<?xml version="1.0" encoding="UTF-8"?>
<?xml-stylesheet type="text/xsl" href="../../xml/xtcHTML.xsl"?>
<problem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="../../xml/xtc.xsd" type="termination">
<trs>
<rules>
<rule>
<lhs>
<funapp>
<name>U11</name>
<arg>
<funapp>
<name>tt</name>
</funapp>
</arg>
<arg>
<var>V1</var>
</arg>
<arg>
<var>V2</var>
</arg>
</funapp>
</lhs>
<rhs>
<funapp>
<name>U12</name>
<arg>
<funapp>
<name>isNat</name>
<arg>
<var>V1</var>
</arg>
</funapp>
</arg>
<arg>
<var>V2</var>
</arg>
</funapp>
</rhs>
</rule>
<rule>
<lhs>
<funapp>
<name>U12</name>
<arg>
<funapp>
<name>tt</name>
</funapp>
</arg>
<arg>
<var>V2</var>
</arg>
</funapp>
</lhs>
<rhs>
<funapp>
<name>U13</name>
<arg>
<funapp>
<name>isNat</name>
<arg>
<var>V2</var>
</arg>
</funapp>
</arg>
</funapp>
</rhs>
</rule>
<rule>
<lhs>
<funapp>
<name>U13</name>
<arg>
<funapp>
<name>tt</name>
</funapp>
</arg>
</funapp>
</lhs>
<rhs>
<funapp>
<name>tt</name>
</funapp>
</rhs>
</rule>
<rule>
<lhs>
<funapp>
<name>U21</name>
<arg>
<funapp>
<name>tt</name>
</funapp>
</arg>
<arg>
<var>V1</var>
</arg>
</funapp>
</lhs>
<rhs>
<funapp>
<name>U22</name>
<arg>
<funapp>
<name>isNat</name>
<arg>
<var>V1</var>
</arg>
</funapp>
</arg>
</funapp>
</rhs>
</rule>
<rule>
<lhs>
<funapp>
<name>U22</name>
<arg>
<funapp>
<name>tt</name>
</funapp>
</arg>
</funapp>
</lhs>
<rhs>
<funapp>
<name>tt</name>
</funapp>
</rhs>
</rule>
<rule>
<lhs>
<funapp>
<name>U31</name>
<arg>
<funapp>
<name>tt</name>
</funapp>
</arg>
<arg>
<var>V1</var>
</arg>
<arg>
<var>V2</var>
</arg>
</funapp>
</lhs>
<rhs>
<funapp>
<name>U32</name>
<arg>
<funapp>
<name>isNat</name>
<arg>
<var>V1</var>
</arg>
</funapp>
</arg>
<arg>
<var>V2</var>
</arg>
</funapp>
</rhs>
</rule>
<rule>
<lhs>
<funapp>
<name>U32</name>
<arg>
<funapp>
<name>tt</name>
</funapp>
</arg>
<arg>
<var>V2</var>
</arg>
</funapp>
</lhs>
<rhs>
<funapp>
<name>U33</name>
<arg>
<funapp>
<name>isNat</name>
<arg>
<var>V2</var>
</arg>
</funapp>
</arg>
</funapp>
</rhs>
</rule>
<rule>
<lhs>
<funapp>
<name>U33</name>
<arg>
<funapp>
<name>tt</name>
</funapp>
</arg>
</funapp>
</lhs>
<rhs>
<funapp>
<name>tt</name>
</funapp>
</rhs>
</rule>
<rule>
<lhs>
<funapp>
<name>U41</name>
<arg>
<funapp>
<name>tt</name>
</funapp>
</arg>
<arg>
<var>N</var>
</arg>
</funapp>
</lhs>
<rhs>
<var>N</var>
</rhs>
</rule>
<rule>
<lhs>
<funapp>
<name>U51</name>
<arg>
<funapp>
<name>tt</name>
</funapp>
</arg>
<arg>
<var>M</var>
</arg>
<arg>
<var>N</var>
</arg>
</funapp>
</lhs>
<rhs>
<funapp>
<name>s</name>
<arg>
<funapp>
<name>plus</name>
<arg>
<var>N</var>
</arg>
<arg>
<var>M</var>
</arg>
</funapp>
</arg>
</funapp>
</rhs>
</rule>
<rule>
<lhs>
<funapp>
<name>U61</name>
<arg>
<funapp>
<name>tt</name>
</funapp>
</arg>
</funapp>
</lhs>
<rhs>
<funapp>
<name>0</name>
</funapp>
</rhs>
</rule>
<rule>
<lhs>
<funapp>
<name>U71</name>
<arg>
<funapp>
<name>tt</name>
</funapp>
</arg>
<arg>
<var>M</var>
</arg>
<arg>
<var>N</var>
</arg>
</funapp>
</lhs>
<rhs>
<funapp>
<name>plus</name>
<arg>
<funapp>
<name>x</name>
<arg>
<var>N</var>
</arg>
<arg>
<var>M</var>
</arg>
</funapp>
</arg>
<arg>
<var>N</var>
</arg>
</funapp>
</rhs>
</rule>
<rule>
<lhs>
<funapp>
<name>and</name>
<arg>
<funapp>
<name>tt</name>
</funapp>
</arg>
<arg>
<var>X</var>
</arg>
</funapp>
</lhs>
<rhs>
<var>X</var>
</rhs>
</rule>
<rule>
<lhs>
<funapp>
<name>isNat</name>
<arg>
<funapp>
<name>0</name>
</funapp>
</arg>
</funapp>
</lhs>
<rhs>
<funapp>
<name>tt</name>
</funapp>
</rhs>
</rule>
<rule>
<lhs>
<funapp>
<name>isNat</name>
<arg>
<funapp>
<name>plus</name>
<arg>
<var>V1</var>
</arg>
<arg>
<var>V2</var>
</arg>
</funapp>
</arg>
</funapp>
</lhs>
<rhs>
<funapp>
<name>U11</name>
<arg>
<funapp>
<name>and</name>
<arg>
<funapp>
<name>isNatKind</name>
<arg>
<var>V1</var>
</arg>
</funapp>
</arg>
<arg>
<funapp>
<name>isNatKind</name>
<arg>
<var>V2</var>
</arg>
</funapp>
</arg>
</funapp>
</arg>
<arg>
<var>V1</var>
</arg>
<arg>
<var>V2</var>
</arg>
</funapp>
</rhs>
</rule>
<rule>
<lhs>
<funapp>
<name>isNat</name>
<arg>
<funapp>
<name>s</name>
<arg>
<var>V1</var>
</arg>
</funapp>
</arg>
</funapp>
</lhs>
<rhs>
<funapp>
<name>U21</name>
<arg>
<funapp>
<name>isNatKind</name>
<arg>
<var>V1</var>
</arg>
</funapp>
</arg>
<arg>
<var>V1</var>
</arg>
</funapp>
</rhs>
</rule>
<rule>
<lhs>
<funapp>
<name>isNat</name>
<arg>
<funapp>
<name>x</name>
<arg>
<var>V1</var>
</arg>
<arg>
<var>V2</var>
</arg>
</funapp>
</arg>
</funapp>
</lhs>
<rhs>
<funapp>
<name>U31</name>
<arg>
<funapp>
<name>and</name>
<arg>
<funapp>
<name>isNatKind</name>
<arg>
<var>V1</var>
</arg>
</funapp>
</arg>
<arg>
<funapp>
<name>isNatKind</name>
<arg>
<var>V2</var>
</arg>
</funapp>
</arg>
</funapp>
</arg>
<arg>
<var>V1</var>
</arg>
<arg>
<var>V2</var>
</arg>
</funapp>
</rhs>
</rule>
<rule>
<lhs>
<funapp>
<name>isNatKind</name>
<arg>
<funapp>
<name>0</name>
</funapp>
</arg>
</funapp>
</lhs>
<rhs>
<funapp>
<name>tt</name>
</funapp>
</rhs>
</rule>
<rule>
<lhs>
<funapp>
<name>isNatKind</name>
<arg>
<funapp>
<name>plus</name>
<arg>
<var>V1</var>
</arg>
<arg>
<var>V2</var>
</arg>
</funapp>
</arg>
</funapp>
</lhs>
<rhs>
<funapp>
<name>and</name>
<arg>
<funapp>
<name>isNatKind</name>
<arg>
<var>V1</var>
</arg>
</funapp>
</arg>
<arg>
<funapp>
<name>isNatKind</name>
<arg>
<var>V2</var>
</arg>
</funapp>
</arg>
</funapp>
</rhs>
</rule>
<rule>
<lhs>
<funapp>
<name>isNatKind</name>
<arg>
<funapp>
<name>s</name>
<arg>
<var>V1</var>
</arg>
</funapp>
</arg>
</funapp>
</lhs>
<rhs>
<funapp>
<name>isNatKind</name>
<arg>
<var>V1</var>
</arg>
</funapp>
</rhs>
</rule>
<rule>
<lhs>
<funapp>
<name>isNatKind</name>
<arg>
<funapp>
<name>x</name>
<arg>
<var>V1</var>
</arg>
<arg>
<var>V2</var>
</arg>
</funapp>
</arg>
</funapp>
</lhs>
<rhs>
<funapp>
<name>and</name>
<arg>
<funapp>
<name>isNatKind</name>
<arg>
<var>V1</var>
</arg>
</funapp>
</arg>
<arg>
<funapp>
<name>isNatKind</name>
<arg>
<var>V2</var>
</arg>
</funapp>
</arg>
</funapp>
</rhs>
</rule>
<rule>
<lhs>
<funapp>
<name>plus</name>
<arg>
<var>N</var>
</arg>
<arg>
<funapp>
<name>0</name>
</funapp>
</arg>
</funapp>
</lhs>
<rhs>
<funapp>
<name>U41</name>
<arg>
<funapp>
<name>and</name>
<arg>
<funapp>
<name>isNat</name>
<arg>
<var>N</var>
</arg>
</funapp>
</arg>
<arg>
<funapp>
<name>isNatKind</name>
<arg>
<var>N</var>
</arg>
</funapp>
</arg>
</funapp>
</arg>
<arg>
<var>N</var>
</arg>
</funapp>
</rhs>
</rule>
<rule>
<lhs>
<funapp>
<name>plus</name>
<arg>
<var>N</var>
</arg>
<arg>
<funapp>
<name>s</name>
<arg>
<var>M</var>
</arg>
</funapp>
</arg>
</funapp>
</lhs>
<rhs>
<funapp>
<name>U51</name>
<arg>
<funapp>
<name>and</name>
<arg>
<funapp>
<name>and</name>
<arg>
<funapp>
<name>isNat</name>
<arg>
<var>M</var>
</arg>
</funapp>
</arg>
<arg>
<funapp>
<name>isNatKind</name>
<arg>
<var>M</var>
</arg>
</funapp>
</arg>
</funapp>
</arg>
<arg>
<funapp>
<name>and</name>
<arg>
<funapp>
<name>isNat</name>
<arg>
<var>N</var>
</arg>
</funapp>
</arg>
<arg>
<funapp>
<name>isNatKind</name>
<arg>
<var>N</var>
</arg>
</funapp>
</arg>
</funapp>
</arg>
</funapp>
</arg>
<arg>
<var>M</var>
</arg>
<arg>
<var>N</var>
</arg>
</funapp>
</rhs>
</rule>
<rule>
<lhs>
<funapp>
<name>x</name>
<arg>
<var>N</var>
</arg>
<arg>
<funapp>
<name>0</name>
</funapp>
</arg>
</funapp>
</lhs>
<rhs>
<funapp>
<name>U61</name>
<arg>
<funapp>
<name>and</name>
<arg>
<funapp>
<name>isNat</name>
<arg>
<var>N</var>
</arg>
</funapp>
</arg>
<arg>
<funapp>
<name>isNatKind</name>
<arg>
<var>N</var>
</arg>
</funapp>
</arg>
</funapp>
</arg>
</funapp>
</rhs>
</rule>
<rule>
<lhs>
<funapp>
<name>x</name>
<arg>
<var>N</var>
</arg>
<arg>
<funapp>
<name>s</name>
<arg>
<var>M</var>
</arg>
</funapp>
</arg>
</funapp>
</lhs>
<rhs>
<funapp>
<name>U71</name>
<arg>
<funapp>
<name>and</name>
<arg>
<funapp>
<name>and</name>
<arg>
<funapp>
<name>isNat</name>
<arg>
<var>M</var>
</arg>
</funapp>
</arg>
<arg>
<funapp>
<name>isNatKind</name>
<arg>
<var>M</var>
</arg>
</funapp>
</arg>
</funapp>
</arg>
<arg>
<funapp>
<name>and</name>
<arg>
<funapp>
<name>isNat</name>
<arg>
<var>N</var>
</arg>
</funapp>
</arg>
<arg>
<funapp>
<name>isNatKind</name>
<arg>
<var>N</var>
</arg>
</funapp>
</arg>
</funapp>
</arg>
</funapp>
</arg>
<arg>
<var>M</var>
</arg>
<arg>
<var>N</var>
</arg>
</funapp>
</rhs>
</rule>
</rules>
<signature>
<funcsym>
<name>U11</name>
<arity>3</arity>
<replacementmap>
<entry>1</entry>
</replacementmap>
</funcsym>
<funcsym>
<name>tt</name>
<arity>0</arity>
<replacementmap/>
</funcsym>
<funcsym>
<name>U12</name>
<arity>2</arity>
<replacementmap>
<entry>1</entry>
</replacementmap>
</funcsym>
<funcsym>
<name>isNat</name>
<arity>1</arity>
<replacementmap/>
</funcsym>
<funcsym>
<name>U13</name>
<arity>1</arity>
<replacementmap>
<entry>1</entry>
</replacementmap>
</funcsym>
<funcsym>
<name>U21</name>
<arity>2</arity>
<replacementmap>
<entry>1</entry>
</replacementmap>
</funcsym>
<funcsym>
<name>U22</name>
<arity>1</arity>
<replacementmap>
<entry>1</entry>
</replacementmap>
</funcsym>
<funcsym>
<name>U31</name>
<arity>3</arity>
<replacementmap>
<entry>1</entry>
</replacementmap>
</funcsym>
<funcsym>
<name>U32</name>
<arity>2</arity>
<replacementmap>
<entry>1</entry>
</replacementmap>
</funcsym>
<funcsym>
<name>U33</name>
<arity>1</arity>
<replacementmap>
<entry>1</entry>
</replacementmap>
</funcsym>
<funcsym>
<name>U41</name>
<arity>2</arity>
<replacementmap>
<entry>1</entry>
</replacementmap>
</funcsym>
<funcsym>
<name>U51</name>
<arity>3</arity>
<replacementmap>
<entry>1</entry>
</replacementmap>
</funcsym>
<funcsym>
<name>s</name>
<arity>1</arity>
<replacementmap>
<entry>1</entry>
</replacementmap>
</funcsym>
<funcsym>
<name>plus</name>
<arity>2</arity>
<replacementmap>
<entry>1</entry>
<entry>2</entry>
</replacementmap>
</funcsym>
<funcsym>
<name>U61</name>
<arity>1</arity>
<replacementmap>
<entry>1</entry>
</replacementmap>
</funcsym>
<funcsym>
<name>0</name>
<arity>0</arity>
<replacementmap/>
</funcsym>
<funcsym>
<name>U71</name>
<arity>3</arity>
<replacementmap>
<entry>1</entry>
</replacementmap>
</funcsym>
<funcsym>
<name>x</name>
<arity>2</arity>
<replacementmap>
<entry>1</entry>
<entry>2</entry>
</replacementmap>
</funcsym>
<funcsym>
<name>and</name>
<arity>2</arity>
<replacementmap>
<entry>1</entry>
</replacementmap>
</funcsym>
<funcsym>
<name>isNatKind</name>
<arity>1</arity>
<replacementmap/>
</funcsym>
</signature>
</trs>
<strategy>FULL</strategy>
<metainformation>
<originalfilename>./TRS/CSR_Maude/my-nat/MYNAT_complete.trs</originalfilename>
</metainformation>
</problem>
