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>Ap</name><arg><funapp><name>Ap</name><arg><funapp><name>Ap</name><arg><funapp><name>S</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>Ap</name><arg><funapp><name>Ap</name><arg><var>x</var></arg><arg><var>z</var></arg></funapp></arg><arg><funapp><name>Ap</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>Ap</name><arg><funapp><name>Ap</name><arg><funapp><name>K</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>Ap</name><arg><funapp><name>I</name></funapp></arg><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>Ap</name><arg><funapp><name>Ap</name><arg><funapp><name>Ap</name><arg><funapp><name>S</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>Ap</name><arg><funapp><name>Ap</name><arg><var>x</var></arg><arg><var>z</var></arg></funapp></arg><arg><funapp><name>Ap</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><label>1</label></ruleLabelingFunctionEntry><ruleLabelingFunctionEntry><rule><lhs><funapp><name>Ap</name><arg><funapp><name>Ap</name><arg><funapp><name>K</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><label>1</label></ruleLabelingFunctionEntry><ruleLabelingFunctionEntry><rule><lhs><funapp><name>Ap</name><arg><funapp><name>I</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><label>1</label></ruleLabelingFunctionEntry></ruleLabelingFunction><ruleLabelingFunction><ruleLabelingFunctionEntry><rule><lhs><funapp><name>Ap</name><arg><funapp><name>Ap</name><arg><funapp><name>Ap</name><arg><funapp><name>S</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>Ap</name><arg><funapp><name>Ap</name><arg><var>x</var></arg><arg><var>z</var></arg></funapp></arg><arg><funapp><name>Ap</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><label>1</label></ruleLabelingFunctionEntry><ruleLabelingFunctionEntry><rule><lhs><funapp><name>Ap</name><arg><funapp><name>Ap</name><arg><funapp><name>K</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><label>1</label></ruleLabelingFunctionEntry><ruleLabelingFunctionEntry><rule><lhs><funapp><name>Ap</name><arg><funapp><name>I</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><label>1</label></ruleLabelingFunctionEntry></ruleLabelingFunction><joinsRS><joinSequences /></joinsRS><joinsSR><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>