details

property	value
status	complete
benchmark	#4.15.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n028.star.cs.uiowa.edu
space	Applicative_AG01_innermost

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	1.95528292656 seconds
cpu usage	4.735108691
max memory	3.2575488E8

stage attributes

key	value
certification-result	CERTIFIED
output-size	41018
starexec-result	YES
certification-time	0.0

output

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</var></arg><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><var>fun</var></arg></funapp></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>filter</name></funapp></arg><arg><var>fun</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>filter2</name></funapp></arg><arg><funapp><name>app</name><arg><var>fun</var></arg><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><var>fun</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>filter</name></funapp></arg><arg><var>fun</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>filter2</name></funapp></arg><arg><funapp><name>app</name><arg><var>fun</var></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>filter</name></funapp></arg><arg><var>fun</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><var>fun</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><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>fun</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><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>fun</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><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>fun</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><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>fun</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>filter</name></funapp></arg><arg><var>fun</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><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>fun</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>filter</name></funapp></arg><arg><var>fun</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><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>fun</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>filter</name></funapp></arg><arg><var>fun</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><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>fun</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>filter</name></funapp></arg><arg><var>fun</var></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><var>fun</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><var>fun</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><var>fun</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><var>fun</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>filter</name></funapp></arg><arg><var>fun</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><var>fun</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><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>fun</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>filter</name></funapp></arg><arg><var>fun</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><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>fun</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>filter</name></funapp></arg><arg><var>fun</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>filter</name></funapp></arg><arg><var>fun</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><var>fun</var></arg><arg><var>x</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><sizeChangeGraph><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><var>fun</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><var>fun</var></arg><arg><var>x</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><sizeChangeGraph><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><var>fun</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><var>fun</var></arg></funapp></arg><arg><var>xs</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><sizeChangeGraph><rule><lhs><funapp><sharp><name>app</name></sharp><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>fun</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>filter</name></funapp></arg><arg><var>fun</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></rhs></rule><edge><position>2</position><strict>false</strict><position>2</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>app</name></sharp><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>fun</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>filter</name></funapp></arg><arg><var>fun</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></rhs></rule><edge><position>2</position><strict>false</strict><position>2</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>f</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>1</name></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>g</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>h</name></funapp></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>filter</name></funapp></arg><arg><var>fun</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><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>app</name><arg><var>fun</var></arg><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><var>fun</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</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>app</name><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>f</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>1</name></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>g</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>f</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>g</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>g</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>g</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>h</name></funapp></arg><arg><var>x</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>app</name><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>f</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>1</name></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>g</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>f</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>g</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>g</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>g</name></funapp></arg><arg><var>x</var></arg></funapp></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>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>f</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>1</name></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>g</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>f</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>g</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>g</name></funapp></arg><arg><var>x</var></arg></funapp></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>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>f</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>1</name></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>g</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>f</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>g</name></funapp></arg><arg><var>x</var></arg></funapp></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>app</name></sharp><arg><funapp><name>h</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>g</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>h</name></funapp></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>h</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>g</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>h</name></funapp></arg><arg><var>x</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></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><var>fun</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><funapp><name>app</name><arg><var>fun</var></arg><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><var>fun</var></arg></funapp></arg><arg><var>xs</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>app</name><arg><funapp><name>map</name></funapp></arg><arg><var>fun</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>cons</name></funapp></arg><arg><funapp><name>app</name><arg><var>fun</var></arg><arg><var>x</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>app</name><arg><funapp><name>filter</name></funapp></arg><arg><var>fun</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>filter2</name></funapp></arg><arg><funapp><name>app</name><arg><var>fun</var></arg><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><var>fun</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>app</name><arg><funapp><name>filter</name></funapp></arg><arg><var>fun</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>app</name><arg><funapp><name>filter2</name></funapp></arg><arg><funapp><name>app</name><arg><var>fun</var></arg><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><var>fun</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>app</name><arg><funapp><name>filter</name></funapp></arg><arg><var>fun</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>filter2</name></funapp></arg><arg><funapp><name>app</name><arg><var>fun</var></arg><arg><var>x</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>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>fun</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><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>fun</var></arg></funapp></arg><arg><var>xs</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>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>fun</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>app</name></sharp><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>fun</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>filter</name></funapp></arg><arg><var>fun</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>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>fun</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>filter</name></funapp></arg><arg><var>fun</var></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: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (6 real / 0 unknown / 0 assumptions / 6 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 Inner certi 67861