YES
<?xml version="1.0"?>
<?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></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>h</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>g</name><arg><funapp><name>a</name></funapp></arg></funapp></lhs><rhs><funapp><name>g</name><arg><funapp><name>g</name><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>h</name><arg><funapp><name>a</name></funapp></arg><arg><funapp><name>a</name></funapp></arg></funapp></lhs><rhs><funapp><name>g</name><arg><funapp><name>g</name><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><crProof><decreasingDiagrams><relativeTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><matrices><dimension>3</dimension><strictDimension>1</strictDimension><domain><naturals/></domain></matrices></domain><degree>1</degree></polynomial></type><interpret><name>f</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a</name><arity>0</arity><polynomial><sum><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>g</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>h</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>f</name><arg><funapp><name>g</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>h</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><trs><rules><rule><lhs><funapp><name>g</name><arg><funapp><name>a</name></funapp></arg></funapp></lhs><rhs><funapp><name>g</name><arg><funapp><name>g</name><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><relativeTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><matrices><dimension>2</dimension><strictDimension>1</strictDimension><domain><naturals/></domain></matrices></domain><degree>1</degree></polynomial></type><interpret><name>f</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a</name><arity>0</arity><polynomial><sum><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>g</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>h</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules/></trs><trs><rules><rule><lhs><funapp><name>g</name><arg><funapp><name>a</name></funapp></arg></funapp></lhs><rhs><funapp><name>g</name><arg><funapp><name>g</name><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><relativeTerminationProof><rIsEmpty/></relativeTerminationProof></ruleRemoval></relativeTerminationProof></ruleRemoval></relativeTerminationProof><ruleLabeling><ruleLabelingFunction><ruleLabelingFunctionEntry><rule><lhs><funapp><name>f</name><arg><funapp><name>g</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>h</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><label>0</label></ruleLabelingFunctionEntry><ruleLabelingFunctionEntry><rule><lhs><funapp><name>g</name><arg><funapp><name>a</name></funapp></arg></funapp></lhs><rhs><funapp><name>g</name><arg><funapp><name>g</name><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></rhs></rule><label>2</label></ruleLabelingFunctionEntry><ruleLabelingFunctionEntry><rule><lhs><funapp><name>h</name><arg><funapp><name>a</name></funapp></arg><arg><funapp><name>a</name></funapp></arg></funapp></lhs><rhs><funapp><name>g</name><arg><funapp><name>g</name><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></rhs></rule><label>0</label></ruleLabelingFunctionEntry></ruleLabelingFunction><joinableCriticalPairs><joinableCriticalPair><rewriteSequence><startTerm><funapp><name>f</name><arg><funapp><name>g</name><arg><funapp><name>g</name><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></arg></funapp></startTerm></rewriteSequence><rewriteSequence><startTerm><funapp><name>f</name><arg><funapp><name>h</name><arg><funapp><name>a</name></funapp></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></startTerm><rewriteStep><positionInTerm><position>1</position></positionInTerm><rule><lhs><funapp><name>h</name><arg><funapp><name>a</name></funapp></arg><arg><funapp><name>a</name></funapp></arg></funapp></lhs><rhs><funapp><name>g</name><arg><funapp><name>g</name><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></rhs></rule><funapp><name>f</name><arg><funapp><name>g</name><arg><funapp><name>g</name><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></arg></funapp></rewriteStep></rewriteSequence></joinableCriticalPair></joinableCriticalPairs></ruleLabeling></decreasingDiagrams></crProof></proof><origin><proofOrigin><tool><name>csi</name><version>csi 1.2.5 [hg: unknown]</version><strategy>(if left-linear then (cr  -dup;(( lpo -quasi || (matrix -dim 1 -ib 3 -ob 4 | matrix -dim 2 -ib 2 -ob 2 | matrix -dim 3 -ib 1 -ob 2 | arctic -dim 2 -ib 2 -ob 2) || (if duplicating then fail else (bounds -rt || bounds -rt -qc))[1] || poly -ib 2 -ob 4 -nl2 -heuristic 1 || fail )[5]*);shift -lstar);(rule_labeling | rule_labeling -left)?;decreasing else fail)!</strategy></tool></proofOrigin></origin></certificationProblem>