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><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></trsC><trsP><rules /></trsP><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>tl</name><arg><funapp><name>nats</name></funapp></arg></funapp></arg></funapp></intermediateTerms></critPairInfo></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><rIsEmpty /></relativeTerminationProof><crProof><compositionalPcpRuleLabeling><ruleLabelingFunction><ruleLabelingFunctionEntry><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><label>5</label></ruleLabelingFunctionEntry><ruleLabelingFunctionEntry><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><label>6</label></ruleLabelingFunctionEntry><ruleLabelingFunctionEntry><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><label>1</label></ruleLabelingFunctionEntry><ruleLabelingFunctionEntry><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><label>1</label></ruleLabelingFunctionEntry><ruleLabelingFunctionEntry><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><label>4</label></ruleLabelingFunctionEntry></ruleLabelingFunction><ruleLabelingFunction><ruleLabelingFunctionEntry><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><label>2</label></ruleLabelingFunctionEntry><ruleLabelingFunctionEntry><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><label>3</label></ruleLabelingFunctionEntry><ruleLabelingFunctionEntry><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><label>1</label></ruleLabelingFunctionEntry><ruleLabelingFunctionEntry><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><label>3</label></ruleLabelingFunctionEntry><ruleLabelingFunctionEntry><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><label>7</label></ruleLabelingFunctionEntry></ruleLabelingFunction><joinsRS><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><labels><maxLeft>5</maxLeft><right>7</right></labels><intermediateTerms><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><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></joinsRS><joinsSR><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><labels><maxLeft>2</maxLeft><right>4</right></labels><intermediateTerms><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><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><funapp><name>tl</name><arg><funapp><name>inc</name><arg><funapp><name>nats</name></funapp></arg></funapp></arg></funapp></intermediateTerms></critPairInfo></joinSequences></joinsSR><trs><rules /></trs><crProof><orthogonal /></crProof></compositionalPcpRuleLabeling></crProof></compositionalPcps></crProof></proof><origin><proofOrigin><tool><name>Hakusan</name><version>0.10</version></tool></proofOrigin></origin></certificationProblem>