YES
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ame>app</name></sharp><arg><funapp><name>map1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>map2</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge><edge><position>2</position><strict>false</strict><position>2</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>filter3</name></sharp><arg><var>fun</var></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>filter24</name></sharp><arg><funapp><name>app</name><arg><var>fun</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>fun</var></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><edge><position>1</position><strict>false</strict><position>2</position></edge><edge><position>2</position><strict>true</strict><position>3</position></edge><edge><position>2</position><strict>true</strict><position>4</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>filter1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>filter3</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge><edge><position>2</position><strict>false</strict><position>2</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>filter23</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>filter24</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge><edge><position>1</position><strict>true</strict><position>2</position></edge><edge><position>1</position><strict>true</strict><position>3</position></edge><edge><position>2</position><strict>false</strict><position>4</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>filter24</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>fun</var></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>filter3</name></sharp><arg><var>fun</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><edge><position>2</position><strict>false</strict><position>1</position></edge><edge><position>4</position><strict>false</strict><position>2</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>filter24</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>fun</var></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>filter3</name></sharp><arg><var>fun</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><edge><position>2</position><strict>false</strict><position>1</position></edge><edge><position>4</position><strict>false</strict><position>2</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>g1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>g2</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>g2</name></sharp><arg><var>x</var></arg><arg><funapp><name>c1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>g2</name></sharp><arg><funapp><name>s1</name><arg><funapp><name>c1</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>g2</name></sharp><arg><var>x</var></arg><arg><funapp><name>c1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>g2</name></sharp><arg><var>x</var></arg><arg><funapp><name>g2</name><arg><funapp><name>s1</name><arg><funapp><name>c1</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>g2</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>if3</name><arg><funapp><name>f1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>g2</name><arg><var>x</var></arg><arg><funapp><name>c1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>g2</name><arg><var>x</var></arg><arg><funapp><name>g2</name><arg><funapp><name>s1</name><arg><funapp><name>c1</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f1</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>f1</name><arg><funapp><name>1</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>f1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f1</name><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>if3</name><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>if3</name><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>y</var></rhs></rule></rules></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>f1</name><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>f1</name><arg><funapp><name>1</name></funapp></arg></funapp><funapp><name>f1</name><arg><funapp><name>s1</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>if3</name><arg><funapp><name>true</name></funapp></arg><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp><funapp><name>if3</name><arg><funapp><name>false</name></funapp></arg><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp><funapp><name>g2</name><arg><funapp><name>s1</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>g2</name><arg><var>x0</var></arg><arg><funapp><name>c1</name><arg><var>x1</var></arg></funapp></arg></funapp></innermostLhss><dpProof><redPairUrProc><orderingConstraintProof><redPair><knuthBendixOrder><w0>1</w0><precedenceWeight><precedenceWeightEntry><name>c1</name><arity>1</arity><precedence>1</precedence><weight>4</weight></precedenceWeightEntry><precedenceWeightEntry><name>g2</name><arity>2</arity><precedence>2</precedence><weight>4</weight></precedenceWeightEntry><precedenceWeightEntry><name>if3</name><arity>3</arity><precedence>3</precedence><weight>1</weight></precedenceWeightEntry><precedenceWeightEntry><name>s1</name><arity>1</arity><precedence>0</precedence><weight>1</weight></precedenceWeightEntry></precedenceWeight><argumentFilter><argumentFilterEntry><sharp><name>g2</name></sharp><arity>2</arity><collapsing>2</collapsing></argumentFilterEntry><argumentFilterEntry><name>c1</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>g2</name><arity>2</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>if3</name><arity>3</arity><nonCollapsing><position>2</position><position>3</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>s1</name><arity>1</arity><nonCollapsing/></argumentFilterEntry></argumentFilter></knuthBendixOrder></redPair></orderingConstraintProof><dps><rules/></dps><usableRules><rules><rule><lhs><funapp><name>g2</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>if3</name><arg><funapp><name>f1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>g2</name><arg><var>x</var></arg><arg><funapp><name>c1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>g2</name><arg><var>x</var></arg><arg><funapp><name>g2</name><arg><funapp><name>s1</name><arg><funapp><name>c1</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>if3</name><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>if3</name><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>y</var></rhs></rule></rules></usableRules><dpProof><pIsEmpty/></dpProof></redPairUrProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>g2</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f1</name></sharp><arg><var>x</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>f</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>f1</name></sharp><arg><var>y1</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>f1</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f1</name></sharp><arg><var>x</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss/><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>f1</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f1</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>g2</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>if3</name></sharp><arg><funapp><name>f1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>if2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>if3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></dpTrans></trsTerminationProof></switchInnermost></trsTerminationProof></uncurry></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 % (12 real / 0 unknown / 0 assumptions / 12 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>