YES
<?xml version="1.0" encoding="UTF-8" standalone="no"?><?xml-stylesheet type="text/xsl" href="cpfHTML.xsl"?><certificationProblem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="cpf.xsd"><input><trsInput><trs><rules><rule><lhs><funapp><name>a__U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U21</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>a__plus</name><arg><funapp><name>mark</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>mark</name><arg><var>M</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__and</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__and</name><arg><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isNat</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__plus</name><arg><var>N</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__U11</name><arg><funapp><name>a__isNat</name><arg><var>N</var></arg></funapp></arg><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__plus</name><arg><var>N</var></arg><arg><funapp><name>s</name><arg><var>M</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__U21</name><arg><funapp><name>a__and</name><arg><funapp><name>a__isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>isNat</name><arg><var>N</var></arg></funapp></arg></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__U11</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>U21</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__U21</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__plus</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__and</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>isNat</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__isNat</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>a__U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U21</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>isNat</name><arg><var>X</var></arg></funapp></rhs></rule></rules></trs><strategy><innermost/></strategy></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><pathOrder><statusPrecedence><statusPrecedenceEntry><name>a__U11</name><arity>2</arity><precedence>1</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>tt</name><arity>0</arity><precedence>4</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>a__U21</name><arity>3</arity><precedence>3</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>s</name><arity>1</arity><precedence>0</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>a__plus</name><arity>2</arity><precedence>3</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>a__and</name><arity>2</arity><precedence>2</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>a__isNat</name><arity>1</arity><precedence>2</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>0</name><arity>0</arity><precedence>5</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>plus</name><arity>2</arity><precedence>3</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>isNat</name><arity>1</arity><precedence>2</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>U11</name><arity>2</arity><precedence>1</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>U21</name><arity>3</arity><precedence>3</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>and</name><arity>2</arity><precedence>2</precedence><mul/></statusPrecedenceEntry></statusPrecedence><argumentFilter><argumentFilterEntry><name>a__U11</name><arity>2</arity><nonCollapsing><position>2</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>tt</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>mark</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>a__U21</name><arity>3</arity><nonCollapsing><position>3</position><position>2</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>s</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>a__plus</name><arity>2</arity><nonCollapsing><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>a__and</name><arity>2</arity><nonCollapsing><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>a__isNat</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>0</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>plus</name><arity>2</arity><nonCollapsing><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>isNat</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>U11</name><arity>2</arity><nonCollapsing><position>2</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>U21</name><arity>3</arity><nonCollapsing><position>3</position><position>2</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>and</name><arity>2</arity><nonCollapsing><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry></argumentFilter></pathOrder></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>mark</name><arg><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__U11</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>U21</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__U21</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__plus</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__and</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>isNat</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__isNat</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>a__U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U21</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>isNat</name><arg><var>X</var></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><knuthBendixOrder><w0>1</w0><precedenceWeight><precedenceWeightEntry><name>tt</name><arity>0</arity><precedence>8</precedence><weight>1</weight></precedenceWeightEntry><precedenceWeightEntry><name>0</name><arity>0</arity><precedence>12</precedence><weight>1</weight></precedenceWeightEntry><precedenceWeightEntry><name>mark</name><arity>1</arity><precedence>13</precedence><weight>0</weight></precedenceWeightEntry><precedenceWeightEntry><name>isNat</name><arity>1</arity><precedence>3</precedence><weight>1</weight></precedenceWeightEntry><precedenceWeightEntry><name>a__isNat</name><arity>1</arity><precedence>5</precedence><weight>1</weight></precedenceWeightEntry><precedenceWeightEntry><name>s</name><arity>1</arity><precedence>11</precedence><weight>1</weight></precedenceWeightEntry><precedenceWeightEntry><name>U11</name><arity>2</arity><precedence>1</precedence><weight>0</weight></precedenceWeightEntry><precedenceWeightEntry><name>a__U11</name><arity>2</arity><precedence>4</precedence><weight>0</weight></precedenceWeightEntry><precedenceWeightEntry><name>U21</name><arity>3</arity><precedence>6</precedence><weight>0</weight></precedenceWeightEntry><precedenceWeightEntry><name>a__U21</name><arity>3</arity><precedence>7</precedence><weight>0</weight></precedenceWeightEntry><precedenceWeightEntry><name>plus</name><arity>2</arity><precedence>0</precedence><weight>0</weight></precedenceWeightEntry><precedenceWeightEntry><name>a__plus</name><arity>2</arity><precedence>2</precedence><weight>0</weight></precedenceWeightEntry><precedenceWeightEntry><name>and</name><arity>2</arity><precedence>9</precedence><weight>0</weight></precedenceWeightEntry><precedenceWeightEntry><name>a__and</name><arity>2</arity><precedence>10</precedence><weight>0</weight></precedenceWeightEntry></precedenceWeight></knuthBendixOrder></redPair></orderingConstraintProof><trs><rules/></trs><trsTerminationProof><rIsEmpty/></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
</version><strategy>Statistics for single proof: 100.00 % (3 real / 0 unknown / 0 assumptions / 3 total proof steps)</strategy><url>http://aprove.informatik.rwth-aachen.de</url></tool><toolUser><firstName>John</firstName><lastName>Doe</lastName></toolUser></proofOrigin><inputOrigin/></origin></certificationProblem>