tpdb-2.2.1: test/AC09.xml

<?xml version="1.0" encoding="UTF-8"?>
<problem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" type="termination" xsi:noNamespaceSchemaLocation="http://dev.aspsimon.org/xtc.xsd">
  <trs>
    <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>
              <funapp>
                <name>i</name>
                <arg>
                  <var>x</var>
                </arg>
              </funapp>
            </arg>
          </funapp>
        </lhs>
        <rhs>
          <funapp>
            <name>0</name>
          </funapp>
        </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>i</name>
                <arg>
                  <var>x</var>
                </arg>
              </funapp>
            </arg>
          </funapp>
        </lhs>
        <rhs>
          <var>x</var>
        </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>times</name>
            <arg>
              <var>x</var>
            </arg>
            <arg>
              <funapp>
                <name>1</name>
              </funapp>
            </arg>
          </funapp>
        </lhs>
        <rhs>
          <var>x</var>
        </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>
              <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>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>
    </rules>
    <signature>
      <funcsym>
        <name>plus</name>
        <arity>2</arity>
        <theory>AC</theory>
      </funcsym>
      <funcsym>
        <name>0</name>
        <arity>0</arity>
      </funcsym>
      <funcsym>
        <name>i</name>
        <arity>1</arity>
      </funcsym>
      <funcsym>
        <name>times</name>
        <arity>2</arity>
        <theory>AC</theory>
      </funcsym>
      <funcsym>
        <name>1</name>
        <arity>0</arity>
      </funcsym>
    </signature>
  </trs>
  <strategy>FULL</strategy>
  <metainformation>
    <originalfilename>./TRS/AProVE_AC/AC09.trs</originalfilename>
  </metainformation>
</problem>