details

property	value
status	complete
benchmark	Ex2_Luc02a_iGM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n124.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	4.20935 seconds
cpu usage	12.2278
user time	11.7011
system time	0.52672
max virtual memory	1.9558276E7
max residence set size	991956.0

stage attributes

key	value
certification-result	CERTIFIED
output-size	107057
starexec-result	YES
certification-time	0.3

output

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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component><dps><rules><rule><lhs><funapp><sharp><name>terms</name></sharp><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>terms</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>terms</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>terms</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>active</name><arg><funapp><name>terms</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>sqr</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>sqr</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>dbl</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>dbl</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>add</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>first</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>first</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>terms</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>cons</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>recip</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>sqr</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>dbl</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>first</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>nil</name></funapp></arg></funapp></innermostLhss><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>terms</name></sharp><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>terms</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>terms</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>terms</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>cons</name></sharp><arg><var>X1</var></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cons</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>cons</name></sharp><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><sharp><name>cons</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>cons</name></sharp><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><sharp><name>cons</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>cons</name></sharp><arg><var>X1</var></arg><arg><funapp><name>active</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cons</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>active</name><arg><funapp><name>terms</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>sqr</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>sqr</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>dbl</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>dbl</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>add</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>first</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>first</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>terms</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>cons</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>recip</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>sqr</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>dbl</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>first</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>nil</name></funapp></arg></funapp></innermostLhss><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>cons</name></sharp><arg><var>X1</var></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cons</name></sharp><arg><var>X1</var></arg><arg><var>X2</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>cons</name></sharp><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><sharp><name>cons</name></sharp><arg><var>X1</var></arg><arg><var>X2</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>cons</name></sharp><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><sharp><name>cons</name></sharp><arg><var>X1</var></arg><arg><var>X2</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>cons</name></sharp><arg><var>X1</var></arg><arg><funapp><name>active</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cons</name></sharp><arg><var>X1</var></arg><arg><var>X2</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></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>recip</name></sharp><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>recip</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>recip</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>recip</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>active</name><arg><funapp><name>terms</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>sqr</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>sqr</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>dbl</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>dbl</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>add</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>first</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>first</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>terms</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>cons</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>recip</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>sqr</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>dbl</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>first</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>nil</name></funapp></arg></funapp></innermostLhss><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>recip</name></sharp><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>recip</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>recip</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>recip</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>sqr</name></sharp><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>sqr</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sqr</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>sqr</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>active</name><arg><funapp><name>terms</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>sqr</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>sqr</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>dbl</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>dbl</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>add</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>first</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>first</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>terms</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>cons</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>recip</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>sqr</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>dbl</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>first</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>nil</name></funapp></arg></funapp></innermostLhss><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>sqr</name></sharp><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>sqr</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>sqr</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>sqr</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>s</name></sharp><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>s</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>active</name><arg><funapp><name>terms</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>sqr</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>sqr</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>dbl</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>dbl</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>add</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>first</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>first</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>terms</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>cons</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>recip</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>sqr</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>dbl</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>first</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>nil</name></funapp></arg></funapp></innermostLhss><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>s</name></sharp><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>s</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>add</name></sharp><arg><var>X1</var></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>add</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>add</name></sharp><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><sharp><name>add</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>add</name></sharp><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><sharp><name>add</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>add</name></sharp><arg><var>X1</var></arg><arg><funapp><name>active</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>add</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>active</name><arg><funapp><name>terms</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>sqr</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>sqr</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>dbl</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>dbl</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>add</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>first</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>first</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>terms</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>cons</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>recip</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>sqr</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>dbl</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>first</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>nil</name></funapp></arg></funapp></innermostLhss><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>add</name></sharp><arg><var>X1</var></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>add</name></sharp><arg><var>X1</var></arg><arg><var>X2</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>add</name></sharp><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><sharp><name>add</name></sharp><arg><var>X1</var></arg><arg><var>X2</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>add</name></sharp><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><sharp><name>add</name></sharp><arg><var>X1</var></arg><arg><var>X2</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>add</name></sharp><arg><var>X1</var></arg><arg><funapp><name>active</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>add</name></sharp><arg><var>X1</var></arg><arg><var>X2</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></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>dbl</name></sharp><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>dbl</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dbl</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>dbl</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>active</name><arg><funapp><name>terms</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>sqr</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>sqr</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>dbl</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>dbl</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>add</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>first</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>first</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>terms</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>cons</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>recip</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>sqr</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>dbl</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>first</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>nil</name></funapp></arg></funapp></innermostLhss><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>dbl</name></sharp><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>dbl</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>dbl</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>dbl</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>first</name></sharp><arg><var>X1</var></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>first</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>first</name></sharp><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><sharp><name>first</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>first</name></sharp><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><sharp><name>first</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>first</name></sharp><arg><var>X1</var></arg><arg><funapp><name>active</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>first</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>active</name><arg><funapp><name>terms</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>sqr</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>sqr</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>dbl</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>dbl</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>add</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>first</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>first</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>terms</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>cons</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>recip</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>sqr</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>dbl</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>first</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>nil</name></funapp></arg></funapp></innermostLhss><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>first</name></sharp><arg><var>X1</var></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>first</name></sharp><arg><var>X1</var></arg><arg><var>X2</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>first</name></sharp><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><sharp><name>first</name></sharp><arg><var>X1</var></arg><arg><var>X2</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>first</name></sharp><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><sharp><name>first</name></sharp><arg><var>X1</var></arg><arg><var>X2</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>first</name></sharp><arg><var>X1</var></arg><arg><funapp><name>active</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>first</name></sharp><arg><var>X1</var></arg><arg><var>X2</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></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></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 % (31 real / 0 unknown / 0 assumptions / 31 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_Innermost Certified 2019-04-01 06.48