details

property	value
status	complete
benchmark	Ex24_Luc06_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n124.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	19.9982 seconds
cpu usage	45.6319
user time	44.3126
system time	1.31926
max virtual memory	3.7265144E7
max residence set size	3898968.0

stage attributes

key	value
certification-result	CERTIFIED
output-size	171162
starexec-result	YES
certification-time	0.4

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>active</name><arg><funapp><name>f</name><arg><funapp><name>b</name></funapp></arg><arg><var>X</var></arg><arg><funapp><name>c</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>f</name><arg><var>X</var></arg><arg><funapp><name>c</name></funapp></arg><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>c</name></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>b</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><var>X1</var></arg><arg><funapp><name>active</name><arg><var>X2</var></arg></funapp></arg><arg><var>X3</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><var>X1</var></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg><arg><var>X3</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>b</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>b</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>c</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>c</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><strategy><innermost/></strategy></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>f</name><arg><funapp><name>b</name></funapp></arg><arg><var>X</var></arg><arg><funapp><name>c</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>X</var></arg><arg><funapp><name>c</name></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>X1</var></arg><arg><funapp><name>active</name><arg><var>X2</var></arg></funapp></arg><arg><var>X3</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>active</name></sharp><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><var>X1</var></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg><arg><var>X3</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>proper</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>proper</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>proper</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>proper</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>proper</name></sharp><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>proper</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>proper</name></sharp><arg><var>X3</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>proper</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>active</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>proper</name><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>b</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>b</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>c</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>c</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><var>X1</var></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg><arg><var>X3</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>f</name><arg><funapp><name>b</name></funapp></arg><arg><var>X</var></arg><arg><funapp><name>c</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>f</name><arg><var>X</var></arg><arg><funapp><name>c</name></funapp></arg><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>c</name></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>b</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><var>X1</var></arg><arg><funapp><name>active</name><arg><var>X2</var></arg></funapp></arg><arg><var>X3</var></arg></funapp></rhs></rule></rules></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>active</name><arg><funapp><name>c</name></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp><funapp><name>f</name><arg><var>x0</var></arg><arg><funapp><name>mark</name><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp><funapp><name>proper</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp><funapp><name>proper</name><arg><funapp><name>b</name></funapp></arg></funapp><funapp><name>proper</name><arg><funapp><name>c</name></funapp></arg></funapp><funapp><name>f</name><arg><funapp><name>ok</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>x2</var></arg></funapp></arg></funapp></innermostLhss><dpProof><narrowingProc><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><positionInTerm><position>1</position></positionInTerm><narrowings><rules><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>f</name><arg><funapp><name>b</name></funapp></arg><arg><var>x0</var></arg><arg><funapp><name>c</name></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><funapp><name>c</name></funapp></arg><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>c</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><funapp><name>b</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><funapp><name>active</name><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule></rules></narrowings><dpProof><narrowingProc><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><positionInTerm><position>1</position></positionInTerm><narrowings><rules><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>f</name><arg><funapp><name>proper</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><funapp><name>b</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>b</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><funapp><name>c</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>c</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></narrowings><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>f</name><arg><funapp><name>proper</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>f</name><arg><funapp><name>b</name></funapp></arg><arg><var>x0</var></arg><arg><funapp><name>c</name></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><funapp><name>c</name></funapp></arg><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><funapp><name>active</name><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><redPairProc><orderingConstraintProof><redPair><interpretation><type><matrixInterpretation><domain><integers/></domain><dimension>2</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><sharp><name>top</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><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><name>mark</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><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></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>f</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>proper</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><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></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>ok</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><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></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>b</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>active</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><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></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</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>top</name></sharp><arg><funapp><name>mark</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>f</name><arg><funapp><name>proper</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><funapp><name>active</name><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><dpProof><semlabProc><model><finiteModel><carrierSize>2</carrierSize><interpret><name>active</name><arity>1</arity><arithFunction><natural>0</natural></arithFunction></interpret><interpret><name>b</name><arity>0</arity><arithFunction><natural>1</natural></arithFunction></interpret><interpret><name>c</name><arity>0</arity><arithFunction><natural>0</natural></arithFunction></interpret><interpret><name>proper</name><arity>1</arity><arithFunction><natural>0</natural></arithFunction></interpret><interpret><name>f</name><arity>3</arity><arithFunction><product><arithFunction><natural>1</natural></arithFunction><arithFunction><variable>2</variable></arithFunction></product></arithFunction></interpret><interpret><sharp><name>top</name></sharp><arity>1</arity><arithFunction><natural>0</natural></arithFunction></interpret><interpret><name>ok</name><arity>1</arity><arithFunction><natural>0</natural></arithFunction></interpret><interpret><name>mark</name><arity>1</arity><arithFunction><natural>0</natural></arithFunction></interpret></finiteModel></model><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></n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umber>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>f</name><numberLabel><number>0</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>proper</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>ok</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>active</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>f</name><numberLabel><number>0</number><number>0</number><number>1</number></numberLabel></labeledSymbol><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>ok</name><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>f</name><numberLabel><number>0</number><number>1</number><number>0</number></numberLabel></labeledSymbol><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>active</name><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>f</name><numberLabel><number>0</number><number>1</number><number>1</number></numberLabel></labeledSymbol><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number><number>1</number></numberLabel></labeledSymbol><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number><number>0</number></numberLabel></labeledSymbol><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number><number>1</number></numberLabel></labeledSymbol><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>proper</name><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>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><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><labeledSymbol><name>c</name><numberLabel/></labeledSymbol><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>b</name><numberLabel/></labeledSymbol><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><dpProof><redPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><labeledSymbol><sharp><name>top</name></sharp><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>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><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><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>proper</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>ok</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>active</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>f</name><numberLabel><number>0</number><number>0</number><number>1</number></numberLabel></labeledSymbol><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>ok</name><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>f</name><numberLabel><number>0</number><number>1</number><number>0</number></numberLabel></labeledSymbol><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>active</name><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>f</name><numberLabel><number>0</number><number>1</number><number>1</number></numberLabel></labeledSymbol><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number><number>1</number></numberLabel></labeledSymbol><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number><number>0</number></numberLabel></labeledSymbol><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number><number>1</number></numberLabel></labeledSymbol><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>proper</name><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>c</name><numberLabel/></labeledSymbol><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>b</name><numberLabel/></labeledSymbol><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><dpProof><redPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><labeledSymbol><sharp><name>top</name></sharp><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>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number><number>1</number></numberLabel></labeledSymbol><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number><number>0</number></numberLabel></labeledSymbol><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number><number>1</number></numberLabel></labeledSymbol><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number><number>1</number></numberLabel></labeledSymbol><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number><number>0</number></numberLabel></labeledSymbol><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number><number>1</number></numberLabel></labeledSymbol><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>b</name><numberLabel/></labeledSymbol><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>c</name><numberLabel/></labeledSymbol><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg><arg><var>X3</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg><arg><var>X3</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</v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ostLhssRemovalProc><innermostLhss><funapp><name>f</name><arg><var>x0</var></arg><arg><funapp><name>mark</name><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp><funapp><name>f</name><arg><funapp><name>ok</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>x2</var></arg></funapp></arg></funapp></innermostLhss><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>proper</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>proper</name></sharp><arg><var>X2</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>proper</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>proper</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>proper</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>proper</name></sharp><arg><var>X3</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>f</name><arg><funapp><name>b</name></funapp></arg><arg><var>X</var></arg><arg><funapp><name>c</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>X</var></arg><arg><funapp><name>c</name></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>X1</var></arg><arg><funapp><name>active</name><arg><var>X2</var></arg></funapp></arg><arg><var>X3</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>proper</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X3</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><var>X1</var></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg><arg><var>X3</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss/><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge><edge><position>2</position><strict>true</strict><position>2</position></edge><edge><position>3</position><strict>true</strict><position>3</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>f</name></sharp><arg><var>X1</var></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg><arg><var>X3</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></rhs></rule><edge><position>1</position><strict>false</strict><position>1</position></edge><edge><position>2</position><strict>true</strict><position>2</position></edge><edge><position>3</position><strict>false</strict><position>3</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component></depGraphProc></dpProof></dpTrans></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 % (23 real / 0 unknown / 0 assumptions / 23 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 TRS_Innermost Certified 2019-04-01 06.48