details

property	value
status	complete
benchmark	#3.55.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n027.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	2.10021209717 seconds
cpu usage	5.284693756
max memory	4.01956864E8

stage attributes

key	value
certification-result	CERTIFIED
output-size	40663
starexec-result	YES
certification-time	0.0

output

/export/starexec/sandbox2/solver/bin/starexec_run_certified /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES <?xml version="1.0" encoding="UTF-8" standalone="no"?><?xml-stylesheet type="text/xsl" href="cpfHTML.xsl"?><certificationProblem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" 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me>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>high</name></sharp><arg><var>n</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>quicksort</name></sharp><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>quicksort</name><arg><funapp><name>low</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><funapp><name>add</name><arg><var>n</var></arg><arg><funapp><name>quicksort</name><arg><funapp><name>high</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>quicksort</name></sharp><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>quicksort</name></sharp><arg><funapp><name>low</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>quicksort</name></sharp><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>low</name></sharp><arg><var>n</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>quicksort</name></sharp><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>quicksort</name></sharp><arg><funapp><name>high</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>quicksort</name></sharp><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>high</name></sharp><arg><var>n</var></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>quicksort</name></sharp><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>quicksort</name></sharp><arg><funapp><name>high</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>quicksort</name></sharp><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>quicksort</name></sharp><arg><funapp><name>low</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>low</name><arg><var>n</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>low</name><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>if_low</name><arg><funapp><name>le</name><arg><var>m</var></arg><arg><var>n</var></arg></funapp></arg><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>if_low</name><arg><funapp><name>false</name></funapp></arg><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>low</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>le</name><arg><funapp><name>0</name></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>le</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>le</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>le</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>if_low</name><arg><funapp><name>true</name></funapp></arg><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>add</name><arg><var>m</var></arg><arg><funapp><name>low</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>high</name><arg><var>n</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>high</name><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>if_high</name><arg><funapp><name>le</name><arg><var>m</var></arg><arg><var>n</var></arg></funapp></arg><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>if_high</name><arg><funapp><name>true</name></funapp></arg><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>high</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>if_high</name><arg><funapp><name>false</name></funapp></arg><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>add</name><arg><var>m</var></arg><arg><funapp><name>high</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>le</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>le</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>le</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>low</name><arg><var>x0</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp><funapp><name>low</name><arg><var>x0</var></arg><arg><funapp><name>add</name><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp><funapp><name>if_low</name><arg><funapp><name>true</name></funapp></arg><arg><var>x0</var></arg><arg><funapp><name>add</name><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp><funapp><name>if_low</name><arg><funapp><name>false</name></funapp></arg><arg><var>x0</var></arg><arg><funapp><name>add</name><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp><funapp><name>high</name><arg><var>x0</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp><funapp><name>high</name><arg><var>x0</var></arg><arg><funapp><name>add</name><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp><funapp><name>if_high</name><arg><funapp><name>true</name></funapp></arg><arg><var>x0</var></arg><arg><funapp><name>add</name><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp><funapp><name>if_high</name><arg><funapp><name>false</name></funapp></arg><arg><var>x0</var></arg><arg><funapp><name>add</name><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></innermostLhss><dpProof><redPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>quicksort</name></sharp><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>-1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>high</name><arity>2</arity><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></interpret><interpret><name>nil</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>add</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>if_high</name><arity>3</arity><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></interpret><interpret><name>le</name><arity>2</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>true</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>low</name><arity>2</arity><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></interpret><interpret><name>if_low</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>-2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>false</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>s</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules/></dps><usableRules><rules><rule><lhs><funapp><name>high</name><arg><var>n</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>high</name><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>if_high</name><arg><funapp><name>le</name><arg><var>m</var></arg><arg><var>n</var></arg></funapp></arg><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>if_high</name><arg><funapp><name>true</name></funapp></arg><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>high</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>low</name><arg><var>n</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>low</name><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>if_low</name><arg><funapp><name>le</name><arg><var>m</var></arg><arg><var>n</var></arg></funapp></arg><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>if_low</name><arg><funapp><name>false</name></funapp></arg><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>low</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>if_low</name><arg><funapp><name>true</name></funapp></arg><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>add</name><arg><var>m</var></arg><arg><funapp><name>low</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>if_high</name><arg><funapp><name>false</name></funapp></arg><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>add</name><arg><var>m</var></arg><arg><funapp><name>high</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><pIsEmpty/></dpProof></redPairUrProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>quicksort</name></sharp><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>low</name></sharp><arg><var>n</var></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>quicksort</name></sharp><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>high</name></sharp><arg><var>n</var></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>quot</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>quot</name></sharp><arg><funapp><name>minus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>minus</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>minus</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>minus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>minus</name><arg><var>x0</var></arg><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>minus</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></innermostLhss><dpProof><redPairProc><orderingConstraintProof><redPair><knuthBendixOrder><w0>1</w0><precedenceWeight><precedenceWeightEntry><name>s</name><arity>1</arity><precedence>0</precedence><weight>1</weight></precedenceWeightEntry></precedenceWeight><argumentFilter><argumentFilterEntry><sharp><name>quot</name></sharp><arity>2</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>s</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>minus</name><arity>2</arity><collapsing>1</collapsing></argumentFilterEntry></argumentFilter></knuthBendixOrder></redPair></orderingConstraintProof><dps><rules/></dps><dpProof><pIsEmpty/></dpProof></redPairProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>low</name></sharp><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>if_low</name></sharp><arg><funapp><name>le</name><arg><var>m</var></arg><arg><var>n</var></arg></funapp></arg><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if_low</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>low</name></sharp><arg><var>n</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if_low</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>low</name></sharp><arg><var>n</var></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>le</name><arg><funapp><name>0</name></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>le</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>le</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>le</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>le</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>le</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>le</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></innermostLhss><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>low</name></sharp><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>if_low</name></sharp><arg><funapp><name>le</name><arg><var>m</var></arg><arg><var>n</var></arg></funapp></arg><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><edge><position>1</position><strict>false</strict><position>2</position></edge><edge><position>2</position><strict>false</strict><position>3</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>if_low</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>low</name></sharp><arg><var>n</var></arg><arg><var>x</var></arg></funapp></rhs></rule><edge><position>2</position><strict>false</strict><position>1</position></edge><edge><position>3</position><strict>true</strict><position>2</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>if_low</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>low</name></sharp><arg><var>n</var></arg><arg><var>x</var></arg></funapp></rhs></rule><edge><position>2</position><strict>false</strict><position>1</position></edge><edge><position>3</position><strict>true</strict><position>2</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>high</name></sharp><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>if_high</name></sharp><arg><funapp><name>le</name><arg><var>m</var></arg><arg><var>n</var></arg></funapp></arg><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if_high</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>high</name></sharp><arg><var>n</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if_high</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>high</name></sharp><arg><var>n</var></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>le</name><arg><funapp><name>0</name></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>le</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>le</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>le</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>le</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>le</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>le</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></innermostLhss><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>high</name></sharp><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>if_high</name></sharp><arg><funapp><name>le</name><arg><var>m</var></arg><arg><var>n</var></arg></funapp></arg><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><edge><position>1</position><strict>false</strict><position>2</position></edge><edge><position>2</position><strict>false</strict><position>3</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>if_high</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>high</name></sharp><arg><var>n</var></arg><arg><var>x</var></arg></funapp></rhs></rule><edge><position>2</position><strict>false</strict><position>1</position></edge><edge><position>3</position><strict>true</strict><position>2</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>if_high</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>high</name></sharp><arg><var>n</var></arg><arg><var>x</var></arg></funapp></rhs></rule><edge><position>2</position><strict>false</strict><position>1</position></edge><edge><position>3</position><strict>true</strict><position>2</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>quot</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>minus</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>low</name></sharp><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>le</name></sharp><arg><var>m</var></arg><arg><var>n</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>high</name></sharp><arg><var>n</var></arg><arg><funapp><name>add</name><arg><var>m</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>le</name></sharp><arg><var>m</var></arg><arg><var>n</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>quicksort</name></sharp><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>quicksort</name><arg><funapp><name>low</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><funapp><name>add</name><arg><var>n</var></arg><arg><funapp><name>quicksort</name><arg><funapp><name>high</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>minus</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>minus</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss/><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>minus</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>minus</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge><edge><position>2</position><strict>true</strict><position>2</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>le</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>le</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss/><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>le</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>le</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge><edge><position>2</position><strict>true</strict><position>2</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss/><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge><edge><position>2</position><strict>false</strict><position>2</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component></depGraphProc></dpProof></dpTrans></trsTerminationProof></switchInnermost></trsTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (26 real / 0 unknown / 0 assumptions / 26 total proof steps)</strategy><url>http://aprove.informatik.rwth-aachen.de</url></tool><toolUser><firstName>John</firstName><lastName>Doe</lastName></toolUser></proofOrigin><inputOrigin/></origin></certificationProblem> popout

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