details

property	value
status	complete
benchmark	pi.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	Waldmann_06_SRS

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	8.61702 seconds
cpu usage	30.8127
user time	29.5211
system time	1.29155
max virtual memory	4.06892E7
max residence set size	3449220.0

stage attributes

key	value
certification-result	CERTIFIED
starexec-result	CERTIFIED YES
certification-time	0.62
bare-result	YES

output

<?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" 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rule><lhs><funapp><sharp><name>2</name></sharp><arg><funapp><name>6</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>2</name><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>2</name></sharp><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>7</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>5</name></sharp><arg><funapp><name>0</name><arg><funapp><name>2</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>2</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>8</name></sharp><arg><funapp><name>8</name><arg><funapp><name>4</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>7</name></sharp><arg><funapp><name>1</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>9</name></sharp><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>5</name></sharp><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>5</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><monoRedPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>9</name><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><sharp><name>5</name></sharp><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><dps><rules><rule><lhs><funapp><sharp><name>5</name></sharp><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>5</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><trs><rules/></trs><usableRules><rules/></usableRules><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>5</name></sharp><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>5</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></monoRedPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>5</name></sharp><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>2</name></sharp><arg><funapp><name>6</name><arg><funapp><name>5</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>8</name></sharp><arg><funapp><name>8</name><arg><funapp><name>4</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>5</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>8</name></sharp><arg><funapp><name>9</name><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>5</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>9</name></sharp><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>2</name></sharp><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>2</name></sharp><arg><funapp><name>6</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>5</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>7</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>7</name></sharp><arg><funapp><name>1</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>2</name><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>2</name></sharp><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>7</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>9</name></sharp><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>2</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><monoRedPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>3</name><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><name>1</name><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><name>4</name><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><name>5</name><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><name>8</name><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><name>9</name><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><name>7</name><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><name>2</name><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><name>6</name><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><name>0</name><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><sharp><name>9</name></sharp><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><sharp><name>8</name></sharp><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><sharp><name>3</name></sharp><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><sharp><name>2</name></sharp><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><sharp><name>7</name></sharp><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><dps><rules><rule><lhs><funapp><sharp><name>8</name></sharp><arg><funapp><name>8</name><arg><funapp><name>4</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>5</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>8</name></sharp><arg><funapp><name>9</name><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>5</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>9</name></sharp><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>2</name></sharp><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>2</name></sharp><arg><funapp><name>6</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>5</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>7</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>7</name></sharp><arg><funapp><name>1</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>2</name><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>2</name></sharp><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>7</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>9</name></sharp><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>2</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>3</name><arg><funapp><name>1</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>4</name><arg><funapp><name>1</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>3</name><arg><funapp><name>5</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>8</name><arg><funapp><name>9</name><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>3</name><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>3</name><arg><funapp><name>2</name><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>3</name><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>9</name><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>9</name><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><name>3</name><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>7</name><arg><funapp><name>1</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>6</name><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>7</name><arg><funapp><name>5</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>0</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>2</name><arg><funapp><name>6</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>4</name><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>9</name><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><name>5</name><arg><funapp><name>0</name><arg><funapp><name>2</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>8</name><arg><funapp><name>4</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>6</name><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>8</name><arg><funapp><name>8</name><arg><funapp><name>4</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>3</name><arg><funapp><name>1</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>4</name><arg><funapp><name>1</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>3</name><arg><funapp><name>5</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>8</name><arg><funapp><name>9</name><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>3</name><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>3</name><arg><funapp><name>2</name><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>3</name><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>9</name><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>9</name><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><name>3</name><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>7</name><arg><funapp><name>1</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>6</name><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>7</name><arg><funapp><name>5</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>0</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>2</name><arg><funapp><name>6</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>4</name><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>9</name><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><name>5</name><arg><funapp><name>0</name><arg><funapp><name>2</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>8</name><arg><funapp><name>4</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>6</name><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>8</name><arg><funapp><name>8</name><arg><funapp><name>4</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><redPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>8</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>8</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>4</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>9</name></sharp><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>4</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>3</name></sharp><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>4</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>2</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>3</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>5</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>9</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>7</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>2</name></sharp><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>4</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>6</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>7</name></sharp><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>4</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>5</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>8</name></sharp><arg><funapp><name>9</name><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>5</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>9</name></sharp><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>2</name></sharp><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>2</name></sharp><arg><funapp><name>6</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>5</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>7</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>7</name></sharp><arg><funapp><name>1</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>2</name><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>2</name></sharp><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>7</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>9</name></sharp><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>2</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>3</name><arg><funapp><name>1</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>4</name><arg><funapp><name>1</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>3</name><arg><funapp><name>5</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>8</name><arg><funapp><name>9</name><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>3</name><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>9</name><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>9</name><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><name>3</name><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>3</name><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>3</name><arg><funapp><name>2</name><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>2</name><arg><funapp><name>6</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>4</name><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>9</name><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><name>5</name><arg><funapp><name>0</name><arg><funapp><name>2</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>8</name><arg><funapp><name>8</name><arg><funapp><name>4</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>8</name><arg><funapp><name>4</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>6</name><arg><var>x1</var></arg></funapp></rhs></rule></rules></usableRules><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>5</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>9</name></sharp><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>5</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>7</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>7</name></sharp><arg><funapp><name>1</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>2</name></sharp><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>2</name></sharp><arg><funapp><name>6</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>2</name><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>2</name></sharp><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>7</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>9</name></sharp><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>2</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><redPairProc><orderingConstraintProof><redPair><interpretation><type><matrixInterpretation><domain><arctic><domain><naturals/></domain></arctic></domain><dimension>3</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><sharp><name>3</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>5</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></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><minusInfinity/></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>9</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>7</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>2</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>3</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>7</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><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><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>2</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>6</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><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><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>8</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>9</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>4</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>5</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>9</name></sharp><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>5</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>7</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>2</name></sharp><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>2</name></sharp><arg><funapp><name>6</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>2</name><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>2</name></sharp><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>7</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>9</name></sharp><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>2</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>5</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>9</name></sharp><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>2</name></sharp><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>2</name></sharp><arg><funapp><name>6</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>2</name><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>2</name></sharp><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>9</name></sharp><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>2</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><redPairProc><orderingConstraintProof><redPair><interpretation><type><matrixInterpretation><domain><arctic><domain><naturals/></domain></arctic></domain><dimension>3</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><sharp><name>9</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>3</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>2</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>3</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>5</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>7</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><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><minusInfinity/></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>2</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>6</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></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><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>8</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>9</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><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>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>4</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></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><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>5</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>9</name></sharp><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>2</name></sharp><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>2</name><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>2</name></sharp><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>9</name></sharp><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>2</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>5</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>9</name></sharp><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>2</name><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>9</name></sharp><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><redPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>3</name></sharp><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><name>5</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>9</name></sharp><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><name>7</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>2</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>3</name><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><name>8</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>9</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>6</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>4</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>2</name><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>2</name><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><redPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>3</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>8</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>5</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>2</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>7</name><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><name>1</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>6</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>9</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>5</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>4</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>3</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules/></dps><usableRules><rules><rule><lhs><funapp><name>7</name><arg><funapp><name>1</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>6</name><arg><funapp><name>9</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>7</name><arg><funapp><name>5</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>0</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>2</name><arg><funapp><name>6</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>4</name><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><pIsEmpty/></dpProof></redPairUrProc></dpProof></component></depGraphProc></dpProof></redPairProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>2</name></sharp><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>2</name></sharp><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>2</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></redPairProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>5</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>7</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>8</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>7</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></redPairProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>3</name></sharp><arg><funapp><name>5</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>8</name></sharp><arg><funapp><name>9</name><arg><funapp><name>7</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></redPairUrProc></dpProof></monoRedPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>9</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>5</name></sharp><arg><funapp><name>0</name><arg><funapp><name>2</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></dpTrans></trsTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (15 real / 0 unknown / 0 assumptions / 15 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> popout

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