details

property	value
status	complete
benchmark	15.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n122.star.cs.uiowa.edu
space	Beerendonk_07

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	13.0495021343 seconds
cpu usage	12.897696008
max memory	1.126617088E9

stage attributes

key	value
certification-result	CERTIFIED
output-size	57302
starexec-result	YES
certification-time	0.1

output

/export/starexec/sandbox/solver/bin/starexec_run_certified /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- 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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>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>gr</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>gr</name><arg><var>y</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>add</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>x</var></arg><arg><funapp><name>p</name><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>add</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>add</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>add</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>gr</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>gr</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>p</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>p</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule></rules></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>gr</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>gr</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>gr</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>add</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp><funapp><name>p</name><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>p</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></innermostLhss><dpProof><narrowingProc><rule><lhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>gr</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><positionInTerm><position>1</position></positionInTerm><narrowings><rules><rule><lhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></narrowings><dpProof><narrowingProc><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>add</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>p</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></rhs></rule><positionInTerm><position>2</position></positionInTerm><narrowings><rules><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><var>y1</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>add</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></narrowings><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><var>y1</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>add</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>x</var></arg><arg><funapp><name>p</name><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>gr</name><arg><var>y</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>add</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>add</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><rewritingProc><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>add</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>1</position><position>1</position></positionInTerm><rule><lhs><funapp><name>add</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>add</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>s</name><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>s</name><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><usableRules><rules><rule><lhs><funapp><name>add</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>add</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule></rules></usableRules><dpProof><rewritingProc><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>s</name><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>1</position></positionInTerm><rule><lhs><funapp><name>gr</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><usableRules><rules><rule><lhs><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>add</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>add</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>gr</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule></rules></usableRules><dpProof><narrowingProc><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>gr</name><arg><var>y</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><positionInTerm><position>1</position></positionInTerm><narrowings><rules><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>y0</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>y0</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>y0</var></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>y0</var></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></rhs></rule></rules></narrowings><dpProof><instantiationProc><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>add</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><instantiations><rules><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>add</name><arg><var>z0</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule></rules></instantiations><dpProof><instantiationProc><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>y0</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>y0</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><instantiations><rules><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule></rules></instantiations><dpProof><instantiationProc><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>y0</var></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>y0</var></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></rhs></rule><instantiations><rules><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></instantiations><dpProof><instantiationProc><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>add</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>x</var></arg><arg><funapp><name>p</name><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><instantiations><rules><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>z0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>p</name><arg><funapp><name>s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></instantiations><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>gr</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>gr</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>p</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>add</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>add</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><rewritingProc><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>z0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>p</name><arg><funapp><name>s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>1</position><position>1</position></positionInTerm><rule><lhs><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>s</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>p</name><arg><funapp><name>s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>z0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>s</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>p</name><arg><funapp><name>s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><usableRules><rules><rule><lhs><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule></rules></usableRules><dpProof><rewritingProc><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>z0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>s</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>p</name><arg><funapp><name>s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>1</position></positionInTerm><rule><lhs><funapp><name>gr</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>p</name><arg><funapp><name>s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>z0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>p</name><arg><funapp><name>s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><usableRules><rules><rule><lhs><funapp><name>gr</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule></rules></usableRules><dpProof><rewritingProc><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>z0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>p</name><arg><funapp><name>s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>3</position></positionInTerm><rule><lhs><funapp><name>p</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>z0</var></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>z0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>z0</var></arg></funapp></rhs></rule><usableRules><rules><rule><lhs><funapp><name>p</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule></rules></usableRules><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>add</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>add</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>gr</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>gr</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule></rules></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>gr</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>gr</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>gr</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>add</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></innermostLhss><dpProof><instantiationProc><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>add</name><arg><var>z0</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><instantiations><rules><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule></rules></instantiations><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss/><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>x0</var></arg><arg><var>y1</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><edge><position>3</position><strict>false</strict><position>3</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></rhs></rule><edge><position>1</position><strict>false</strict><position>1</position></edge><edge><position>2</position><strict>false</strict><position>2</position></edge><edge><position>3</position><strict>false</strict><position>3</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>z0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>z0</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>gr</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>gr</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule></rules></usableRules><dpProof><rewritingProc><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>1</position><position>1</position></positionInTerm><rule><lhs><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><usableRules><rules><rule><lhs><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule></rules></usableRules><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>z0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>z0</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss/><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>z0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>z0</var></arg></funapp></rhs></rule><edge><position>1</position><strict>false</strict><position>1</position></edge><edge><position>2</position><strict>false</strict><position>2</position></edge><edge><position>3</position><strict>true</strict><position>3</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>y1</var></arg></funapp></rhs></rule><edge><position>2</position><strict>false</strict><position>2</position></edge><edge><position>3</position><strict>false</strict><position>3</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><edge><position>2</position><strict>false</strict><position>2</position></edge><edge><position>3</position><strict>false</strict><position>3</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></rewritingProc></dpProof></usableRulesProc></dpProof></component></depGraphProc></dpProof></instantiationProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></rewritingProc></dpProof></rewritingProc></dpProof></rewritingProc></dpProof></usableRulesProc></dpProof></instantiationProc></dpProof></instantiationProc></dpProof></instantiationProc></dpProof></instantiationProc></dpProof></narrowingProc></dpProof></rewritingProc></dpProof></rewritingProc></dpProof></component></depGraphProc></dpProof></narrowingProc></dpProof></narrowingProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>gr</name></sharp><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>gr</name></sharp><arg><funapp><name>add</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>gr</name></sharp><arg><var>y</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>gr</name></sharp><arg><funapp><name>add</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>gr</name></sharp><arg><funapp><name>add</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></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>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></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>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></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>cond2</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>p</name></sharp><arg><var>x</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>p</name></sharp><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>gr</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>gr</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss/><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>gr</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>gr</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge><edge><position>2</position><strict>true</strict><position>2</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>add</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></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>true</realScc><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss/><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>add</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>add</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge><edge><position>2</position><strict>false</strict><position>2</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component></depGraphProc></dpProof></dpTrans></trsTerminationProof></switchInnermost></trsTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (38 real / 0 unknown / 0 assumptions / 38 total proof steps)</strategy><url>http://aprove.informatik.rwth-aachen.de</url></tool><toolUser><firstName>John</firstName><lastName>Doe</lastName></toolUser></proofOrigin><inputOrigin/></origin></certificationProblem> popout

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all output return to TRS Standard Certified