details

property	value
status	complete
benchmark	Ex6Recursor.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	Applicative_05

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	66.2015 seconds
cpu usage	123.5
user time	120.456
system time	3.0445
max virtual memory	1.880088E7
max residence set size	5314960.0

stage attributes

key	value
certification-result	CERTIFIED
starexec-result	CERTIFIED YES
certification-time	1.23
bare-result	YES

output

<?xml version="1.0" encoding="UTF-8" standalone="no"?><?xml-stylesheet type="text/xsl" href="cpfHTML.xsl"?><certificationProblem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="cpf.xsd"><input><trsInput><trs><rules><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>rec</name></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>rec</name></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>app</name><arg><var>f</var></arg><arg><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>rec</name></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><uncurry><uncurryInformation><name>app</name><uncurriedSymbols><uncurriedSymbolEntry><name>rec</name><arity>0</arity><name>rec</name><name>rec1</name><name>rec2</name><name>rec3</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>0</name><arity>0</arity><name>0</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>s</name><arity>0</arity><name>s</name><name>s1</name></uncurriedSymbolEntry></uncurriedSymbols><uncurryRules><rules><rule><lhs><funapp><name>app</name><arg><funapp><name>rec</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>rec1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>rec1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>rec3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><var>y1</var></arg></funapp></rhs></rule></rules></uncurryRules><etaRules><rules/></etaRules></uncurryInformation><trs><rules><rule><lhs><funapp><name>rec3</name><arg><var>f</var></arg><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>rec3</name><arg><var>f</var></arg><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>app</name><arg><var>f</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>rec</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>rec1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>rec1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>rec3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><var>y1</var></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><switchInnermost><wcrProof><joinableCriticalPairsBFS>10</joinableCriticalPairsBFS></wcrProof><trsTerminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><var>f</var></arg><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><var>f</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><var>f</var></arg><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><var>f</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><var>f</var></arg><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpProof><redPairProc><orderingConstraintProof><redPair><interpretation><type><matrixInterpretation><domain><arctic><domain><naturals/></domain></arctic></domain><dimension>1</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><sharp><name>rec3</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>3</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><vector><coefficient><integer>2</integer></coefficient></vector></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><vector><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>s1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><vector><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>app</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>app</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>rec3</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>3</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><vector><coefficient><integer>2</integer></coefficient></vector></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><vector><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>rec2</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>2</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>rec</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>3</integer></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>rec1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>3</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>s</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>3</integer></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><var>f</var></arg><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><var>f</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><var>f</var></arg><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></dps><dpProof><narrowingProc><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><var>f</var></arg><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><var>f</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><positionInTerm><position>1</position></positionInTerm><narrowings><rules><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec</name></funapp></arg><arg><var>y1</var></arg><arg><funapp><name>s1</name><arg><var>y2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec1</name><arg><funapp><name>s1</name><arg><var>y2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec</name></funapp></arg><arg><var>y1</var></arg><arg><var>y2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg><arg><funapp><name>s1</name><arg><var>y2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><funapp><name>s1</name><arg><var>y2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>y2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg><arg><funapp><name>s1</name><arg><var>y2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>y2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>s</name></funapp></arg><arg><var>y1</var></arg><arg><funapp><name>s1</name><arg><var>y2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>s</name></funapp></arg><arg><var>y1</var></arg><arg><var>y2</var></arg></funapp></arg></funapp></rhs></rule></rules></narrowings><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><var>f</var></arg><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg><arg><funapp><name>s1</name><arg><var>y2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><funapp><name>s1</name><arg><var>y2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>y2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg><arg><funapp><name>s1</name><arg><var>y2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>y2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><rewritingProc><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg><arg><funapp><name>s1</name><arg><var>y2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>y2</var></arg></funapp></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>1</position></positionInTerm><rule><lhs><funapp><name>rec3</name><arg><var>f</var></arg><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>app</name><arg><var>f</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>x0</var></arg><arg><funapp><name>s1</name><arg><var>y2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>y2</var></arg></funapp></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg><arg><funapp><name>s1</name><arg><var>y2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>x0</var></arg><arg><funapp><name>s1</name><arg><var>y2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>y2</var></arg></funapp></arg></funapp></rhs></rule><usableRules><rules><rule><lhs><funapp><name>rec3</name><arg><var>f</var></arg><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>app</name><arg><var>f</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>rec3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>rec</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>rec1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>rec1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>rec3</name><arg><var>f</var></arg><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule></rules></usableRules><dpProof><forwardInstantiationProc><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><var>f</var></arg><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><instantiations><rules><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_3</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_3</var></arg></funapp></arg></funapp></rhs></rule></rules></instantiations><usableRules><rules/></usableRules><dpProof><forwardInstantiationProc><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><instantiations><rules><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y_3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_3</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_3</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></instantiations><usableRules><rules/></usableRules><dpProof><narrowingProc><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg><arg><funapp><name>s1</name><arg><var>y2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><funapp><name>s1</name><arg><var>y2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>y2</var></arg></funapp></arg></funapp></rhs></rule><positionInTerm><position>2</position></positionInTerm><narrowings><rules><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>rec1</name><arg><var>y0</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec1</name><arg><var>y0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></narrowings><dpProof><rewritingProc><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>rec1</name><arg><var>y0</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec1</name><arg><var>y0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>2</position><position>1</position></positionInTerm><rule><lhs><funapp><name>app</name><arg><funapp><name>rec1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec1</name><arg><var>y0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec1</name><arg><var>y0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><usableRules><rules><rule><lhs><funapp><name>app</name><arg><funapp><name>rec1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></usableRules><dpProof><rewritingProc><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec1</name><arg><var>y0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>2</position></positionInTerm><rule><lhs><funapp><name>app</name><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>rec3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec1</name><arg><var>y0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec1</name><arg><var>y0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><usableRules><rules><rule><lhs><funapp><name>rec3</name><arg><var>f</var></arg><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>rec3</name><arg><var>f</var></arg><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>app</name><arg><var>f</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>rec3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>rec</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>rec1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>rec1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><var>y1</var></arg></funapp></rhs></rule></rules></usableRules><dpProof><narrowingProc><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg><arg><funapp><name>s1</name><arg><var>y2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>x0</var></arg><arg><funapp><name>s1</name><arg><var>y2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>y2</var></arg></funapp></arg></funapp></rhs></rule><positionInTerm><position>2</position></positionInTerm><narrowings><rules><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>y0</var></arg><arg><var>y1</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>y0</var></arg><arg><var>y1</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></narrowings><dpProof><rewritingProc><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>y0</var></arg><arg><var>y1</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>x1</var></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>1</position><position>2</position></positionInTerm><rule><lhs><funapp><name>rec3</name><arg><var>f</var></arg><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></rhs></rule><usableRules><rules><rule><lhs><funapp><name>rec3</name><arg><var>f</var></arg><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule></rules></usableRules><dpProof><rewritingProc><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>y0</var></arg><arg><var>y1</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>1</position><position>2</position></positionInTerm><rule><lhs><funapp><name>rec3</name><arg><var>f</var></arg><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>app</name><arg><var>f</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>y0</var></arg><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>y0</var></arg><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><usableRules><rules><rule><lhs><funapp><name>rec3</name><arg><var>f</var></arg><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>app</name><arg><var>f</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>rec3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>rec</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>rec1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>rec1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>rec3</name><arg><var>f</var></arg><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule></rules></usableRules><dpProof><rewritingProc><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>y0</var></arg><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>2</position><position>1</position></positionInTerm><rule><lhs><funapp><name>app</name><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>rec3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>y0</var></arg><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>rec3</name><arg><var>y0</var></arg><arg><var>y1</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>y0</var></arg><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>rec3</name><arg><var>y0</var></arg><arg><var>y1</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><usableRules><rules><rule><lhs><funapp><name>rec3</name><arg><var>f</var></arg><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>app</name><arg><var>f</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>rec3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>rec</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>rec1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>rec1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>rec3</name><arg><var>f</var></arg><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule></rules></usableRules><dpProof><rewritingProc><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>y0</var></arg><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>rec3</name><arg><var>y0</var></arg><arg><var>y1</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>2</position><position>1</position></positionInTerm><rule><lhs><funapp><name>rec3</name><arg><var>f</var></arg><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>app</name><arg><var>f</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>y0</var></arg><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>y0</var></arg><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>y0</var></arg><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>y0</var></arg><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><usableRules><rules><rule><lhs><funapp><name>rec3</name><arg><var>f</var></arg><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>app</name><arg><var>f</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>rec3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>rec</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>rec1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>rec1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>rec3</name><arg><var>f</var></arg><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule></rules></usableRules><dpProof><forwardInstantiationProc><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>x1</var></arg></funapp></rhs></rule><instantiations><rules><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><funapp><name>rec2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y_3</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y_3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><funapp><name>rec2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_3</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_3</var></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>3</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><sharp><name>rec3</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>s1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</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></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>rec1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>rec2</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>2</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>2</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><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>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>app</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>rec3</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>2</integer></coefficient><coefficient><integer>2</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>2</integer></coefficient><coefficient><integer>2</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>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><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>app</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>2</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>rec</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>3</integer></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>s</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_3</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y_3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_3</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_3</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec1</name><arg><var>y0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>y0</var></arg><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>y0</var></arg><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></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>3</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><sharp><name>rec3</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>s1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>rec1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>rec2</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><minusInfinity/></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>app</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>rec3</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>app</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</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>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>rec</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>s</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_3</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec1</name><arg><var>y0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>y0</var></arg><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>y0</var></arg><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></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>3</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><sharp><name>rec3</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>s1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>rec1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>2</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>rec2</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>app</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>rec3</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>2</integer></coefficient><coefficient><integer>2</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</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>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>app</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>rec</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>2</integer></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>s</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_3</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec1</name><arg><var>y0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>y0</var></arg><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>y0</var></arg><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><var>y1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></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>3</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><sharp><name>rec3</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>s1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>rec1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>rec2</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>3</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>3</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>3</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>3</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</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><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>3</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>app</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>rec3</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>3</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>3</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>3</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>3</integer></coefficient></vector><vector><coefficient><integer>3</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>3</integer></coefficient></vector><vector><coefficient><integer>3</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>3</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><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>3</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>3</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector><vector><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>app</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>3</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</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><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>3</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>rec</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>3</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>s</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><minusInfinity/></coefficient><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_3</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><var>y0</var></arg><arg><funapp><name>s1</name><arg><var>x2</var></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec1</name><arg><var>y0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><dpProof><redPairUrProc><orderingConstraintProof><redPair><knuthBendixOrder><w0>1</w0><precedenceWeight><precedenceWeightEntry><name>rec1</name><arity>1</arity><precedence>1</precedence><weight>1</weight></precedenceWeightEntry></precedenceWeight><argumentFilter><argumentFilterEntry><sharp><name>rec3</name></sharp><arity>3</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>rec1</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>rec2</name><arity>2</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><sharp><name>app</name></sharp><arity>2</arity><collapsing>1</collapsing></argumentFilterEntry></argumentFilter></knuthBendixOrder></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_3</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><usableRules><rules/></usableRules><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec2</name><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_3</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_3</var></arg></funapp></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>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_3</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_3</var></arg></funapp></arg></funapp></rhs></rule><edge><position>1</position><strict>false</strict><position>1</position></edge><edge><position>2</position><strict>false</strict><position>2</position></edge><edge><position>3</position><strict>true</strict><position>3</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></rhs></rule><edge><position>1</position><strict>false</strict><position>1</position></edge><edge><position>2</position><strict>false</strict><position>2</position></edge><edge><position>3</position><strict>true</strict><position>3</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><funapp><name>s1</name><arg><var>y_2</var></arg></funapp></arg></funapp></rhs></rule><edge><position>1</position><strict>false</strict><position>1</position></edge><edge><position>2</position><strict>false</strict><position>2</position></edge><edge><position>3</position><strict>true</strict><position>3</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component></depGraphProc></dpProof></redPairUrProc></dpProof></redPairProc></dpProof></redPairProc></dpProof></redPairProc></dpProof></redPairProc></dpProof></forwardInstantiationProc></dpProof></rewritingProc></dpProof></rewritingProc></dpProof></rewritingProc></dpProof></rewritingProc></dpProof></narrowingProc></dpProof></rewritingProc></dpProof></rewritingProc></dpProof></narrowingProc></dpProof></forwardInstantiationProc></dpProof></forwardInstantiationProc></dpProof></rewritingProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>rec</name></funapp></arg><arg><var>y1</var></arg><arg><funapp><name>s1</name><arg><var>y2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>rec1</name><arg><funapp><name>s1</name><arg><var>y2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>rec</name></funapp></arg><arg><var>y1</var></arg><arg><var>y2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>rec3</name></sharp><arg><funapp><name>s</name></funapp></arg><arg><var>y1</var></arg><arg><funapp><name>s1</name><arg><var>y2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><var>y2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>rec3</name><arg><funapp><name>s</name></funapp></arg><arg><var>y1</var></arg><arg><var>y2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></narrowingProc></dpProof></redPairProc></dpProof></dpTrans></trsTerminationProof></switchInnermost></trsTerminationProof></uncurry></trsTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (27 real / 0 unknown / 0 assumptions / 27 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

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to TRS Standard Certified