details

property	value
status	complete
benchmark	Ex2_Luc03b_iGM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n032.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	3.21718 seconds
cpu usage	8.55311
user time	8.17672
system time	0.376387
max virtual memory	1.992484E7
max residence set size	655452.0

stage attributes

key	value
certification-result	CERTIFIED
output-size	90377
starexec-result	YES
certification-time	0.3

output

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r></arg><arg><var>Z</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><funapp><name>len</name><arg><var>Z</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>fst</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>Y</var></arg><arg><var>Z</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cons</name></sharp><arg><var>Y</var></arg><arg><funapp><name>fst</name><arg><var>X</var></arg><arg><var>Z</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>from</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cons</name></sharp><arg><var>X</var></arg><arg><funapp><name>from</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cons</name></sharp><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>from</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>from</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>from</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>from</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>add</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>add</name></sharp><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>add</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>add</name></sharp><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>len</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>Z</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>len</name></sharp><arg><var>Z</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>len</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>len</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>fst</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>fst</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>fst</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>fst</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>fst</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>fst</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>fst</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>fst</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>fst</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>fst</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>active</name><arg><funapp><name>from</name><arg><var>x0</var></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>len</name><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>len</name><arg><funapp><name>cons</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>fst</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>nil</name></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>cons</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>from</name><arg><var>x0</var></arg></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>len</name><arg><var>x0</var></arg></funapp></arg></funapp></innermostLhss><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>fst</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>fst</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>fst</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>fst</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>fst</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>fst</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>fst</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>fst</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>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>fst</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>fst</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>active</name><arg><funapp><name>from</name><arg><var>x0</var></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>len</name><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>len</name><arg><funapp><name>cons</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>fst</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>nil</name></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>cons</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>from</name><arg><var>x0</var></arg></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>len</name><arg><var>x0</var></arg></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>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>fst</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>fst</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>active</name><arg><funapp><name>from</name><arg><var>x0</var></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>len</name><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>len</name><arg><funapp><name>cons</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>fst</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>nil</name></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>cons</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>from</name><arg><var>x0</var></arg></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>len</name><arg><var>x0</var></arg></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>from</name></sharp><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>from</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>from</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>from</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>fst</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>fst</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>active</name><arg><funapp><name>from</name><arg><var>x0</var></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>len</name><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>len</name><arg><funapp><name>cons</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>fst</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>nil</name></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>cons</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>from</name><arg><var>x0</var></arg></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>len</name><arg><var>x0</var></arg></funapp></arg></funapp></innermostLhss><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>from</name></sharp><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>from</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>from</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>from</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>fst</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>fst</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>active</name><arg><funapp><name>from</name><arg><var>x0</var></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>len</name><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>len</name><arg><funapp><name>cons</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>fst</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>nil</name></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>cons</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>from</name><arg><var>x0</var></arg></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>len</name><arg><var>x0</var></arg></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>len</name></sharp><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>len</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>len</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>len</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>fst</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>fst</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>active</name><arg><funapp><name>from</name><arg><var>x0</var></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>len</name><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp><funapp><name>active</name><arg><funapp><name>len</name><arg><funapp><name>cons</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>fst</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>nil</name></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>cons</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>mark</name><arg><funapp><name>from</name><arg><var>x0</var></arg></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>len</name><arg><var>x0</var></arg></funapp></arg></funapp></innermostLhss><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>len</name></sharp><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>len</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>len</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>len</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></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 % (28 real / 0 unknown / 0 assumptions / 28 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