YES
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<name>s1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><funapp><name>half1</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>bits1</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>bits1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><funapp><name>bits1</name><arg><funapp><name>half1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>map2</name><arg><var>f</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>map2</name><arg><var>f</var></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons2</name><arg><funapp><name>app</name><arg><var>f</var></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>map2</name><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>filter3</name><arg><var>f</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>filter3</name><arg><var>f</var></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>filter24</name><arg><funapp><name>app</name><arg><var>f</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>filter24</name><arg><funapp><name>true</name></funapp></arg><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>filter3</name><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>filter24</name><arg><funapp><name>false</name></funapp></arg><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>filter3</name><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>half</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>half1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>bits</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>bits1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>map1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>map1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>map2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>cons1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>cons1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>cons2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>filter</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>filter1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>filter1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>filter3</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>filter2</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>filter21</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>filter21</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>filter22</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>filter22</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>filter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/name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>cons1</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>filter</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>filter1</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>filter2</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>filter21</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>filter22</name><arity>2</arity><nonCollapsing><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>filter23</name><arity>3</arity><nonCollapsing><position>3</position><position>2</position><position>1</position></nonCollapsing></argumentFilterEntry></argumentFilter></pathOrder></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>half1</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>half1</name><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>half1</name><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><funapp><name>half1</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>bits1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><funapp><name>bits1</name><arg><funapp><name>half1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><switchInnermost><wcrProof><joinableCriticalPairsBFS>10</joinableCriticalPairsBFS></wcrProof><trsTerminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><name>half1</name></sharp><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>half1</name></sharp><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>bits1</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>bits1</name></sharp><arg><funapp><name>half1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>bits1</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>half1</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>bits1</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>bits1</name></sharp><arg><funapp><name>half1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>half1</name><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>half1</name><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><funapp><name>half1</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>half1</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule></rules></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>half1</name><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>half1</name><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp><funapp><name>half1</name><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp></innermostLhss><dpProof><monoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>half1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>s1</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>bits1</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>bits1</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>bits1</name></sharp><arg><funapp><name>half1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>half1</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule></rules></trs><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><switchToTRS><trsTerminationProof><bounds><type><match/></type><bound>1</bound><finalStates><state>0</state><state>1</state><state>2</state></finalStates><treeAutomaton><finalStates><state>0</state><state>1</state><state>2</state></finalStates><transitions><transition><lhs><sharp><name>bits1</name></sharp><height>0</height><state>0</state></lhs><rhs><state>0</state></rhs></transition><transition><lhs><sharp><name>bits1</name></sharp><height>0</height><state>1</state></lhs><rhs><state>0</state></rhs></transition><transition><lhs><sharp><name>bits1</name></sharp><height>0</height><state>2</state></lhs><rhs><state>0</state></rhs></transition><transition><lhs><name>s1</name><height>0</height><state>0</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>s1</name><height>0</height><state>1</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>s1</name><height>0</height><state>2</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>half1</name><height>0</height><state>0</state></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>half1</name><height>0</height><state>1</state></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>half1</name><height>0</height><state>2</state></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>s1</name><height>1</height><state>0</state></lhs><rhs><state>4</state></rhs></transition><transition><lhs><name>half1</name><height>1</height><state>4</state></lhs><rhs><state>3</state></rhs></transition><transition><lhs><sharp><name>bits1</name></sharp><height>1</height><state>3</state></lhs><rhs><state>0</state></rhs></transition><transition><lhs><name>s1</name><height>1</height><state>1</state></lhs><rhs><state>4</state></rhs></transition><transition><lhs><name>s1</name><height>1</height><state>2</state></lhs><rhs><state>4</state></rhs></transition></transitions></treeAutomaton></bounds></trsTerminationProof></switchToTRS></dpProof></usableRulesProc></dpProof></monoRedPairProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>bits1</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>half1</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>half1</name></sharp><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>half1</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>half1</name></sharp><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>half1</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></switchInnermost></trsTerminationProof></ruleRemoval></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 % (14 real / 0 unknown / 0 assumptions / 14 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>