details

property	value
status	complete
benchmark	17.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	Beerendonk_07

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	12.5968 seconds
cpu usage	22.5658
user time	22.0173
system time	0.548484
max virtual memory	1.870884E7
max residence set size	1157376.0

stage attributes

key	value
certification-result	CERTIFIED
starexec-result	CERTIFIED YES
certification-time	0.89
bare-result	YES

output

<?xml version="1.0" encoding="UTF-8" standalone="no"?><?xml-stylesheet type="text/xsl" href="cpfHTML.xsl"?><certificationProblem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" 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ue</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><var>y</var></arg></funapp></rhs></rule><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><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><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><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><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>eq</name><arg><var>x</var></arg><arg><var>y</var></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>eq</name></sharp><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><funapp><name>p</name><arg><var>x</var></arg></funapp></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>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><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><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>x</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><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>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><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><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>p</name></sharp><arg><var>y</var></arg></funapp></rhs></rule><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><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><rule><lhs><funapp><sharp><name>eq</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>eq</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpProof><depGraphProc><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>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><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><var>y</var></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>eq</name><arg><var>x</var></arg><arg><var>y</var></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><funapp><name>p</name><arg><var>x</var></arg></funapp></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><funapp><name>p</name><arg><var>y</var></arg></funapp></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><rule><lhs><funapp><name>eq</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>eq</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>eq</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>false</name></funapp></rhs></rule><rule><lhs><funapp><name>eq</name><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><name>eq</name><arg><var>x</var></arg><arg><var>y</var></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>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>gr</name><arg><var>x</var></arg><arg><var>y</var></arg></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><funapp><name>eq</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>eq</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>eq</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>eq</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>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>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>1</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>x0</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><var>x0</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>p</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>x0</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>x1</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>x1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>p</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></arg><arg><var>x1</var></arg></funapp></rhs></rule></rules></narrowings><dpProof><rewritingProc><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><var>x0</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>p</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>x0</var></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>2</position></positionInTerm><rule><lhs><funapp><name>p</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><var>x0</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><var>x0</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></rhs></rule><usableRules><rules><rule><lhs><funapp><name>p</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></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>x1</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>x1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>p</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></arg><arg><var>x1</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><funapp><name>p</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></arg><arg><var>x1</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>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>p</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></arg><arg><var>x1</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><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>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>p</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></arg><arg><var>x1</var></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>2</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><var>x0</var></arg><arg><var>x1</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>x1</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>x1</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><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><var>y</var></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>x0</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>x0</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><funapp><name>0</name></funapp></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><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>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>gr</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><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></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>x0</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><var>x0</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>x0</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><funapp><name>p</name><arg><var>x</var></arg></funapp></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>0</name></funapp></arg><arg><var>x0</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>x0</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>eq</name><arg><var>x</var></arg><arg><var>y</var></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><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>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></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><funapp><name>0</name></funapp></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>x1</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>x1</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><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>gr</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><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></rhs></rule></rules></dps><realScc>true</realScc><dpProof><narrowingProc><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><funapp><name>p</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></rhs></rule><positionInTerm><position>1</position></positionInTerm><narrowings><rules><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><var>x0</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>p</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>x0</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</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>x1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>p</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></arg><arg><var>x1</var></arg></funapp></rhs></rule></rules></narrowings><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><var>x0</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><var>x0</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>p</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>x0</var></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>2</position></positionInTerm><rule><lhs><funapp><name>p</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><var>x0</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>x0</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><var>x0</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><var>x0</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></rhs></rule><usableRules><rules><rule><lhs><funapp><name>p</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</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>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</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>x1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>p</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></arg><arg><var>x1</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><funapp><name>p</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></arg><arg><var>x1</var></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>p</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></arg><arg><var>x1</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><rewritingProc><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>p</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></arg><arg><var>x1</var></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>2</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><var>x0</var></arg><arg><var>x1</var></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</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>x1</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><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>eq</name><arg><var>x</var></arg><arg><var>y</var></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><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>true</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>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>0</name></funapp></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>false</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></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>s</name><arg><var>x0</var></arg></funapp></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><funapp><name>s</name><arg><var>x0</var></arg></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>eq</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><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></rhs></rule></rules></narrowings><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></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>s</name><arg><var>x0</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><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>true</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>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><var>x0</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>x0</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>x0</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>x0</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>x0</var></arg></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>s</name><arg><var>x0</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><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>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></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><funapp><name>0</name></funapp></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>x1</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>x1</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><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>gr</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><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></rhs></rule><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><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></lhs><rhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>eq</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><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></rhs></rule><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</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>x1</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><narrowingProc><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><funapp><name>p</name><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><positionInTerm><position>1</position></positionInTerm><narrowings><rules><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><var>x0</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>p</name><arg><var>x0</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</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>x1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>p</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></narrowings><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><funapp><name>0</name></funapp></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><funapp><name>0</name></funapp></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>x1</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>x1</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><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>gr</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><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></rhs></rule><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><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></lhs><rhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>eq</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><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></rhs></rule><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</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>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</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>x1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>p</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><rewritingProc><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</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>x1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>p</name><arg><var>x1</var></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>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>p</name><arg><var>x1</var></arg></funapp></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></lhs><rhs><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><funapp><name>p</name><arg><var>x1</var></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><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><usableRulesProc><usableRules><rules><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><rule><lhs><funapp><name>eq</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>eq</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>eq</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>false</name></funapp></rhs></rule><rule><lhs><funapp><name>eq</name><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><name>eq</name><arg><var>x</var></arg><arg><var>y</var></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>gr</name><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><name>gr</name><arg><var>x</var></arg><arg><var>y</var></arg></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>eq</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>eq</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>eq</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>eq</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>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>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></lhs><rhs><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><funapp><name>p</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><positionInTerm><position>3</position></positionInTerm><narrowings><rules><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>s</name><arg><var>y0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>y0</var></arg></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>s</name><arg><var>y0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>y0</var></arg></funapp></arg><arg><var>x0</var></arg></funapp></rhs></rule></rules></narrowings><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>s</name><arg><var>y0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>y0</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><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</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>x1</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><funapp><name>0</name></funapp></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><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>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>gr</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><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></rhs></rule><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><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></lhs><rhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>eq</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><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></rhs></rule><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</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>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>s</name><arg><var>y0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>y0</var></arg></funapp></arg><arg><var>x0</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>eq</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>eq</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>eq</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>false</name></funapp></rhs></rule><rule><lhs><funapp><name>eq</name><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><name>eq</name><arg><var>x</var></arg><arg><var>y</var></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>gr</name><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><name>gr</name><arg><var>x</var></arg><arg><var>y</var></arg></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>eq</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>eq</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>eq</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>eq</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></innermostLhss><dpProof><instantiationProc><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>x1</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>x1</var></arg></funapp></rhs></rule><instantiations><rules><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>0</name></funapp></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>z0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>s</name><arg><var>z1</var></arg></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><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>gr</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><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></rhs></rule><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><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></lhs><rhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>eq</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><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></rhs></rule><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</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>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>s</name><arg><var>y0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>y0</var></arg></funapp></arg><arg><var>x0</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>z0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>s</name><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><instantiationProc><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</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>x1</var></arg></funapp></rhs></rule><instantiations><rules><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>s</name><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule></rules></instantiations><dpProof><forwardInstantiationProc><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>s</name><arg><var>y0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>y0</var></arg></funapp></arg><arg><var>x0</var></arg></funapp></rhs></rule><instantiations><rules><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y_1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><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><funapp><name>s</name><arg><var>y_1</var></arg></funapp></arg></funapp></rhs></rule></rules></instantiations><usableRules><rules/></usableRules><dpProof><forwardInstantiationProc><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>s</name><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><instantiations><rules><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y_0</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>y_0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></instantiations><usableRules><rules/></usableRules><dpProof><forwardInstantiationProc><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>s</name><arg><var>z1</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>s</name><arg><funapp><name>s</name><arg><var>y_0</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>y_0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></instantiations><usableRules><rules/></usableRules><dpProof><forwardInstantiationProc><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><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></lhs><rhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>eq</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><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></rhs></rule><instantiations><rules><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>eq</name><arg><var>x0</var></arg><arg><funapp><name>s</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y_1</var></arg></funapp></arg></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>eq</name><arg><funapp><name>s</name><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y_1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></instantiations><usableRules><rules><rule><lhs><funapp><name>eq</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>eq</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>eq</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>false</name></funapp></rhs></rule><rule><lhs><funapp><name>eq</name><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><name>eq</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></usableRules><dpProof><forwardInstantiationProc><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><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>gr</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><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></rhs></rule><instantiations><rules><rule><lhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y_1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>s</name><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y_1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x1</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>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>gr</name><arg><var>x0</var></arg><arg><funapp><name>s</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></instantiations><usableRules><rules><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>gr</name><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><name>gr</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></usableRules><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><funapp><name>s</name><arg><var>y_0</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>y_0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></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><funapp><name>s</name><arg><var>y_1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>gr</name><arg><funapp><name>s</name><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y_1</var></arg></funapp></arg></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><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><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>gr</name><arg><var>x0</var></arg><arg><funapp><name>s</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y_2</var></arg></funapp></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><sizeChangeGraph><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>eq</name><arg><var>x0</var></arg><arg><funapp><name>s</name><arg><var>y_2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y_2</var></arg></funapp></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><sizeChangeGraph><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y_1</var></arg></funapp></arg></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>eq</name><arg><funapp><name>s</name><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y_1</var></arg></funapp></arg></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><sizeChangeGraph><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y_1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><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><funapp><name>s</name><arg><var>y_1</var></arg></funapp></arg></funapp></rhs></rule><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>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y_0</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>y_0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></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></sizeChangeProc></dpProof></forwardInstantiationProc></dpProof></forwardInstantiationProc></dpProof></forwardInstantiationProc></dpProof></forwardInstantiationProc></dpProof></forwardInstantiationProc></dpProof></instantiationProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>z0</var></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>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></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><funapp><name>0</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss/><dpProof><forwardInstantiationProc><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>z0</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>true</name></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y_0</var></arg></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>y_0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule></rules></instantiations><usableRules><rules/></usableRules><dpProof><forwardInstantiationProc><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><funapp><name>0</name></funapp></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><funapp><name>0</name></funapp></arg></funapp></rhs></rule><instantiations><rules><rule><lhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y_0</var></arg></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y_0</var></arg></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule></rules></instantiations><usableRules><rules/></usableRules><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y_0</var></arg></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y_0</var></arg></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></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><sizeChangeGraph><rule><lhs><funapp><sharp><name>cond2</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y_0</var></arg></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>y_0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></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></sizeChangeProc></dpProof></forwardInstantiationProc></dpProof></forwardInstantiationProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component></depGraphProc></dpProof></instantiationProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component></depGraphProc></dpProof></narrowingProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></rewritingProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><var>x0</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>x0</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>x0</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>x0</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>0</name></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>0</name></funapp></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>x0</var></arg></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>s</name><arg><var>x0</var></arg></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><var>x0</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><var>x0</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>p</name><arg><var>x0</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules><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>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>cond3</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><var>x0</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></rhs></rule><positionInTerm><position>1</position></positionInTerm><narrowings><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>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</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>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</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>s</name><arg><var>x0</var></arg></funapp></arg></funapp></rhs></rule></rules></narrowings><dpProof><depGraphProc><component><dps><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>x0</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>s</name><arg><var>x0</var></arg></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><funapp><name>0</name></funapp></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>false</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>x0</var></arg></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><var>x0</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><var>x0</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>p</name><arg><var>x0</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>x0</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>x0</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><narrowingProc><rule><lhs><funapp><sharp><name>cond3</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp></lhs><rhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>gr</name><arg><var>x0</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>p</name><arg><var>x0</var></arg></funapp></arg></funapp></rhs></rule><positionInTerm><position>1</position></positionInTerm><narrowings><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>false</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>p</name><arg><funapp><name>0</name></funapp></arg></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>s</name><arg><var>x0</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>x0</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></narrowings><dpProof><depGraphProc><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>s</name><arg><var>x0</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>x0</var></arg></funapp></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>x0</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>x0</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>x0</var></arg></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>s</name><arg><var>x0</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><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><innermostLhssRemovalProc><innermostLhss><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><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>s</name><arg><var>x0</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>x0</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>x0</var></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>s</name><arg><var>x0</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>x0</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/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss/><dpProof><forwardInstantiationProc><rule><lhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>x0</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>x0</var></arg></funapp></rhs></rule><instantiations><rules><rule><lhs><funapp><sharp><name>cond1</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>y_0</var></arg></funapp></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><funapp><name>s</name><arg><var>y_0</var></arg></funapp></arg></funapp></rhs></rule></rules></instantiations><usableRules><rules/></usableRules><dpProof><forwardInstantiationProc><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>s</name><arg><var>x0</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>x0</var></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>s</name><arg><funapp><name>s</name><arg><var>y_0</var></arg></funapp></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>s</name><arg><var>y_0</var></arg></funapp></arg></funapp></rhs></rule></rules></instantiations><usableRules><rules/></usableRules><dpProof><forwardInstantiationProc><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>x0</var></arg></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>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><funapp><name>s</name><arg><var>y_0</var></arg></funapp></arg></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>s</name><arg><funapp><name>s</name><arg><var>y_0</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></instantiations><usableRules><rules/></usableRules><dpProof><sizeChangeProc><subtermCriterion/><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><funapp><name>s</name><arg><var>y_0</var></arg></funapp></arg></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>s</name><arg><funapp><name>s</name><arg><var>y_0</var></arg></funapp></arg></funapp></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><sizeChangeGraph><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>s</name><arg><funapp><name>s</name><arg><var>y_0</var></arg></funapp></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>s</name><arg><var>y_0</var></arg></funapp></arg></funapp></rhs></rule><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><funapp><name>s</name><arg><var>y_0</var></arg></funapp></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><funapp><name>s</name><arg><var>y_0</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></forwardInstantiationProc></dpProof></forwardInstantiationProc></dpProof></forwardInstantiationProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></rewritingProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></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>false</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>p</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></narrowingProc></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>true</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>true</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>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></depGraphProc></dpProof></narrowingProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component></depGraphProc></dpProof></narrowingProc></dpProof></component></depGraphProc></dpProof></narrowingProc></dpProof></rewritingProc></dpProof></rewritingProc></dpProof></rewritingProc></dpProof></narrowingProc></dpProof></component></depGraphProc></dpProof></narrowingProc></dpProof></rewritingProc></dpProof></rewritingProc></dpProof></rewritingProc></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><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>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>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>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>eq</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>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>false</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><component><dps><rules><rule><lhs><funapp><sharp><name>eq</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>eq</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>eq</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>eq</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></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 % (64 real / 0 unknown / 0 assumptions / 64 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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