/export/starexec/sandbox/solver/bin/starexec_run_certified /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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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><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>f</name><arg><var>y</var></arg><arg><funapp><name>f</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><var>x</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>y</var></arg><arg><funapp><name>f</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><var>x</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpProof><forwardInstantiationProc><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><var>x</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>y</var></arg><arg><funapp><name>f</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><instantiations><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y_0</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><var>y_0</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><funapp><name>f</name><arg><var>y_0</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></instantiations><dpProof><forwardInstantiationProc><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><var>x</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><instantiations><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><var>y_0</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><var>y_0</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><var>y_0</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y_1</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><var>y_0</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y_1</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></instantiations><dpProof><redPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><rationals><delta><rational><numerator>3</numerator><denominator>256</denominator></rational></delta></rationals></domain><degree>1</degree></polynomial></type><interpret><sharp><name>f</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><rational><numerator>0</numerator><denominator>1</denominator></rational></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><rational><numerator>0</numerator><denominator>1</denominator></rational></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><rational><numerator>1</numerator><denominator>4</denominator></rational></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>f</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><rational><numerator>0</numerator><denominator>1</denominator></rational></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><rational><numerator>0</numerator><denominator>1</denominator></rational></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><rational><numerator>1</numerator><denominator>4</denominator></rational></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>a</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><rational><numerator>1</numerator><denominator>4</denominator></rational></coefficient></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><var>y_0</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><var>y_0</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><var>y_0</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y_1</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><var>y_0</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y_1</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><var>y_0</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><var>y_0</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><var>x1</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge><edge><position>2</position><strict>false</strict><position>2</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><var>y_0</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y_1</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><var>y_0</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y_1</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge><edge><position>2</position><strict>false</strict><position>2</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></redPairProc></dpProof></forwardInstantiationProc></dpProof></forwardInstantiationProc></dpProof></dpTrans></trsTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished
</version><strategy>Statistics for single proof: 100.00 % (5 real / 0 unknown / 0 assumptions / 5 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>