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>max</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>max</name><arg><funapp><name>0</name></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>y</var></rhs></rule><rule><lhs><funapp><name>max</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>max</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>max</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>max</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><crProof><decreasingDiagrams><relativeTerminationProof><rIsEmpty/></relativeTerminationProof><ruleLabeling><ruleLabelingFunction><ruleLabelingFunctionEntry><rule><lhs><funapp><name>max</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><label>1</label></ruleLabelingFunctionEntry><ruleLabelingFunctionEntry><rule><lhs><funapp><name>max</name><arg><funapp><name>0</name></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>y</var></rhs></rule><label>0</label></ruleLabelingFunctionEntry><ruleLabelingFunctionEntry><rule><lhs><funapp><name>max</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>max</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><label>0</label></ruleLabelingFunctionEntry><ruleLabelingFunctionEntry><rule><lhs><funapp><name>max</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>max</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><label>2</label></ruleLabelingFunctionEntry></ruleLabelingFunction><joinableCriticalPairs><joinableCriticalPair><rewriteSequence><startTerm><funapp><name>0</name></funapp></startTerm></rewriteSequence><rewriteSequence><startTerm><funapp><name>0</name></funapp></startTerm></rewriteSequence></joinableCriticalPair><joinableCriticalPair><rewriteSequence><startTerm><var>x</var></startTerm></rewriteSequence><rewriteSequence><startTerm><funapp><name>max</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></startTerm><rewriteStep><positionInTerm/><rule><lhs><funapp><name>max</name><arg><funapp><name>0</name></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>y</var></rhs></rule><var>x</var></rewriteStep></rewriteSequence></joinableCriticalPair><joinableCriticalPair><rewriteSequence><startTerm><funapp><name>0</name></funapp></startTerm></rewriteSequence><rewriteSequence><startTerm><funapp><name>0</name></funapp></startTerm></rewriteSequence></joinableCriticalPair><joinableCriticalPair><rewriteSequence><startTerm><var>y</var></startTerm></rewriteSequence><rewriteSequence><startTerm><funapp><name>max</name><arg><var>y</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></startTerm><rewriteStep><positionInTerm/><rule><lhs><funapp><name>max</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><var>y</var></rewriteStep></rewriteSequence></joinableCriticalPair><joinableCriticalPair><rewriteSequence><startTerm><funapp><name>s</name><arg><funapp><name>max</name><arg><var>x54</var></arg><arg><var>x55</var></arg></funapp></arg></funapp></startTerm><rewriteStep><positionInTerm><position>1</position></positionInTerm><rule><lhs><funapp><name>max</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>max</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><funapp><name>s</name><arg><funapp><name>max</name><arg><var>x55</var></arg><arg><var>x54</var></arg></funapp></arg></funapp></rewriteStep></rewriteSequence><rewriteSequence><startTerm><funapp><name>max</name><arg><funapp><name>s</name><arg><var>x55</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x54</var></arg></funapp></arg></funapp></startTerm><rewriteStep><positionInTerm/><rule><lhs><funapp><name>max</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>max</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><funapp><name>s</name><arg><funapp><name>max</name><arg><var>x55</var></arg><arg><var>x54</var></arg></funapp></arg></funapp></rewriteStep></rewriteSequence></joinableCriticalPair><joinableCriticalPair><rewriteSequence><startTerm><funapp><name>max</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></startTerm><rewriteStep><positionInTerm/><rule><lhs><funapp><name>max</name><arg><funapp><name>0</name></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>y</var></rhs></rule><var>x</var></rewriteStep></rewriteSequence><rewriteSequence><startTerm><var>x</var></startTerm></rewriteSequence></joinableCriticalPair><joinableCriticalPair><rewriteSequence><startTerm><funapp><name>max</name><arg><var>y</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></startTerm><rewriteStep><positionInTerm/><rule><lhs><funapp><name>max</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><var>y</var></rewriteStep></rewriteSequence><rewriteSequence><startTerm><var>y</var></startTerm></rewriteSequence></joinableCriticalPair><joinableCriticalPair><rewriteSequence><startTerm><funapp><name>max</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></startTerm><rewriteStep><positionInTerm/><rule><lhs><funapp><name>max</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>max</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><funapp><name>s</name><arg><funapp><name>max</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></arg></funapp></rewriteStep></rewriteSequence><rewriteSequence><startTerm><funapp><name>s</name><arg><funapp><name>max</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></startTerm><rewriteStep><positionInTerm><position>1</position></positionInTerm><rule><lhs><funapp><name>max</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>max</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><funapp><name>s</name><arg><funapp><name>max</name><arg><var>y</var></arg><arg><var>x</var></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 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>