YES
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</funapp></arg></funapp></lhs><rhs><funapp><sharp><name>g</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>d</name></sharp><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>d</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>d</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>d</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>active</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>c</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>h</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>f</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>c</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>g</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>d</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>h</name><arg><var>x0</var></arg></funapp></arg></funapp></innermostLhss><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>d</name></sharp><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>d</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>d</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>d</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>h</name></sharp><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>h</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>h</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>h</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>active</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>c</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>h</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>f</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>c</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>g</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>d</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>h</name><arg><var>x0</var></arg></funapp></arg></funapp></innermostLhss><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>h</name></sharp><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>h</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>h</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>h</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component></depGraphProc></dpProof></dpTrans></trsTerminationProof></ruleRemoval></trsTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
</version><strategy>Statistics for single proof: 100.00 % (21 real / 0 unknown / 0 assumptions / 21 total proof steps)</strategy><url>http://aprove.informatik.rwth-aachen.de</url></tool><toolUser><firstName>John</firstName><lastName>Doe</lastName></toolUser></proofOrigin><inputOrigin/></origin></certificationProblem>