details

property	value
status	complete
benchmark	#3.22.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n151.star.cs.uiowa.edu
space	Applicative_first_order_05

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	2.07456 seconds
cpu usage	4.94633
user time	4.72326
system time	0.22307
max virtual memory	1.8590732E7
max residence set size	338960.0

stage attributes

key	value
certification-result	CERTIFIED
starexec-result	CERTIFIED YES
certification-time	0.42
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" 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app></arg></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>filter2</name></funapp></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>filter</name></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>filter2</name></funapp></arg><arg><funapp><name>false</name></funapp></arg></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>filter</name></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><uncurry><uncurryInformation><name>app</name><uncurriedSymbols><uncurriedSymbolEntry><name>times</name><arity>0</arity><name>times</name><name>times1</name><name>times2</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>plus</name><arity>0</arity><name>plus</name><name>plus1</name><name>plus2</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>s</name><arity>0</arity><name>s</name><name>s1</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>0</name><arity>0</arity><name>0</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>map</name><arity>0</arity><name>map</name><name>map1</name><name>map2</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>nil</name><arity>0</arity><name>nil</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>cons</name><arity>0</arity><name>cons</name><name>cons1</name><name>cons2</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>filter</name><arity>0</arity><name>filter</name><name>filter1</name><name>filter3</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>filter2</name><arity>0</arity><name>filter2</name><name>filter21</name><name>filter22</name><name>filter23</name><name>filter24</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>true</name><arity>0</arity><name>true</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>false</name><arity>0</arity><name>false</name></uncurriedSymbolEntry></uncurriedSymbols><uncurryRules><rules><rule><lhs><funapp><name>app</name><arg><funapp><name>times</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>times1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>times1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>times2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>plus</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>plus1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>plus1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>plus2</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>app</name><arg><funapp><name>map</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>map1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>map1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>map2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>cons1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>cons1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>cons2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>filter</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>filter1</name><a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n>1</position></edge><edge><position>2</position><strict>false</strict><position>2</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>filter3</name></sharp><arg><var>f</var></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>filter24</name></sharp><arg><funapp><name>app</name><arg><var>f</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><edge><position>1</position><strict>false</strict><position>2</position></edge><edge><position>2</position><strict>true</strict><position>3</position></edge><edge><position>2</position><strict>true</strict><position>4</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>filter1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>filter3</name></sharp><arg><var>x0</var></arg><arg><var>y1</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>app</name></sharp><arg><funapp><name>filter23</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>filter24</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge><edge><position>1</position><strict>true</strict><position>2</position></edge><edge><position>1</position><strict>true</strict><position>3</position></edge><edge><position>2</position><strict>false</strict><position>4</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>filter24</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>filter3</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><edge><position>2</position><strict>false</strict><position>1</position></edge><edge><position>4</position><strict>false</strict><position>2</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>filter24</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>filter3</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><edge><position>2</position><strict>false</strict><position>1</position></edge><edge><position>4</position><strict>false</strict><position>2</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>times1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>times2</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>times2</name></sharp><arg><var>x</var></arg><arg><funapp><name>plus2</name><arg><var>y</var></arg><arg><funapp><name>s1</name><arg><var>z</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>times2</name></sharp><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>times2</name></sharp><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>times2</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>times2</name></sharp><arg><var>x</var></arg><arg><funapp><name>plus2</name><arg><var>y</var></arg><arg><funapp><name>s1</name><arg><var>z</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>times2</name></sharp><arg><var>x</var></arg><arg><funapp><name>plus2</name><arg><var>y</var></arg><arg><funapp><name>times2</name><arg><funapp><name>s1</name><arg><var>z</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><monoRedPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>times2</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>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>plus2</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>s1</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>times2</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>times2</name></sharp><arg><var>x</var></arg><arg><funapp><name>plus2</name><arg><var>y</var></arg><arg><funapp><name>s1</name><arg><var>z</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>times2</name></sharp><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>times2</name></sharp><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>times2</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>times2</name></sharp><arg><var>x</var></arg><arg><funapp><name>plus2</name><arg><var>y</var></arg><arg><funapp><name>s1</name><arg><var>z</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>times2</name></sharp><arg><var>x</var></arg><arg><funapp><name>plus2</name><arg><var>y</var></arg><arg><funapp><name>times2</name><arg><funapp><name>s1</name><arg><var>z</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>times2</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>plus2</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>plus2</name><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><funapp><name>plus2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>times2</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>plus2</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>plus2</name><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><funapp><name>plus2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><monoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>times2</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>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>plus2</name><arity>2</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><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>s1</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>times2</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>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>times2</name></sharp><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>times2</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>times2</name></sharp><arg><var>x</var></arg><arg><funapp><name>plus2</name><arg><var>y</var></arg><arg><funapp><name>s1</name><arg><var>z</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>times2</name></sharp><arg><var>x</var></arg><arg><funapp><name>plus2</name><arg><var>y</var></arg><arg><funapp><name>times2</name><arg><funapp><name>s1</name><arg><var>z</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>times2</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>plus2</name><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><funapp><name>plus2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><dpProof><monoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>times2</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>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>plus2</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>s1</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>times2</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>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>times2</name></sharp><arg><var>x</var></arg><arg><funapp><name>plus2</name><arg><var>y</var></arg><arg><funapp><name>s1</name><arg><var>z</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>times2</name></sharp><arg><var>x</var></arg><arg><funapp><name>plus2</name><arg><var>y</var></arg><arg><funapp><name>times2</name><arg><funapp><name>s1</name><arg><var>z</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>times2</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule></rules></trs><dpProof><switchInnermostProc><wcrProof><joinableCriticalPairsBFS>20</joinableCriticalPairsBFS></wcrProof><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>times2</name></sharp><arg><var>x</var></arg><arg><funapp><name>plus2</name><arg><var>y</var></arg><arg><funapp><name>s1</name><arg><var>z</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>times2</name></sharp><arg><var>x</var></arg><arg><funapp><name>plus2</name><arg><var>y</var></arg><arg><funapp><name>times2</name><arg><funapp><name>s1</name><arg><var>z</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><edge><position>1</position><strict>false</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></switchInnermostProc></dpProof></monoRedPairProc></dpProof></monoRedPairProc></dpProof></monoRedPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>times2</name></sharp><arg><var>x</var></arg><arg><funapp><name>plus2</name><arg><var>y</var></arg><arg><funapp><name>s1</name><arg><var>z</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>times2</name></sharp><arg><funapp><name>s1</name><arg><var>z</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>times2</name></sharp><arg><var>x</var></arg><arg><funapp><name>plus2</name><arg><var>y</var></arg><arg><funapp><name>s1</name><arg><var>z</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>plus2</name></sharp><arg><funapp><name>times2</name><arg><var>x</var></arg><arg><funapp><name>plus2</name><arg><var>y</var></arg><arg><funapp><name>times2</name><arg><funapp><name>s1</name><arg><var>z</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>times2</name><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>z</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>times2</name></sharp><arg><var>x</var></arg><arg><funapp><name>plus2</name><arg><var>y</var></arg><arg><funapp><name>s1</name><arg><var>z</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>plus2</name></sharp><arg><var>y</var></arg><arg><funapp><name>times2</name><arg><funapp><name>s1</name><arg><var>z</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>times2</name></sharp><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>plus2</name></sharp><arg><funapp><name>times2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>plus1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus2</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>plus2</name></sharp><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>plus2</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>s1</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>plus2</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>plus2</name></sharp><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>plus2</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>plus2</name></sharp><arg><var>x</var></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>plus2</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><edge><position>1</position><strict>false</strict><position>1</position></edge><edge><position>2</position><strict>true</strict><position>2</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></monoRedPairUrProc></dpProof></component></depGraphProc></dpProof></dpTrans></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 % (11 real / 0 unknown / 0 assumptions / 11 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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