details

property	value
status	complete
benchmark	dup01.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n150.star.cs.uiowa.edu
space	Trafo_06

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	9.45238 seconds
cpu usage	33.4157
user time	31.5995
system time	1.81619
max virtual memory	6.3031832E7
max residence set size	4148292.0

stage attributes

key	value
certification-result	CERTIFIED
starexec-result	CERTIFIED YES
certification-time	0.68
bare-result	YES

output

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efficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>8</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a16</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>10</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a23</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a24</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>4</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a25</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>6</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a26</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>8</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a34</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a35</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>4</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a36</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>6</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a45</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a46</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>4</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a56</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>a34</name><arg><funapp><name>a34</name><arg><funapp><name>a12</name><arg><funapp><name>a12</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a12</name><arg><funapp><name>a12</name><arg><funapp><name>a34</name><arg><funapp><name>a34</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a45</name><arg><funapp><name>a45</name><arg><funapp><name>a12</name><arg><funapp><name>a12</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a12</name><arg><funapp><name>a12</name><arg><funapp><name>a45</name><arg><funapp><name>a45</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a56</name><arg><funapp><name>a56</name><arg><funapp><name>a12</name><arg><funapp><name>a12</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a12</name><arg><funapp><name>a12</name><arg><funapp><name>a56</name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me></sharp><arg><funapp><name>a34</name><arg><funapp><name>a56</name><arg><funapp><name>a56</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a56</name></sharp><arg><funapp><name>a56</name><arg><funapp><name>a34</name><arg><funapp><name>a34</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a34</name></sharp><arg><funapp><name>a56</name><arg><funapp><name>a56</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a56</name></sharp><arg><funapp><name>a56</name><arg><funapp><name>a34</name><arg><funapp><name>a34</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a56</name></sharp><arg><funapp><name>a56</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a56</name></sharp><arg><funapp><name>a56</name><arg><funapp><name>a34</name><arg><funapp><name>a34</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a56</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>a56</name></sharp><arg><funapp><name>a56</name><arg><funapp><name>a12</name><arg><funapp><name>a12</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a56</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a56</name></sharp><arg><funapp><name>a56</name><arg><funapp><name>a12</name><arg><funapp><name>a12</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a56</name></sharp><arg><funapp><name>a56</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a56</name></sharp><arg><funapp><name>a56</name><arg><funapp><name>a23</name><arg><funapp><name>a23</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a56</name></sharp><arg><funapp><name>a56</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a56</name></sharp><arg><funapp><name>a56</name><arg><funapp><name>a23</name><arg><funapp><name>a23</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a56</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a56</name></sharp><arg><funapp><name>a56</name><arg><funapp><name>a34</name><arg><funapp><name>a34</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a56</name></sharp><arg><funapp><name>a56</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a56</name></sharp><arg><funapp><name>a56</name><arg><funapp><name>a34</name><arg><funapp><name>a34</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a56</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>a56</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>a12</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>a23</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>a34</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>a56</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>a56</name></sharp><arg><funapp><name>a56</name><arg><funapp><name>a12</n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</arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a12</name><arg><funapp><name>a12</name><arg><funapp><name>a34</name><arg><funapp><name>a34</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><monoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>a56</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>a12</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>a23</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>a34</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>a56</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></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>a56</name></sharp><arg><funapp><name>a56</name><arg><funapp><name>a12</name><arg><funapp><name>a12</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a56</name></sharp><arg><funapp><name>a56</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a56</name></sharp><arg><funapp><name>a56</name><arg><funapp><name>a23</name><arg><funapp><name>a23</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a56</name></sharp><arg><funapp><name>a56</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a56</name></sharp><arg><funapp><name>a56</name><arg><funapp><name>a34</name><arg><funapp><name>a34</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a56</name></sharp><arg><funapp><name>a56</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>a56</name><arg><funapp><name>a56</name><arg><funapp><name>a12</name><arg><funapp><name>a12</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a12</name><arg><funapp><name>a12</name><arg><funapp><name>a56</name><arg><funapp><name>a56</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a56</name><arg><funapp><name>a56</name><arg><funapp><name>a23</name><arg><funapp><name>a23</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a23</name><arg><funapp><name>a23</name><arg><funapp><name>a56</name><arg><funapp><name>a56</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a56</name><arg><funapp><name>a56</name><arg><funapp><name>a34</name><arg><funapp><name>a34</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a34</name><arg><funapp><name>a34</name><arg><funapp><name>a56</name><arg><funapp><name>a56</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a34</name><arg><funapp><name>a34</name><arg><funapp><name>a12</name><arg><funapp><name>a12</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a12</name><arg><funapp><name>a12</name><arg><funapp><name>a34</name><arg><funapp><name>a34</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><dpProof><monoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>a56</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>a12</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>a23</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>a34</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><sharp><name>a56</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></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>a56</name></sharp><arg><funapp><name>a56</name><arg><funapp><name>a12</name><arg><funapp><name>a12</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a56</name></sharp><arg><funapp><name>a56</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a56</name></sharp><arg><funapp><name>a56</name><arg><funapp><name>a23</name><arg><funapp><name>a23</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a56</name></sharp><arg><funapp><name>a56</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>a56</name><arg><funapp><name>a56</name><arg><funapp><name>a12</name><arg><funapp><name>a12</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a12</name><arg><funapp><name>a12</name><arg><funapp><name>a56</name><arg><funapp><name>a56</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a56</name><arg><funapp><name>a56</name><arg><funapp><name>a23</name><arg><funapp><name>a23</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a23</name><arg><funapp><name>a23</name><arg><funapp><name>a56</name><arg><funapp><name>a56</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a34</name><arg><funapp><name>a34</name><arg><funapp><name>a12</name><arg><funapp><name>a12</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a12</name><arg><funapp><name>a12</name><arg><funapp><name>a34</name><arg><funapp><name>a34</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><dpProof><switchInnermostProc><wcrProof><joinableCriticalPairsBFS>20</joinableCriticalPairsBFS></wcrProof><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>a56</name><arg><funapp><name>a56</name><arg><funapp><name>a12</name><arg><funapp><name>a12</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a12</name><arg><funapp><name>a12</name><arg><funapp><name>a56</name><arg><funapp><name>a56</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a56</name><arg><funapp><name>a56</name><arg><funapp><name>a23</name><arg><funapp><name>a23</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a23</name><arg><funapp><name>a23</name><arg><funapp><name>a56</name><arg><funapp><name>a56</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>a56</name><arg><funapp><name>a56</name><arg><funapp><name>a12</name><arg><funapp><name>a12</name><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp><funapp><name>a56</name><arg><funapp><name>a56</name><arg><funapp><name>a23</name><arg><funapp><name>a23</name><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></innermostLhss><dpProof><redPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>a56</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>a56</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>a12</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>a23</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></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>a56</name></sharp><arg><funapp><name>a56</name><arg><funapp><name>a23</name><arg><funapp><name>a23</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a56</name></sharp><arg><funapp><name>a56</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><dpProof><monoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>a56</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>a12</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>a23</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>a56</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></interpretation></redPair></orderingConstraintProof><dps><rules/></dps><trs><rules><rule><lhs><funapp><name>a56</name><arg><funapp><name>a56</name><arg><funapp><name>a12</name><arg><funapp><name>a12</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a12</name><arg><funapp><name>a12</name><arg><funapp><name>a56</name><arg><funapp><name>a56</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><dpProof><pIsEmpty/></dpProof></monoRedPairProc></dpProof></redPairProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></switchInnermostProc></dpProof></monoRedPairProc></dpProof></monoRedPairProc></dpProof></monoRedPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>a56</name></sharp><arg><funapp><name>a56</name><arg><funapp><name>a34</name><arg><funapp><name>a34</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a34</name></sharp><arg><funapp><name>a34</name><arg><funapp><name>a56</name><arg><funapp><name>a56</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>a56</name></sharp><arg><funapp><name>a56</name><arg><funapp><name>a34</name><arg><funapp><name>a34</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a34</name></sharp><arg><funapp><name>a56</name><arg><funapp><name>a56</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>a34</name></sharp><arg><funapp><name>a34</name><arg><funapp><name>a12</name><arg><funapp><name>a12</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a34</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a34</name></sharp><arg><funapp><name>a34</name><arg><funapp><name>a12</name><arg><funapp><name>a12</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a34</name></sharp><arg><funapp><name>a34</name><arg><var>x1</var></arg></funapp></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>a34</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>a12</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>a34</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>a34</name></sharp><arg><funapp><name>a34</name><arg><funapp><name>a12</name><arg><funapp><name>a12</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a34</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a34</name></sharp><arg><funapp><name>a34</name><arg><funapp><name>a12</name><arg><funapp><name>a12</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a34</name></sharp><arg><funapp><name>a34</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>a34</name><arg><funapp><name>a34</name><arg><funapp><name>a12</name><arg><funapp><name>a12</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a12</name><arg><funapp><name>a12</name><arg><funapp><name>a34</name><arg><funapp><name>a34</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>a34</name><arg><funapp><name>a34</name><arg><funapp><name>a12</name><arg><funapp><name>a12</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a12</name><arg><funapp><name>a12</name><arg><funapp><name>a34</name><arg><funapp><name>a34</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><switchInnermostProc><wcrProof><joinableCriticalPairsBFS>20</joinableCriticalPairsBFS></wcrProof><dpProof><monoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>a34</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>a12</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>a34</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></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>a34</name></sharp><arg><funapp><name>a34</name><arg><funapp><name>a12</name><arg><funapp><name>a12</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a34</name></sharp><arg><funapp><name>a34</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>a34</name><arg><funapp><name>a34</name><arg><funapp><name>a12</name><arg><funapp><name>a12</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a12</name><arg><funapp><name>a12</name><arg><funapp><name>a34</name><arg><funapp><name>a34</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><dpProof><redPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>a34</name></sharp><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>-2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>a34</name><arity>1</arity><polynomial><variable>1</variable></polynomial></interpret><interpret><name>a12</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules/></dps><dpProof><pIsEmpty/></dpProof></redPairProc></dpProof></monoRedPairProc></dpProof></switchInnermostProc></dpProof></monoRedPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>a45</name></sharp><arg><funapp><name>a45</name><arg><funapp><name>a12</name><arg><funapp><name>a12</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a45</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a45</name></sharp><arg><funapp><name>a45</name><arg><funapp><name>a12</name><arg><funapp><name>a12</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a45</name></sharp><arg><funapp><name>a45</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a45</name></sharp><arg><funapp><name>a45</name><arg><funapp><name>a23</name><arg><funapp><name>a23</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a45</name></sharp><arg><funapp><name>a45</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a45</name></sharp><arg><funapp><name>a45</name><arg><funapp><name>a23</name><arg><funapp><name>a23</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a45</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>a45</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>a12</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>a23</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>a45</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>a45</name></sharp><arg><funapp><name>a45</name><arg><funapp><name>a12</name><arg><funapp><name>a12</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a45</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a45</name></sharp><arg><funapp><name>a45</name><arg><funapp><name>a12</name><arg><funapp><name>a12</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a45</name></sharp><arg><funapp><name>a45</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a45</name></sharp><arg><funapp><name>a45</name><arg><funapp><name>a23</name><arg><funapp><name>a23</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a45</name></sharp><arg><funapp><name>a45</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a45</name></sharp><arg><funapp><name>a45</name><arg><funapp><name>a23</name><arg><funapp><name>a23</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a45</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>a45</name><arg><funapp><name>a45</name><arg><funapp><name>a12</name><arg><funapp><name>a12</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a12</name><arg><funapp><name>a12</name><arg><funapp><name>a45</name><arg><funapp><name>a45</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a45</name><arg><funapp><name>a45</name><arg><funapp><name>a23</name><arg><funapp><name>a23</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a23</name><arg><funapp><name>a23</name><arg><funapp><name>a45</name><arg><funapp><name>a45</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>a45</name><arg><funapp><name>a45</name><arg><funapp><name>a12</name><arg><funapp><name>a12</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a12</name><arg><funapp><name>a12</name><arg><funapp><name>a45</name><arg><funapp><name>a45</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a45</name><arg><funapp><name>a45</name><arg><funapp><name>a23</name><arg><funapp><name>a23</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a23</name><arg><funapp><name>a23</name><arg><funapp><name>a45</name><arg><funapp><name>a45</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><switchInnermostProc><wcrProof><joinableCriticalPairsBFS>20</joinableCriticalPairsBFS></wcrProof><dpProof><monoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>a45</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>a12</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>a23</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>a45</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></interpretation></redPair></orderingConstraintProof><dps><rules/></dps><trs><rules><rule><lhs><funapp><name>a45</name><arg><funapp><name>a45</name><arg><funapp><name>a23</name><arg><funapp><name>a23</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a23</name><arg><funapp><name>a23</name><arg><funapp><name>a45</name><arg><funapp><name>a45</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><dpProof><pIsEmpty/></dpProof></monoRedPairProc></dpProof></switchInnermostProc></dpProof></monoRedPairUrProc></dpProof></component></depGraphProc></dpProof></dpTrans></trsTerminationProof></ruleRemoval></trsTerminationProof></stringReversal></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 % (22 real / 0 unknown / 0 assumptions / 22 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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