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><funapp><name>H</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>F</name><arg><funapp><name>H</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>F</name><arg><var>x</var></arg><arg><funapp><name>G</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>F</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>G</name><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>I</name><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><crProof><compositionalPcpRuleLabeling><ruleLabelingFunction><ruleLabelingFunctionEntry><rule><lhs><funapp><name>F</name><arg><funapp><name>H</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>F</name><arg><funapp><name>H</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><label>0</label></ruleLabelingFunctionEntry><ruleLabelingFunctionEntry><rule><lhs><funapp><name>F</name><arg><var>x</var></arg><arg><funapp><name>G</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>F</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>G</name><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><label>1</label></ruleLabelingFunctionEntry><ruleLabelingFunctionEntry><rule><lhs><funapp><name>I</name><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><label>0</label></ruleLabelingFunctionEntry></ruleLabelingFunction><joinsRS><joinSequences><critPairInfo><left><funapp><name>F</name><arg><funapp><name>I</name><arg><funapp><name>H</name><arg><var>y1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>G</name><arg><var>x0_2</var></arg></funapp></arg></funapp></left><peak><funapp><name>F</name><arg><funapp><name>H</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>H</name><arg><var>y1</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>I</name><arg><funapp><name>G</name><arg><var>x0_2</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></right><overlapPositions><positionInTerm /></overlapPositions><labels><maxLeft>1</maxLeft><right>0</right></labels><intermediateTerms><funapp><name>F</name><arg><funapp><name>H</name><arg><var>y1</var></arg></funapp></arg><arg><funapp><name>G</name><arg><var>x0_2</var></arg></funapp></arg></funapp><funapp><name>F</name><arg><funapp><name>H</name><arg><var>y1</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>G</name><arg><var>x0_2</var></arg></funapp></arg></funapp></arg></funapp></intermediateTerms></critPairInfo><critPairInfo><left><funapp><name>F</name><arg><funapp><name>H</name><arg><var>x0_1</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>I</name><arg><funapp><name>G</name><arg><var>y2</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></left><peak><funapp><name>F</name><arg><funapp><name>H</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>I</name><arg><funapp><name>H</name><arg><var>x0_1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>G</name><arg><var>y2</var></arg></funapp></arg></funapp></right><overlapPositions><positionInTerm /></overlapPositions><labels><maxLeft>0</maxLeft><right>1</right></labels><intermediateTerms><funapp><name>F</name><arg><funapp><name>H</name><arg><var>x0_1</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>G</name><arg><var>y2</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>F</name><arg><funapp><name>H</name><arg><var>x0_1</var></arg></funapp></arg><arg><funapp><name>G</name><arg><var>y2</var></arg></funapp></arg></funapp></intermediateTerms></critPairInfo></joinSequences></joinsRS><trs><rules><rule><lhs><funapp><name>F</name><arg><funapp><name>H</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>F</name><arg><funapp><name>H</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>I</name><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule></rules></trs><crProof><compositionalPcpRuleLabeling><ruleLabelingFunction><ruleLabelingFunctionEntry><rule><lhs><funapp><name>F</name><arg><funapp><name>H</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>F</name><arg><funapp><name>H</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><label>1</label></ruleLabelingFunctionEntry><ruleLabelingFunctionEntry><rule><lhs><funapp><name>I</name><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><label>1</label></ruleLabelingFunctionEntry></ruleLabelingFunction><joinsRS><joinSequences /></joinsRS><trs><rules /></trs><crProof><orthogonal /></crProof></compositionalPcpRuleLabeling></crProof></compositionalPcpRuleLabeling></crProof></proof><origin><proofOrigin><tool><name>Hakusan</name><version>0.10</version></tool></proofOrigin></origin></certificationProblem>