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>R</name><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><name>r</name><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>r</name><arg><funapp><name>p</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>p</name><arg><funapp><name>p</name><arg><funapp><name>r</name><arg><funapp><name>P</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>r</name><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><var>x1</var></rhs></rule><rule><lhs><funapp><name>r</name><arg><funapp><name>P</name><arg><funapp><name>P</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>P</name><arg><funapp><name>P</name><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>p</name><arg><funapp><name>P</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><var>x1</var></rhs></rule><rule><lhs><funapp><name>P</name><arg><funapp><name>p</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><var>x1</var></rhs></rule><rule><lhs><funapp><name>r</name><arg><funapp><name>R</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><var>x1</var></rhs></rule><rule><lhs><funapp><name>R</name><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><var>x1</var></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><stringReversal><trs><rules><rule><lhs><funapp><name>R</name><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><name>r</name><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>p</name><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>P</name><arg><funapp><name>r</name><arg><funapp><name>p</name><arg><funapp><name>p</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>r</name><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><var>x1</var></rhs></rule><rule><lhs><funapp><name>P</name><arg><funapp><name>P</name><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>r</name><arg><funapp><name>P</name><arg><funapp><name>P</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>P</name><arg><funapp><name>p</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><var>x1</var></rhs></rule><rule><lhs><funapp><name>p</name><arg><funapp><name>P</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><var>x1</var></rhs></rule><rule><lhs><funapp><name>R</name><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><var>x1</var></rhs></rule><rule><lhs><funapp><name>r</name><arg><funapp><name>R</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><var>x1</var></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>R</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>r</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>p</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>P</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>p</name><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>P</name><arg><funapp><name>r</name><arg><funapp><name>p</name><arg><funapp><name>p</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>r</name><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><var>x1</var></rhs></rule><rule><lhs><funapp><name>P</name><arg><funapp><name>P</name><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>r</name><arg><funapp><name>P</name><arg><funapp><name>P</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>P</name><arg><funapp><name>p</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><var>x1</var></rhs></rule><rule><lhs><funapp><name>p</name><arg><funapp><name>P</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><var>x1</var></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>p</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>r</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>P</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>p</name><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>P</name><arg><funapp><name>r</name><arg><funapp><name>p</name><arg><funapp><name>p</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>P</name><arg><funapp><name>P</name><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>r</name><arg><funapp><name>P</name><arg><funapp><name>P</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>P</name><arg><funapp><name>p</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><var>x1</var></rhs></rule><rule><lhs><funapp><name>p</name><arg><funapp><name>P</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><var>x1</var></rhs></rule></rules></trs><trsTerminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><name>p</name></sharp><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>P</name></sharp><arg><funapp><name>r</name><arg><funapp><name>p</name><arg><funapp><name>p</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>p</name></sharp><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>p</name></sharp><arg><funapp><name>p</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>p</name></sharp><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>p</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>P</name></sharp><arg><funapp><name>P</name><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>P</name></sharp><arg><funapp><name>P</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>P</name></sharp><arg><funapp><name>P</name><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>P</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>p</name></sharp><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>p</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>p</name></sharp><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>p</name></sharp><arg><funapp><name>p</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><monoRedPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>p</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>r</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>P</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>p</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>p</name></sharp><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>p</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>p</name></sharp><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>p</name></sharp><arg><funapp><name>p</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>p</name><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>P</name><arg><funapp><name>r</name><arg><funapp><name>p</name><arg><funapp><name>p</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>p</name><arg><funapp><name>P</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><var>x1</var></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>p</name><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>P</name><arg><funapp><name>r</name><arg><funapp><name>p</name><arg><funapp><name>p</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>p</name><arg><funapp><name>P</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><var>x1</var></rhs></rule></rules></usableRules><dpProof><switchInnermostProc><wcrProof><joinableCriticalPairsBFS>20</joinableCriticalPairsBFS></wcrProof><dpProof><redPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>p</name></sharp><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>-1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>p</name><arity>1</arity><polynomial><variable>1</variable></polynomial></interpret><interpret><name>r</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>P</name><arity>1</arity><polynomial><variable>1</variable></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules/></dps><dpProof><pIsEmpty/></dpProof></redPairProc></dpProof></switchInnermostProc></dpProof></monoRedPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>p</name></sharp><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>P</name></sharp><arg><funapp><name>r</name><arg><funapp><name>p</name><arg><funapp><name>p</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>P</name></sharp><arg><funapp><name>P</name><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>P</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>P</name></sharp><arg><funapp><name>P</name><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>P</name></sharp><arg><funapp><name>P</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><monoRedPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>P</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>r</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>p</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>P</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>P</name></sharp><arg><funapp><name>P</name><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>P</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>P</name></sharp><arg><funapp><name>P</name><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>P</name></sharp><arg><funapp><name>P</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>P</name><arg><funapp><name>P</name><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>r</name><arg><funapp><name>P</name><arg><funapp><name>P</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>P</name><arg><funapp><name>p</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><var>x1</var></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>P</name><arg><funapp><name>P</name><arg><funapp><name>r</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>r</name><arg><funapp><name>P</name><arg><funapp><name>P</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>P</name><arg><funapp><name>p</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><var>x1</var></rhs></rule></rules></usableRules><dpProof><switchInnermostProc><wcrProof><joinableCriticalPairsBFS>20</joinableCriticalPairsBFS></wcrProof><dpProof><redPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>P</name></sharp><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>-1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>P</name><arity>1</arity><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></interpret><interpret><name>r</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>p</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules/></dps><dpProof><pIsEmpty/></dpProof></redPairProc></dpProof></switchInnermostProc></dpProof></monoRedPairUrProc></dpProof></component></depGraphProc></dpProof></dpTrans></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></stringReversal></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 % (13 real / 0 unknown / 0 assumptions / 13 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>