <lhs>
                  <funapp>
                   <name>minus</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>minus</name>
                   <arg>
                    <var>x</var>
                   </arg>
                   <arg>
                    <var>y</var>
                   </arg>
                  </funapp>
                 </rhs>
                </rule>
               </rules>
              </usableRules>
              <dpProof>
               <depGraphProc>
                <component>
                 <dps>
                  <rules>
                   <rule>
                    <lhs>
                     <funapp>
                      <sharp>
                      <name>plus</name></sharp>
                      <arg>
                       <funapp>
                        <name>plus</name>
                        <arg>
                         <var>x</var>
                        </arg>
                        <arg>
                         <funapp>
                          <name>s</name>
                          <arg>
                           <funapp>
                            <name>0</name>
                           </funapp>
                          </arg>
                         </funapp>
                        </arg>
                       </funapp>
                      </arg>
                      <arg>
                       <funapp>
                        <name>plus</name>
                        <arg>
                         <var>y</var>
                        </arg>
                        <arg>
                         <funapp>
                          <name>s</name>
                          <arg>
                           <funapp>
                            <name>s</name>
                            <arg>
                             <var>z</var>
                            </arg>
                           </funapp>
                          </arg>
                         </funapp>
                        </arg>
                       </funapp>
                      </arg>
                     </funapp>
                    </lhs>
                    <rhs>
                     <funapp>
                      <sharp>
                      <name>plus</name></sharp>
                      <arg>
                       <funapp>
                        <name>plus</name>
                        <arg>
                         <var>y</var>
                        </arg>
                        <arg>
                         <funapp>
                          <name>s</name>
                          <arg>
                           <funapp>
                            <name>s</name>
                            <arg>
                             <var>z</var>
                            </arg>
                           </funapp>
                          </arg>
                         </funapp>
                        </arg>
                       </funapp>
                      </arg>
                      <arg>
                       <funapp>
                        <name>plus</name>
                        <arg>
                         <var>x</var>
                        </arg>
                        <arg>
                         <funapp>
                          <name>s</name>
                          <arg>
                           <funapp>
                            <name>0</name>
                           </funapp>
                          </arg>
                         </funapp>
                        </arg>
                       </funapp>
                      </arg>
                     </funapp>
                    </rhs>
                   </rule>
                  </rules>
                 </dps>
                 <realScc>true</realScc>
                 <dpProof>
                  <unknownProof>
                   <description>Failed!
                   </description>
                  </unknownProof>
                 </dpProof>
                </component>
               </depGraphProc>
              </dpProof>
             </redPairUrProc>
            </dpProof>
           </component>
          </depGraphProc>
         </dpProof>
        </redPairUrProc>
       </dpProof>
      </component>
     </depGraphProc>
    </dpProof>
   </dpTrans>
  </trsTerminationProof>
 </proof>
 <origin>
  <proofOrigin>
   <tool>
    <name>NaTT</name>
    <version>certifiable-1.6</version>
   </tool>
  </proofOrigin>
 </origin>
</certificationProblem>