details

property	value
status	complete
benchmark	list-sum-prod-bin.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	CiME_04

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	3.13742 seconds
cpu usage	4.1809
user time	3.98687
system time	0.194028
max virtual memory	1.8724888E7
max residence set size	315804.0

stage attributes

key	value
certification-result	CERTIFIED
starexec-result	CERTIFIED YES
certification-time	0.22
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>0</name><arg><funapp><name>#</name></funapp></arg></funapp></lhs><rhs><funapp><name>#</name></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><var>x</var></arg><arg><funapp><name>#</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>#</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>0</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>0</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>+</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>#</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>*</name><arg><funapp><name>#</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>#</name></funapp></rhs></rule><rule><lhs><funapp><name>*</name><arg><funapp><name>0</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>*</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>*</name><arg><funapp><name>1</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>+</name><arg><funapp><name>0</name><arg><funapp><name>*</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>sum</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>#</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>sum</name><arg><funapp><name>cons</name><arg><var>x</var></arg><arg><var>l</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>+</name><arg><var>x</var></arg><arg><funapp><name>sum</name><arg><var>l</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>prod</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>#</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>prod</name><arg><funapp><name>cons</name><arg><var>x</var></arg><arg><var>l</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>*</name><arg><var>x</var></arg><arg><funapp><name>prod</name><arg><var>l</var></arg></funapp></arg></funapp></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><name>+</name></sharp><arg><funapp><name>0</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>0</name></sharp><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>+</name></sharp><arg><funapp><name>0</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>+</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>+</name></sharp><arg><funapp><name>0</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>+</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>+</name></sharp><arg><funapp><name>1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>+</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>+</name></sharp><arg><funapp><name>1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>0</name></sharp><arg><funapp><name>+</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>#</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>+</name></sharp><arg><funapp><name>1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>+</name></sharp><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>#</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>+</name></sharp><arg><funapp><name>1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>+</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>0</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>0</name></sharp><arg><funapp><name>*</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>0</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>*</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>1</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>+</name></sharp><arg><funapp><name>0</name><arg><funapp><name>*</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>1</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>0</name></sharp><arg><funapp><name>*</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>1</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>*</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>0</name></sharp><arg><funapp><name>#</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>cons</name><arg><var>x</var></arg><arg><var>l</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>+</name></sharp><arg><var>x</var></arg><arg><funapp><name>sum</name><arg><var>l</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>cons</name><arg><var>x</var></arg><arg><var>l</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>sum</name></sharp><arg><var>l</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prod</name></sharp><arg><funapp><name>cons</name><arg><var>x</var></arg><arg><var>l</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>*</name></sharp><arg><var>x</var></arg><arg><funapp><name>prod</name><arg><var>l</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prod</name></sharp><arg><funapp><name>cons</name><arg><var>x</var></arg><arg><var>l</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>prod</name></sharp><arg><var>l</var></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>prod</name></sharp><arg><funapp><name>cons</name><arg><var>x</var></arg><arg><var>l</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>prod</name></sharp><arg><var>l</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><switchInnermostProc><wcrProof><joinableCriticalPairsBFS>20</joinableCriticalPairsBFS></wcrProof><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss/><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>prod</name></sharp><arg><funapp><name>cons</name><arg><var>x</var></arg><arg><var>l</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>prod</name></sharp><arg><var>l</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></switchInnermostProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>prod</name></sharp><arg><funapp><name>cons</name><arg><var>x</var></arg><arg><var>l</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>*</name></sharp><arg><var>x</var></arg><arg><funapp><name>prod</name><arg><var>l</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>1</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>*</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>0</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>*</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><monoRedPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>*</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>1</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>*</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>0</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>*</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><trs><rules/></trs><usableRules><rules/></usableRules><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>1</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>*</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><sizeChangeGraph><rule><lhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>0</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>*</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></monoRedPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>cons</name><arg><var>x</var></arg><arg><var>l</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>sum</name></sharp><arg><var>l</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><switchInnermostProc><wcrProof><joinableCriticalPairsBFS>20</joinableCriticalPairsBFS></wcrProof><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss/><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>cons</name><arg><var>x</var></arg><arg><var>l</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>sum</name></sharp><arg><var>l</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></switchInnermostProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>1</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>+</name></sharp><arg><funapp><name>0</name><arg><funapp><name>*</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>cons</name><arg><var>x</var></arg><arg><var>l</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>+</name></sharp><arg><var>x</var></arg><arg><funapp><name>sum</name><arg><var>l</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>+</name></sharp><arg><funapp><name>0</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>+</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>+</name></sharp><arg><funapp><name>0</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>+</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>+</name></sharp><arg><funapp><name>1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>+</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>+</name></sharp><arg><funapp><name>1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>+</name></sharp><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>#</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>+</name></sharp><arg><funapp><name>1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>+</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><monoRedPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>+</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>+</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>+</name></sharp><arg><funapp><name>0</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>+</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>+</name></sharp><arg><funapp><name>0</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>+</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>+</name></sharp><arg><funapp><name>1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>+</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>+</name></sharp><arg><funapp><name>1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>+</name></sharp><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>#</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>+</name></sharp><arg><funapp><name>1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>+</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>+</name><arg><var>x</var></arg><arg><funapp><name>#</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>#</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>0</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>0</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>+</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>#</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>0</name><arg><funapp><name>#</name></funapp></arg></funapp></lhs><rhs><funapp><name>#</name></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>+</name><arg><var>x</var></arg><arg><funapp><name>#</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>#</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>0</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>0</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>+</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>#</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>0</name><arg><funapp><name>#</name></funapp></arg></funapp></lhs><rhs><funapp><name>#</name></funapp></rhs></rule></rules></usableRules><dpProof><monoRedPairProc><orderingConstraintProof><redPair><knuthBendixOrder><w0>1</w0><precedenceWeight><precedenceWeightEntry><name>#</name><arity>0</arity><precedence>4</precedence><weight>2</weight></precedenceWeightEntry><precedenceWeightEntry><name>0</name><arity>1</arity><precedence>0</precedence><weight>1</weight></precedenceWeightEntry><precedenceWeightEntry><name>1</name><arity>1</arity><precedence>1</precedence><weight>3</weight></precedenceWeightEntry><precedenceWeightEntry><name>+</name><arity>2</arity><precedence>2</precedence><weight>0</weight></precedenceWeightEntry><precedenceWeightEntry><sharp><name>+</name></sharp><arity>2</arity><precedence>3</precedence><weight>0</weight></precedenceWeightEntry></precedenceWeight></knuthBendixOrder></redPair></orderingConstraintProof><dps><rules/></dps><trs><rules/></trs><dpProof><pIsEmpty/></dpProof></monoRedPairProc></dpProof></monoRedPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>+</name></sharp><arg><funapp><name>0</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>0</name></sharp><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>+</name></sharp><arg><funapp><name>1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>0</name></sharp><arg><funapp><name>+</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>#</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>0</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>0</name></sharp><arg><funapp><name>*</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>1</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>0</name></sharp><arg><funapp><name>*</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>0</name></sharp><arg><funapp><name>#</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></dpTrans></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 % (15 real / 0 unknown / 0 assumptions / 15 total proof steps)</strategy><url>http://aprove.informatik.rwth-aachen.de</url></tool><toolUser><firstName>John</firstName><lastName>Doe</lastName></toolUser></proofOrigin><inputOrigin/></origin></certificationProblem> popout

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all output return to TRS Standard Certified