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>f</name><arg><var>x1</var></arg><arg><funapp><name>g</name><arg><var>x2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><var>x1</var></arg><arg><funapp><name>g</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>g</name><arg><var>y1</var></arg></funapp></arg><arg><var>y2</var></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>g</name><arg><var>y1</var></arg></funapp></arg><arg><funapp><name>g</name><arg><var>y1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>g</name><arg><funapp><name>a</name></funapp></arg></funapp></lhs><rhs><funapp><name>g</name><arg><funapp><name>b</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>b</name></funapp></lhs><rhs><funapp><name>a</name></funapp></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><crProof><compositionalPcpRuleLabeling><ruleLabelingFunction><ruleLabelingFunctionEntry><rule><lhs><funapp><name>f</name><arg><var>x1</var></arg><arg><funapp><name>g</name><arg><var>x2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><var>x1</var></arg><arg><funapp><name>g</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><label>3</label></ruleLabelingFunctionEntry><ruleLabelingFunctionEntry><rule><lhs><funapp><name>f</name><arg><funapp><name>g</name><arg><var>y1</var></arg></funapp></arg><arg><var>y2</var></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>g</name><arg><var>y1</var></arg></funapp></arg><arg><funapp><name>g</name><arg><var>y1</var></arg></funapp></arg></funapp></rhs></rule><label>4</label></ruleLabelingFunctionEntry><ruleLabelingFunctionEntry><rule><lhs><funapp><name>g</name><arg><funapp><name>a</name></funapp></arg></funapp></lhs><rhs><funapp><name>g</name><arg><funapp><name>b</name></funapp></arg></funapp></rhs></rule><label>2</label></ruleLabelingFunctionEntry><ruleLabelingFunctionEntry><rule><lhs><funapp><name>b</name></funapp></lhs><rhs><funapp><name>a</name></funapp></rhs></rule><label>5</label></ruleLabelingFunctionEntry></ruleLabelingFunction><ruleLabelingFunction><ruleLabelingFunctionEntry><rule><lhs><funapp><name>f</name><arg><var>x1</var></arg><arg><funapp><name>g</name><arg><var>x2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><var>x1</var></arg><arg><funapp><name>g</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><label>7</label></ruleLabelingFunctionEntry><ruleLabelingFunctionEntry><rule><lhs><funapp><name>f</name><arg><funapp><name>g</name><arg><var>y1</var></arg></funapp></arg><arg><var>y2</var></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>g</name><arg><var>y1</var></arg></funapp></arg><arg><funapp><name>g</name><arg><var>y1</var></arg></funapp></arg></funapp></rhs></rule><label>1</label></ruleLabelingFunctionEntry><ruleLabelingFunctionEntry><rule><lhs><funapp><name>g</name><arg><funapp><name>a</name></funapp></arg></funapp></lhs><rhs><funapp><name>g</name><arg><funapp><name>b</name></funapp></arg></funapp></rhs></rule><label>6</label></ruleLabelingFunctionEntry><ruleLabelingFunctionEntry><rule><lhs><funapp><name>b</name></funapp></lhs><rhs><funapp><name>a</name></funapp></rhs></rule><label>8</label></ruleLabelingFunctionEntry></ruleLabelingFunction><joinsRS><joinSequences><critPairInfo><left><funapp><name>f</name><arg><funapp><name>g</name><arg><var>x0_1</var></arg></funapp></arg><arg><funapp><name>g</name><arg><var>x0_1</var></arg></funapp></arg></funapp></left><peak><funapp><name>f</name><arg><funapp><name>g</name><arg><var>x0_1</var></arg></funapp></arg><arg><funapp><name>g</name><arg><var>y2</var></arg></funapp></arg></funapp></peak><right><funapp><name>f</name><arg><funapp><name>g</name><arg><var>x0_1</var></arg></funapp></arg><arg><funapp><name>g</name><arg><funapp><name>g</name><arg><var>x0_1</var></arg></funapp></arg></funapp></arg></funapp></right><overlapPositions><positionInTerm /></overlapPositions><labels><maxLeft>4</maxLeft><right>7</right></labels><intermediateTerms><funapp><name>f</name><arg><funapp><name>g</name><arg><var>x0_1</var></arg></funapp></arg><arg><funapp><name>g</name><arg><var>x0_1</var></arg></funapp></arg></funapp><funapp><name>f</name><arg><funapp><name>g</name><arg><var>x0_1</var></arg></funapp></arg><arg><funapp><name>g</name><arg><funapp><name>g</name><arg><var>x0_1</var></arg></funapp></arg></funapp></arg></funapp></intermediateTerms></critPairInfo><critPairInfo><left><funapp><name>f</name><arg><var>y1</var></arg><arg><funapp><name>g</name><arg><funapp><name>b</name></funapp></arg></funapp></arg></funapp></left><peak><funapp><name>f</name><arg><var>y1</var></arg><arg><funapp><name>g</name><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></peak><right><funapp><name>f</name><arg><var>y1</var></arg><arg><funapp><name>g</name><arg><var>y1</var></arg></funapp></arg></funapp></right><overlapPositions><positionInTerm><position>2</position></positionInTerm></overlapPositions><labels><maxLeft>2</maxLeft><right>7</right></labels><intermediateTerms><funapp><name>f</name><arg><var>y1</var></arg><arg><funapp><name>g</name><arg><var>y1</var></arg></funapp></arg></funapp></intermediateTerms></critPairInfo><critPairInfo><left><funapp><name>f</name><arg><funapp><name>g</name><arg><var>y1</var></arg></funapp></arg><arg><funapp><name>g</name><arg><funapp><name>g</name><arg><var>y1</var></arg></funapp></arg></funapp></arg></funapp></left><peak><funapp><name>f</name><arg><funapp><name>g</name><arg><var>y1</var></arg></funapp></arg><arg><funapp><name>g</name><arg><var>x0_2</var></arg></funapp></arg></funapp></peak><right><funapp><name>f</name><arg><funapp><name>g</name><arg><var>y1</var></arg></funapp></arg><arg><funapp><name>g</name><arg><var>y1</var></arg></funapp></arg></funapp></right><overlapPositions><positionInTerm /></overlapPositions><labels><maxLeft>3</maxLeft><right>1</right></labels><intermediateTerms><funapp><name>f</name><arg><funapp><name>g</name><arg><var>y1</var></arg></funapp></arg><arg><funapp><name>g</name><arg><funapp><name>g</name><arg><var>y1</var></arg></funapp></arg></funapp></arg></funapp></intermediateTerms></critPairInfo><critPairInfo><left><funapp><name>f</name><arg><funapp><name>g</name><arg><funapp><name>b</name></funapp></arg></funapp></arg><arg><var>y2</var></arg></funapp></left><peak><funapp><name>f</name><arg><funapp><name>g</name><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><var>y2</var></arg></funapp></peak><right><funapp><name>f</name><arg><funapp><name>g</name><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><funapp><name>g</name><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></right><overlapPositions><positionInTerm><position>1</position></positionInTerm></overlapPositions><labels><maxLeft>2</maxLeft><right>1</right></labels><intermediateTerms><funapp><name>f</name><arg><funapp><name>g</name><arg><funapp><name>b</name></funapp></arg></funapp></arg><arg><var>y2</var></arg></funapp><funapp><name>f</name><arg><funapp><name>g</name><arg><funapp><name>b</name></funapp></arg></funapp></arg><arg><funapp><name>g</name><arg><funapp><name>b</name></funapp></arg></funapp></arg></funapp></intermediateTerms></critPairInfo></joinSequences></joinsRS><joinsSR><joinSequences><critPairInfo><left><funapp><name>f</name><arg><funapp><name>g</name><arg><var>x0_1</var></arg></funapp></arg><arg><funapp><name>g</name><arg><var>x0_1</var></arg></funapp></arg></funapp></left><peak><funapp><name>f</name><arg><funapp><name>g</name><arg><var>x0_1</var></arg></funapp></arg><arg><funapp><name>g</name><arg><var>y2</var></arg></funapp></arg></funapp></peak><right><funapp><name>f</name><arg><funapp><name>g</name><arg><var>x0_1</var></arg></funapp></arg><arg><funapp><name>g</name><arg><funapp><name>g</name><arg><var>x0_1</var></arg></funapp></arg></funapp></arg></funapp></right><overlapPositions><positionInTerm /></overlapPositions><labels><maxLeft>1</maxLeft><right>3</right></labels><intermediateTerms><funapp><name>f</name><arg><funapp><name>g</name><arg><var>x0_1</var></arg></funapp></arg><arg><funapp><name>g</name><arg><var>x0_1</var></arg></funapp></arg></funapp><funapp><name>f</name><arg><funapp><name>g</name><arg><var>x0_1</var></arg></funapp></arg><arg><funapp><name>g</name><arg><funapp><name>g</name><arg><var>x0_1</var></arg></funapp></arg></funapp></arg></funapp></intermediateTerms></critPairInfo><critPairInfo><left><funapp><name>f</name><arg><var>y1</var></arg><arg><funapp><name>g</name><arg><funapp><name>b</name></funapp></arg></funapp></arg></funapp></left><peak><funapp><name>f</name><arg><var>y1</var></arg><arg><funapp><name>g</name><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></peak><right><funapp><name>f</name><arg><var>y1</var></arg><arg><funapp><name>g</name><arg><var>y1</var></arg></funapp></arg></funapp></right><overlapPositions><positionInTerm><position>2</position></positionInTerm></overlapPositions><labels><maxLeft>6</maxLeft><right>3</right></labels><intermediateTerms><funapp><name>f</name><arg><var>y1</var></arg><arg><funapp><name>g</name><arg><funapp><name>b</name></funapp></arg></funapp></arg></funapp><funapp><name>f</name><arg><var>y1</var></arg><arg><funapp><name>g</name><arg><var>y1</var></arg></funapp></arg></funapp></intermediateTerms></critPairInfo><critPairInfo><left><funapp><name>f</name><arg><funapp><name>g</name><arg><var>y1</var></arg></funapp></arg><arg><funapp><name>g</name><arg><funapp><name>g</name><arg><var>y1</var></arg></funapp></arg></funapp></arg></funapp></left><peak><funapp><name>f</name><arg><funapp><name>g</name><arg><var>y1</var></arg></funapp></arg><arg><funapp><name>g</name><arg><var>x0_2</var></arg></funapp></arg></funapp></peak><right><funapp><name>f</name><arg><funapp><name>g</name><arg><var>y1</var></arg></funapp></arg><arg><funapp><name>g</name><arg><var>y1</var></arg></funapp></arg></funapp></right><overlapPositions><positionInTerm /></overlapPositions><labels><maxLeft>7</maxLeft><right>4</right></labels><intermediateTerms><funapp><name>f</name><arg><funapp><name>g</name><arg><var>y1</var></arg></funapp></arg><arg><funapp><name>g</name><arg><funapp><name>g</name><arg><var>y1</var></arg></funapp></arg></funapp></arg></funapp></intermediateTerms></critPairInfo><critPairInfo><left><funapp><name>f</name><arg><funapp><name>g</name><arg><funapp><name>b</name></funapp></arg></funapp></arg><arg><var>y2</var></arg></funapp></left><peak><funapp><name>f</name><arg><funapp><name>g</name><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><var>y2</var></arg></funapp></peak><right><funapp><name>f</name><arg><funapp><name>g</name><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><funapp><name>g</name><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></right><overlapPositions><positionInTerm><position>1</position></positionInTerm></overlapPositions><labels><maxLeft>6</maxLeft><right>4</right></labels><intermediateTerms><funapp><name>f</name><arg><funapp><name>g</name><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><var>y2</var></arg></funapp><funapp><name>f</name><arg><funapp><name>g</name><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><funapp><name>g</name><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></intermediateTerms></critPairInfo></joinSequences></joinsSR><trs><rules /></trs><crProof><orthogonal /></crProof></compositionalPcpRuleLabeling></crProof></proof><origin><proofOrigin><tool><name>Hakusan</name><version>0.10</version></tool></proofOrigin></origin></certificationProblem>