YES
<?xml version="1.0" encoding="UTF-8" standalone="no"?><?xml-stylesheet type="text/xsl" href="cpfHTML.xsl"?><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>g</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>g</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><funapp><name>g</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>g</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>g</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>g</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule></rules></trs><strategy><innermost/></strategy></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>g</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>g</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><funapp><name>g</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>g</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>g</name></sharp><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>g</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>g</name></sharp><arg><var>x</var></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>g</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>g</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><funapp><name>g</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>g</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>g</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>g</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>g</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>g</name><arg><funapp><name>0</name></funapp></arg></funapp></innermostLhss><dpProof><rewritingProc><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>g</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>g</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><funapp><name>g</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>1</position></positionInTerm><rule><lhs><funapp><name>g</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>g</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>g</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><funapp><name>g</name><arg><var>x</var></arg></funapp></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>g</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>g</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><funapp><name>g</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><usableRules><rules><rule><lhs><funapp><name>g</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>g</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>g</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule></rules></usableRules><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>g</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule></rules></usableRules><dpProof><rewritingProc><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>g</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>g</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><funapp><name>g</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>1</position><position>1</position></positionInTerm><rule><lhs><funapp><name>g</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><funapp><name>g</name><arg><var>x</var></arg></funapp></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>g</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><funapp><name>g</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><usableRules><rules><rule><lhs><funapp><name>g</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule></rules></usableRules><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><instantiationProc><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>g</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><funapp><name>g</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><instantiations><rules/></instantiations><dpProof><pIsEmpty/></dpProof></instantiationProc></dpProof></usableRulesProc></dpProof></rewritingProc></dpProof></usableRulesProc></dpProof></rewritingProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>g</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>g</name></sharp><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>g</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>g</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>g</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></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></depGraphProc></dpProof></dpTrans></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 % (13 real / 0 unknown / 0 assumptions / 13 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>