details

property	value
status	complete
benchmark	size-12-alpha-3-num-86.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n093.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	12.8834 seconds
cpu usage	46.6998
user time	45.123
system time	1.57677
max virtual memory	6.1223016E7
max residence set size	4312944.0

stage attributes

key	value
certification-result	CERTIFIED
output-size	26462
starexec-result	YES
certification-time	0.1

output

YES <?xml version="1.0" encoding="UTF-8" standalone="no"?><?xml-stylesheet type="text/xsl" href="cpfHTML.xsl"?><certificationProblem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="cpf.xsd"><input><trsInput><trs><rules><rule><lhs><funapp><name>a</name><arg><var>x1</var></arg></funapp></lhs><rhs><var>x1</var></rhs></rule><rule><lhs><funapp><name>a</name><arg><funapp><name>a</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>b</name><arg><funapp><name>a</name><arg><funapp><name>c</name><arg><funapp><name>b</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>b</name><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><name>c</name><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>b</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a</name><arg><var>x1</var></arg></funapp></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><stringReversal><trs><rules><rule><lhs><funapp><name>a</name><arg><var>x1</var></arg></funapp></lhs><rhs><var>x1</var></rhs></rule><rule><lhs><funapp><name>a</name><arg><funapp><name>a</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>b</name><arg><funapp><name>c</name><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>b</name><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><name>c</name><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>b</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a</name><arg><var>x1</var></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><name>a</name></sharp><arg><funapp><name>a</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>b</name></sharp><arg><funapp><name>c</name><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a</name></sharp><arg><funapp><name>a</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>c</name></sharp><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a</name></sharp><arg><funapp><name>a</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a</name></sharp><arg><funapp><name>b</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a</name></sharp><arg><funapp><name>a</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>b</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>b</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>c</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>c</name></sharp><arg><funapp><name>b</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><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>a</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><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>a</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>b</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>c</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><minusInfinity/></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><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></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>b</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><minusInfinity/></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><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</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><sharp><name>c</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><minusInfinity/></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>a</name></sharp><arg><funapp><name>a</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>b</name></sharp><arg><funapp><name>c</name><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a</name></sharp><arg><funapp><name>a</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>c</name></sharp><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a</name></sharp><arg><funapp><name>a</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>b</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>b</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>c</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>c</name></sharp><arg><funapp><name>b</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><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>a</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>1</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>a</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><minusInfinity/></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>1</integer></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>b</name></sharp><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><minusInfinity/></coefficient></vector><vector><coefficient><integer>1</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>c</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><minusInfinity/></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><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient></vector><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></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>b</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>1</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><sharp><name>c</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><minusInfinity/></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>a</name></sharp><arg><funapp><name>a</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>b</name></sharp><arg><funapp><name>c</name><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a</name></sharp><arg><funapp><name>a</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>c</name></sharp><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a</name></sharp><arg><funapp><name>a</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>b</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>c</name></sharp><arg><funapp><name>b</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>a</name></sharp><arg><funapp><name>a</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>c</name></sharp><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>c</name></sharp><arg><funapp><name>b</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a</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>a</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>1</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>a</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>1</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>c</name></sharp><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>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>b</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><minusInfinity/></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>c</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><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><minusInfinity/></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></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>a</name></sharp><arg><funapp><name>a</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>c</name></sharp><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><dpProof><redPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>c</name></sharp><arity>1</arity><polynomial><coefficient><integer>-2</integer></coefficient></polynomial></interpret><interpret><name>a</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></sum></polynomial></interpret><interpret><name>b</name><arity>1</arity><polynomial><coefficient><integer>2</integer></coefficient></polynomial></interpret><interpret><name>c</name><arity>1</arity><polynomial><coefficient><integer>-2</integer></coefficient></polynomial></interpret><interpret><sharp><name>a</name></sharp><arity>1</arity><polynomial><coefficient><integer>1</integer></coefficient></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules/></dps><usableRules><rules/></usableRules><dpProof><pIsEmpty/></dpProof></redPairUrProc></dpProof></redPairProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>a</name></sharp><arg><funapp><name>a</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>b</name></sharp><arg><funapp><name>c</name><arg><funapp><name>a</name><arg><funapp><name>b</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>a</name></sharp><arg><funapp><name>a</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>b</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></redPairProc></dpProof></redPairProc></dpProof></dpTrans></trsTerminationProof></stringReversal></trsTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (8 real / 0 unknown / 0 assumptions / 8 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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all output return to SRS_Standard 2019-03-22 06.20