details

property	value
status	complete
benchmark	z01.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n147.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	AProVE23
configuration	certified
runtime (wallclock)	65.7162158489 seconds
cpu usage	205.668379804
max memory	6.839332864E9

stage attributes

key	value
certification-result	CERTIFIED
starexec-result	YES
certification-time	0.02

output

/export/starexec/sandbox/solver/bin/starexec_run_certified /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- 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><funapp><name>f</name></funapp></arg><arg><funapp><name>a</name><arg><funapp><name>f</name></funapp></arg><arg><funapp><name>a</name><arg><funapp><name>g</name></funapp></arg><arg><funapp><name>a</name><arg><funapp><name>g</name></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a</name><arg><funapp><name>g</name></funapp></arg><arg><funapp><name>a</name><arg><funapp><name>g</name></funapp></arg><arg><funapp><name>a</name><arg><funapp><name>g</name></funapp></arg><arg><funapp><name>a</name><arg><funapp><name>f</name></funapp></arg><arg><funapp><name>a</name><arg><funapp><name>f</name></funapp></arg><arg><funapp><name>a</name><arg><funapp><name>f</name></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><uncurry><uncurryInformation><name>a</name><uncurriedSymbols><uncurriedSymbolEntry><name>f</name><arity>0</arity><name>f</name><name>f1</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>g</name><arity>0</arity><name>g</name><name>g1</name></uncurriedSymbolEntry></uncurriedSymbols><uncurryRules><rules><rule><lhs><funapp><name>a</name><arg><funapp><name>f</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>f1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a</name><arg><funapp><name>g</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>g1</name><arg><var>y1</var></arg></funapp></rhs></rule></rules></uncurryRules><etaRules><rules/></etaRules></uncurryInformation><trs><rules><rule><lhs><funapp><name>f1</name><arg><funapp><name>f1</name><arg><funapp><name>g1</name><arg><funapp><name>g1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>g1</name><arg><funapp><name>g1</name><arg><funapp><name>g1</name><arg><funapp><name>f1</name><arg><funapp><name>f1</name><arg><funapp><name>f1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a</name><arg><funapp><name>f</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>f1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a</name><arg><funapp><name>g</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>g1</name><arg><var>y1</var></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>f1</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>g1</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>a</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>f</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>g</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>f1</name><arg><funapp><name>f1</name><arg><funapp><name>g1</name><arg><funapp><name>g1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>g1</name><arg><funapp><name>g1</name><arg><funapp><name>g1</name><arg><funapp><name>f1</name><arg><funapp><name>f1</name><arg><funapp><name>f1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><switchInnermost><wcrProof><joinableCriticalPairsBFS>10</joinableCriticalPairsBFS></wcrProof><trsTerminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><name>f1</name></sharp><arg><funapp><name>f1</name><arg><funapp><name>g1</name><arg><funapp><name>g1</name><arg><var>x</var></arg></f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/lhs><rhs><funapp><sharp><name>f1</name></sharp><arg><funapp><name>f1</name><arg><funapp><name>g1</name><arg><funapp><name>g1</name><arg><var>y_0</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f1</name></sharp><arg><funapp><name>f1</name><arg><funapp><name>g1</name><arg><funapp><name>g1</name><arg><funapp><name>f1</name><arg><funapp><name>g1</name><arg><funapp><name>g1</name><arg><funapp><name>f1</name><arg><funapp><name>g1</name><arg><funapp><name>g1</name><arg><var>y_0</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f1</name></sharp><arg><funapp><name>f1</name><arg><funapp><name>g1</name><arg><funapp><name>g1</name><arg><funapp><name>f1</name><arg><funapp><name>g1</name><arg><funapp><name>g1</name><arg><var>y_0</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></instantiations><usableRules><rules/></usableRules><dpProof><redPairProc><orderingConstraintProof><redPair><interpretation><type><matrixInterpretation><domain><arctic><domain><naturals/></domain></arctic></domain><dimension>4</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><sharp><name>f1</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><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><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><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>f1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>1</integer></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><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><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><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>g1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><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><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><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><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>f1</name></sharp><arg><funapp><name>f1</name><arg><funapp><name>g1</name><arg><funapp><name>g1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f1</name></sharp><arg><funapp><name>f1</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f1</name></sharp><arg><funapp><name>f1</name><arg><funapp><name>g1</name><arg><funapp><name>g1</name><arg><funapp><name>f1</name><arg><funapp><name>g1</name><arg><funapp><name>g1</name><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f1</name></sharp><arg><funapp><name>f1</name><arg><funapp><name>g1</name><arg><funapp><name>g1</name><arg><funapp><name>g1</name><arg><funapp><name>f1</name><arg><funapp><name>f1</name><arg><funapp><name>f1</name><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f1</name></sharp><arg><funapp><name>f1</name><arg><funapp><name>g1</name><arg><funapp><name>g1</name><arg><funapp><name>f1</name><arg><funapp><name>g1</name><arg><funapp><name>g1</name><arg><var>y_0</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f1</name></sharp><arg><funapp><name>f1</name><arg><funapp><name>g1</name><arg><funapp><name>g1</name><arg><var>y_0</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><dpProof><redPairProc><orderingConstraintProof><redPair><interpretation><type><matrixInterpretation><domain><arctic><domain><naturals/></domain></arctic></domain><dimension>4</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><sharp><name>f1</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient><coefficient><minusInfinity/></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><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><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>f1</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><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><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>g1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>1</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><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><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>f1</name></sharp><arg><funapp><name>f1</name><arg><funapp><name>g1</name><arg><funapp><name>g1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f1</name></sharp><arg><funapp><name>f1</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><dpProof><semlabProc><model><finiteModel><carrierSize>2</carrierSize><interpret><name>f1</name><arity>1</arity><arithFunction><sum><arithFunction><natural>1</natural></arithFunction><arithFunction><product><arithFunction><natural>1</natural></arithFunction><arithFunction><variable>1</variable></arithFunction></product></arithFunction></sum></arithFunction></interpret><interpret><name>g1</name><arity>1</arity><arithFunction><natural>0</natural></arithFunction></interpret><interpret><sharp><name>f1</name></sharp><arity>1</arity><arithFunction><natural>0</natural></arithFunction></interpret></finiteModel></model><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>f1</name></sharp><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>f1</name></sharp><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>f1</name></sharp><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g1</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>f1</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f1</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><labeledSymbol><name>f1</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>g1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g1</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f1</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f1</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g1</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>g1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f1</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f1</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><innermostLhss><funapp><labeledSymbol><name>f1</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp><funapp><labeledSymbol><name>f1</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g1</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></innermostLhss><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>f1</name></sharp><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>f1</name></sharp><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x</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><labeledSymbol><sharp><name>f1</name></sharp><numberLabel><number>1</number></numberLabel></labeledSymbol><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><labeledSymbol><name>f1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><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><labeledSymbol><name>g1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><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/></dps><trs><rules/></trs><usableRules><rules/></usableRules><dpProof><pIsEmpty/></dpProof></monoRedPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>f1</name></sharp><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g1</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g1</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>f1</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f1</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></semlabProc></dpProof></redPairProc></dpProof></redPairProc></dpProof></forwardInstantiationProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>f1</name></sharp><arg><funapp><name>f1</name><arg><funapp><name>g1</name><arg><funapp><name>g1</name><arg><funapp><name>g1</name><arg><funapp><name>g1</name><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f1</name></sharp><arg><funapp><name>g1</name><arg><funapp><name>g1</name><arg><funapp><name>g1</name><arg><funapp><name>f1</name><arg><funapp><name>f1</name><arg><funapp><name>f1</name><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></narrowingProc></dpProof></dpTrans></trsTerminationProof></switchInnermost></trsTerminationProof></ruleRemoval></trsTerminationProof></uncurry></trsTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished </version><strategy>Statistics for single proof: 100.00 % (13 real / 0 unknown / 0 assumptions / 13 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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