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TRS_Innermost Certified 2019-04-01 06.48 pair #433315503
details
property
value
status
complete
benchmark
#4.35.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n018.star.cs.uiowa.edu
space
AG01_innermost
run statistics
property
value
solver
AProVE
configuration
certified
runtime (wallclock)
3.12294 seconds
cpu usage
5.34597
user time
5.11249
system time
0.233482
max virtual memory
1.85302E7
max residence set size
386192.0
stage attributes
key
value
certification-result
CERTIFIED
output-size
31068
starexec-result
YES
certification-time
0.1
output
YES <?xml version="1.0" encoding="UTF-8" standalone="no"?><?xml-stylesheet type="text/xsl" href="cpfHTML.xsl"?><certificationProblem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="cpf.xsd"><input><trsInput><trs><rules><rule><lhs><funapp><name>and</name><arg><funapp><name>true</name></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>y</var></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>false</name></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>eq</name><arg><funapp><name>nil</name></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>eq</name><arg><funapp><name>cons</name><arg><var>t</var></arg><arg><var>l</var></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>eq</name><arg><funapp><name>nil</name></funapp></arg><arg><funapp><name>cons</name><arg><var>t</var></arg><arg><var>l</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>eq</name><arg><funapp><name>cons</name><arg><var>t</var></arg><arg><var>l</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>t'</var></arg><arg><var>l'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>eq</name><arg><var>t</var></arg><arg><var>t'</var></arg></funapp></arg><arg><funapp><name>eq</name><arg><var>l</var></arg><arg><var>l'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>eq</name><arg><funapp><name>var</name><arg><var>l</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>l'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>eq</name><arg><var>l</var></arg><arg><var>l'</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>eq</name><arg><funapp><name>var</name><arg><var>l</var></arg></funapp></arg><arg><funapp><name>apply</name><arg><var>t</var></arg><arg><var>s</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>eq</name><arg><funapp><name>var</name><arg><var>l</var></arg></funapp></arg><arg><funapp><name>lambda</name><arg><var>x</var></arg><arg><var>t</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>eq</name><arg><funapp><name>apply</name><arg><var>t</var></arg><arg><var>s</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>l</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>eq</name><arg><funapp><name>apply</name><arg><var>t</var></arg><arg><var>s</var></arg></funapp></arg><arg><funapp><name>apply</name><arg><var>t'</var></arg><arg><var>s'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>eq</name><arg><var>t</var></arg><arg><var>t'</var></arg></funapp></arg><arg><funapp><name>eq</name><arg><var>s</var></arg><arg><var>s'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>eq</name><arg><funapp><name>apply</name><arg><var>t</var></arg><arg><var>s</var></arg></funapp></arg><arg><funapp><name>lambda</name><arg><var>x</var></arg><arg><var>t</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>eq</name><arg><funapp><name>lambda</name><arg><var>x</var></arg><arg><var>t</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>l</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>eq</name><arg><funapp><name>lambda</name><arg><var>x</var></arg><arg><var>t</var></arg></funapp></arg><arg><funapp><name>apply</name><arg><var>t</var></arg><arg><var>s</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>eq</name><arg><funapp><name>lambda</name><arg><var>x</var></arg><arg><var>t</var></arg></funapp></arg><arg><funapp><name>lambda</name><arg><var>x'</var></arg><arg><var>t'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>eq</name><arg><var>x</var></arg><arg><var>x'</var></arg></funapp></arg><arg><funapp><name>eq</name><arg><var>t</var></arg><arg><var>t'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>if</name><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>var</name><arg><var>k</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>l'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>var</name><arg><var>k</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>if</name><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>var</name><arg><var>k</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>l'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>var</name><arg><var>l'</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ren</name><arg><funapp><name>var</name><arg><var>l</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>k</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>l'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>if</name><arg><funapp><name>eq</name><arg><var>l</var></arg><arg><var>l'</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>k</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>l'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>ren</name><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>apply</name><arg><var>t</var></arg><arg><var>s</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>apply</name><arg><funapp><name>ren</name><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>t</var></arg></funapp></arg><arg><funapp><name>ren</name><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>s</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>ren</name><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>lambda</name><arg><var>z</var></arg><arg><var>t</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>lambda</name><arg><funapp><name>var</name><arg><funapp><name>cons</name><arg><var>x</var></arg><arg><funapp><name>cons</name><arg><var>y</var></arg><arg><funapp><name>cons</name><arg><funapp><name>lambda</name><arg><var>z</var></arg><arg><var>t</var></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>ren</name><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>ren</name><arg><var>z</var></arg><arg><funapp><name>var</name><arg><funapp><name>cons</name><arg><var>x</var></arg><arg><funapp><name>cons</name><arg><var>y</var></arg><arg><funapp><name>cons</name><arg><funapp><name>lambda</name><arg><var>z</var></arg><arg><var>t</var></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>t</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><strategy><innermost/></strategy></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><name>eq</name></sharp><arg><funapp><name>cons</name><arg><var>t</var></arg><arg><var>l</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>t'</var></arg><arg><var>l'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>eq</name><arg><var>t</var></arg><arg><var>t'</var></arg></funapp></arg><arg><funapp><name>eq</name><arg><var>l</var></arg><arg><var>l'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eq</name></sharp><arg><funapp><name>cons</name><arg><var>t</var></arg><arg><var>l</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>t'</var></arg><arg><var>l'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>eq</name></sharp><arg><var>t</var></arg><arg><var>t'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eq</name></sharp><arg><funapp><name>cons</name><arg><var>t</var></arg><arg><var>l</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>t'</var></arg><arg><var>l'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>eq</name></sharp><arg><var>l</var></arg><arg><var>l'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eq</name></sharp><arg><funapp><name>var</name><arg><var>l</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>l'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>eq</name></sharp><arg><var>l</var></arg><arg><var>l'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eq</name></sharp><arg><funapp><name>apply</name><arg><var>t</var></arg><arg><var>s</var></arg></funapp></arg><arg><funapp><name>apply</name><arg><var>t'</var></arg><arg><var>s'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>eq</name><arg><var>t</var></arg><arg><var>t'</var></arg></funapp></arg><arg><funapp><name>eq</name><arg><var>s</var></arg><arg><var>s'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eq</name></sharp><arg><funapp><name>apply</name><arg><var>t</var></arg><arg><var>s</var></arg></funapp></arg><arg><funapp><name>apply</name><arg><var>t'</var></arg><arg><var>s'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>eq</name></sharp><arg><var>t</var></arg><arg><var>t'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eq</name></sharp><arg><funapp><name>apply</name><arg><var>t</var></arg><arg><var>s</var></arg></funapp></arg><arg><funapp><name>apply</name><arg><var>t'</var></arg><arg><var>s'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>eq</name></sharp><arg><var>s</var></arg><arg><var>s'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eq</name></sharp><arg><funapp><name>lambda</name><arg><var>x</var></arg><arg><var>t</var></arg></funapp></arg><arg><funapp><name>lambda</name><arg><var>x'</var></arg><arg><var>t'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>eq</name><arg><var>x</var></arg><arg><var>x'</var></arg></funapp></arg><arg><funapp><name>eq</name><arg><var>t</var></arg><arg><var>t'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eq</name></sharp><arg><funapp><name>lambda</name><arg><var>x</var></arg><arg><var>t</var></arg></funapp></arg><arg><funapp><name>lambda</name><arg><var>x'</var></arg><arg><var>t'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>eq</name></sharp><arg><var>x</var></arg><arg><var>x'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eq</name></sharp><arg><funapp><name>lambda</name><arg><var>x</var></arg><arg><var>t</var></arg></funapp></arg><arg><funapp><name>lambda</name><arg><var>x'</var></arg><arg><var>t'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>eq</name></sharp><arg><var>t</var></arg><arg><var>t'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>ren</name></sharp><arg><funapp><name>var</name><arg><var>l</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>k</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>l'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>eq</name><arg><var>l</var></arg><arg><var>l'</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>k</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>l'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>ren</name></sharp><arg><funapp><name>var</name><arg><var>l</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>k</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>l'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>eq</name></sharp><arg><var>l</var></arg><arg><var>l'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>ren</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>apply</name><arg><var>t</var></arg><arg><var>s</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>ren</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>t</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>ren</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>apply</name><arg><var>t</var></arg><arg><var>s</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>ren</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>s</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>ren</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>lambda</name><arg><var>z</var></arg><arg><var>t</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>ren</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>ren</name><arg><var>z</var></arg><arg><funapp><name>var</name><arg><funapp><name>cons</name><arg><var>x</var></arg><arg><funapp><name>cons</name><arg><var>y</var></arg><arg><funapp><name>cons</name><arg><funapp><name>lambda</name><arg><var>z</var></arg><arg><var>t</var></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>t</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>ren</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>lambda</name><arg><var>z</var></arg><arg><var>t</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>ren</name></sharp><arg><var>z</var></arg><arg><funapp><name>var</name><arg><funapp><name>cons</name><arg><var>x</var></arg><arg><funapp><name>cons</name><arg><var>y</var></arg><arg><funapp><name>cons</name><arg><funapp><name>lambda</name><arg><var>z</var></arg><arg><var>t</var></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>t</var></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>ren</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>apply</name><arg><var>t</var></arg><arg><var>s</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>ren</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>s</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>ren</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>apply</name><arg><var>t</var></arg><arg><var>s</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>ren</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>t</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>ren</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>lambda</name><arg><var>z</var></arg><arg><var>t</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>ren</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>ren</name><arg><var>z</var></arg><arg><funapp><name>var</name><arg><funapp><name>cons</name><arg><var>x</var></arg><arg><funapp><name>cons</name><arg><var>y</var></arg><arg><funapp><name>cons</name><arg><funapp><name>lambda</name><arg><var>z</var></arg><arg><var>t</var></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>t</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>ren</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>lambda</name><arg><var>z</var></arg><arg><var>t</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>ren</name></sharp><arg><var>z</var></arg><arg><funapp><name>var</name><arg><funapp><name>cons</name><arg><var>x</var></arg><arg><funapp><name>cons</name><arg><var>y</var></arg><arg><funapp><name>cons</name><arg><funapp><name>lambda</name><arg><var>z</var></arg><arg><var>t</var></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>t</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><redPairUrProc><orderingConstraintProof><redPair><knuthBendixOrder><w0>1</w0><precedenceWeight><precedenceWeightEntry><name>apply</name><arity>2</arity><precedence>3</precedence><weight>1</weight></precedenceWeightEntry><precedenceWeightEntry><name>lambda</name><arity>2</arity><precedence>0</precedence><weight>1</weight></precedenceWeightEntry><precedenceWeightEntry><name>ren</name><arity>3</arity><precedence>4</precedence><weight>0</weight></precedenceWeightEntry><precedenceWeightEntry><name>var</name><arity>1</arity><precedence>1</precedence><weight>1</weight></precedenceWeightEntry><precedenceWeightEntry><name>if</name><arity>3</arity><precedence>2</precedence><weight>1</weight></precedenceWeightEntry></precedenceWeight><argumentFilter><argumentFilterEntry><sharp><name>ren</name></sharp><arity>3</arity><collapsing>3</collapsing></argumentFilterEntry><argumentFilterEntry><name>apply</name><arity>2</arity><nonCollapsing><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>lambda</name><arity>2</arity><nonCollapsing><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>ren</name><arity>3</arity><nonCollapsing><position>3</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>var</name><arity>1</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>if</name><arity>3</arity><nonCollapsing/></argumentFilterEntry></argumentFilter></knuthBendixOrder></redPair></orderingConstraintProof><dps><rules/></dps><usableRules><rules><rule><lhs><funapp><name>ren</name><arg><funapp><name>var</name><arg><var>l</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>k</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>l'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>if</name><arg><funapp><name>eq</name><arg><var>l</var></arg><arg><var>l'</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>k</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>l'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>ren</name><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>apply</name><arg><var>t</var></arg><arg><var>s</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>apply</name><arg><funapp><name>ren</name><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>t</var></arg></funapp></arg><arg><funapp><name>ren</name><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>s</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>ren</name><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>lambda</name><arg><var>z</var></arg><arg><var>t</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>lambda</name><arg><funapp><name>var</name><arg><funapp><name>cons</name><arg><var>x</var></arg><arg><funapp><name>cons</name><arg><var>y</var></arg><arg><funapp><name>cons</name><arg><funapp><name>lambda</name><arg><var>z</var></arg><arg><var>t</var></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>ren</name><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>ren</name><arg><var>z</var></arg><arg><funapp><name>var</name><arg><funapp><name>cons</name><arg><var>x</var></arg><arg><funapp><name>cons</name><arg><var>y</var></arg><arg><funapp><name>cons</name><arg><funapp><name>lambda</name><arg><var>z</var></arg><arg><var>t</var></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>t</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>if</name><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>var</name><arg><var>k</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>l'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>var</name><arg><var>k</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>if</name><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>var</name><arg><var>k</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>l'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>var</name><arg><var>l'</var></arg></funapp></rhs></rule></rules></usableRules><dpProof><pIsEmpty/></dpProof></redPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>ren</name></sharp><arg><funapp><name>var</name><arg><var>l</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>k</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>l'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>eq</name></sharp><arg><var>l</var></arg><arg><var>l'</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>eq</name></sharp><arg><funapp><name>cons</name><arg><var>t</var></arg><arg><var>l</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>t'</var></arg><arg><var>l'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>eq</name></sharp><arg><var>l</var></arg><arg><var>l'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eq</name></sharp><arg><funapp><name>cons</name><arg><var>t</var></arg><arg><var>l</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>t'</var></arg><arg><var>l'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>eq</name></sharp><arg><var>t</var></arg><arg><var>t'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eq</name></sharp><arg><funapp><name>var</name><arg><var>l</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>l'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>eq</name></sharp><arg><var>l</var></arg><arg><var>l'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eq</name></sharp><arg><funapp><name>apply</name><arg><var>t</var></arg><arg><var>s</var></arg></funapp></arg><arg><funapp><name>apply</name><arg><var>t'</var></arg><arg><var>s'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>eq</name></sharp><arg><var>t</var></arg><arg><var>t'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eq</name></sharp><arg><funapp><name>apply</name><arg><var>t</var></arg><arg><var>s</var></arg></funapp></arg><arg><funapp><name>apply</name><arg><var>t'</var></arg><arg><var>s'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>eq</name></sharp><arg><var>s</var></arg><arg><var>s'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eq</name></sharp><arg><funapp><name>lambda</name><arg><var>x</var></arg><arg><var>t</var></arg></funapp></arg><arg><funapp><name>lambda</name><arg><var>x'</var></arg><arg><var>t'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>eq</name></sharp><arg><var>x</var></arg><arg><var>x'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eq</name></sharp><arg><funapp><name>lambda</name><arg><var>x</var></arg><arg><var>t</var></arg></funapp></arg><arg><funapp><name>lambda</name><arg><var>x'</var></arg><arg><var>t'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>eq</name></sharp><arg><var>t</var></arg><arg><var>t'</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>cons</name><arg><var>t</var></arg><arg><var>l</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>t'</var></arg><arg><var>l'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>eq</name></sharp><arg><var>l</var></arg><arg><var>l'</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge><edge><position>2</position><strict>true</strict><position>2</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>eq</name></sharp><arg><funapp><name>cons</name><arg><var>t</var></arg><arg><var>l</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>t'</var></arg><arg><var>l'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>eq</name></sharp><arg><var>t</var></arg><arg><var>t'</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge><edge><position>2</position><strict>true</strict><position>2</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>eq</name></sharp><arg><funapp><name>var</name><arg><var>l</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>l'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>eq</name></sharp><arg><var>l</var></arg><arg><var>l'</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge><edge><position>2</position><strict>true</strict><position>2</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>eq</name></sharp><arg><funapp><name>apply</name><arg><var>t</var></arg><arg><var>s</var></arg></funapp></arg><arg><funapp><name>apply</name><arg><var>t'</var></arg><arg><var>s'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>eq</name></sharp><arg><var>t</var></arg><arg><var>t'</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge><edge><position>2</position><strict>true</strict><position>2</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>eq</name></sharp><arg><funapp><name>apply</name><arg><var>t</var></arg><arg><var>s</var></arg></funapp></arg><arg><funapp><name>apply</name><arg><var>t'</var></arg><arg><var>s'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>eq</name></sharp><arg><var>s</var></arg><arg><var>s'</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge><edge><position>2</position><strict>true</strict><position>2</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>eq</name></sharp><arg><funapp><name>lambda</name><arg><var>x</var></arg><arg><var>t</var></arg></funapp></arg><arg><funapp><name>lambda</name><arg><var>x'</var></arg><arg><var>t'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>eq</name></sharp><arg><var>x</var></arg><arg><var>x'</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge><edge><position>2</position><strict>true</strict><position>2</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>eq</name></sharp><arg><funapp><name>lambda</name><arg><var>x</var></arg><arg><var>t</var></arg></funapp></arg><arg><funapp><name>lambda</name><arg><var>x'</var></arg><arg><var>t'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>eq</name></sharp><arg><var>t</var></arg><arg><var>t'</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>eq</name></sharp><arg><funapp><name>cons</name><arg><var>t</var></arg><arg><var>l</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>t'</var></arg><arg><var>l'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>eq</name><arg><var>t</var></arg><arg><var>t'</var></arg></funapp></arg><arg><funapp><name>eq</name><arg><var>l</var></arg><arg><var>l'</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>eq</name></sharp><arg><funapp><name>apply</name><arg><var>t</var></arg><arg><var>s</var></arg></funapp></arg><arg><funapp><name>apply</name><arg><var>t'</var></arg><arg><var>s'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>eq</name><arg><var>t</var></arg><arg><var>t'</var></arg></funapp></arg><arg><funapp><name>eq</name><arg><var>s</var></arg><arg><var>s'</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>eq</name></sharp><arg><funapp><name>lambda</name><arg><var>x</var></arg><arg><var>t</var></arg></funapp></arg><arg><funapp><name>lambda</name><arg><var>x'</var></arg><arg><var>t'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>eq</name><arg><var>x</var></arg><arg><var>x'</var></arg></funapp></arg><arg><funapp><name>eq</name><arg><var>t</var></arg><arg><var>t'</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>ren</name></sharp><arg><funapp><name>var</name><arg><var>l</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>k</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>l'</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>eq</name><arg><var>l</var></arg><arg><var>l'</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>k</var></arg></funapp></arg><arg><funapp><name>var</name><arg><var>l'</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></dpTrans></trsTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (7 real / 0 unknown / 0 assumptions / 7 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>
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return to TRS_Innermost Certified 2019-04-01 06.48