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>f</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>g</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>g</name><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><strategy><innermost/></strategy></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><semlab><model><rootLabeling/></model><trs><rules><rule><lhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>s</name></symbolLabel></labeledSymbol><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>s</name></symbolLabel></labeledSymbol><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>s</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>s</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>s</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>s</name><symbolLabel><name>s</name></symbolLabel></labeledSymbol><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>s</name></symbolLabel></labeledSymbol><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>s</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>s</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>s</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>s</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>s</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>s</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel/></labeledSymbol></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>s</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>s</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel/></labeledSymbol></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><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><labeledSymbol><name>f</name><symbolLabel><name>s</name></symbolLabel></labeledSymbol><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><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><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><labeledSymbol><name>f</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><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><labeledSymbol><name>s</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>s</name><symbolLabel><name>s</name></symbolLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>s</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>s</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>g</name><symbolLabel><name>s</name></symbolLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>0</name><symbolLabel/></labeledSymbol><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>s</name></symbolLabel></labeledSymbol><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>s</name></symbolLabel></labeledSymbol><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><var>x</var></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><symbolLabel><name>s</name></symbolLabel></labeledSymbol><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><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><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><labeledSymbol><name>f</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules/></trs><trsTerminationProof><rIsEmpty/></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></semlab></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 % (4 real / 0 unknown / 0 assumptions / 4 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>