YES
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<certificationProblem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="cpf.xsd"><input><trsInput><trs><rules><rule><lhs><funapp><name>nats</name></funapp></lhs><rhs><funapp><name>:</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>inc</name><arg><funapp><name>nats</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>inc</name><arg><funapp><name>:</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>:</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>inc</name><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>hd</name><arg><funapp><name>:</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>tl</name><arg><funapp><name>:</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><var>y</var></rhs></rule><rule><lhs><funapp><name>inc</name><arg><funapp><name>tl</name><arg><funapp><name>nats</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>tl</name><arg><funapp><name>inc</name><arg><funapp><name>nats</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><crProof><compositionalPcps><trsC><rules /></trsC><trsP><rules><rule><lhs><funapp><name>inc</name><arg><funapp><name>tl</name><arg><funapp><name>nats</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>inc</name><arg><funapp><name>tl</name><arg><funapp><name>:</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>inc</name><arg><funapp><name>nats</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>inc</name><arg><funapp><name>tl</name><arg><funapp><name>nats</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>tl</name><arg><funapp><name>inc</name><arg><funapp><name>nats</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trsP><joinSequences /><joinSequences><critPairInfo><left><funapp><name>inc</name><arg><funapp><name>tl</name><arg><funapp><name>:</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>inc</name><arg><funapp><name>nats</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></left><peak><funapp><name>inc</name><arg><funapp><name>tl</name><arg><funapp><name>nats</name></funapp></arg></funapp></arg></funapp></peak><right><funapp><name>tl</name><arg><funapp><name>inc</name><arg><funapp><name>nats</name></funapp></arg></funapp></arg></funapp></right><overlapPositions><positionInTerm><position>1</position><position>1</position></positionInTerm></overlapPositions><intermediateTerms><funapp><name>inc</name><arg><funapp><name>inc</name><arg><funapp><name>nats</name></funapp></arg></funapp></arg></funapp><funapp><name>tl</name><arg><funapp><name>:</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>inc</name><arg><funapp><name>inc</name><arg><funapp><name>nats</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp><funapp><name>tl</name><arg><funapp><name>inc</name><arg><funapp><name>:</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>inc</name><arg><funapp><name>nats</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></intermediateTerms></critPairInfo></joinSequences><relativeTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><matrices><dimension>2</dimension><strictDimension>1</strictDimension><domain><naturals /></domain></matrices></domain><degree>1</degree></polynomial></type><interpret><name>:</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>2</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>2</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><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>tl</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>2</integer></coefficient></vector><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>nats</name><arity>0</arity><polynomial><sum><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>hd</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>2</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>inc</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules /></trs><trs><rules><rule><lhs><funapp><name>nats</name></funapp></lhs><rhs><funapp><name>:</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>inc</name><arg><funapp><name>nats</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>inc</name><arg><funapp><name>:</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>:</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>inc</name><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>hd</name><arg><funapp><name>:</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule></rules></trs><relativeTerminationProof><rIsEmpty /></relativeTerminationProof></ruleRemoval></relativeTerminationProof><crProof><orthogonal /></crProof></compositionalPcps></crProof></proof><origin><proofOrigin><tool><name>Hakusan</name><version>0.10</version></tool></proofOrigin></origin></certificationProblem>