details

property	value
status	complete
benchmark	thiemann03.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n050.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	2.87145590782 seconds
cpu usage	7.864651372
max memory	4.97446912E8

stage attributes

key	value
certification-result	CERTIFIED
output-size	33246
starexec-result	YES
certification-time	0.1

output

/export/starexec/sandbox/solver/bin/starexec_run_certified /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES <?xml version="1.0" encoding="UTF-8" standalone="no"?><?xml-stylesheet type="text/xsl" href="cpfHTML.xsl"?><certificationProblem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="cpf.xsd"><input><trsInput><trs><rules><rule><lhs><funapp><name>null</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>null</name><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>tail</name><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>tail</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>head</name><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>n</var></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>nil</name></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>y</var></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>add</name><arg><var>n</var></arg><arg><funapp><name>app</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>reverse</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>reverse</name><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>reverse</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>add</name><arg><var>n</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>shuffle</name><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>shuff</name><arg><var>x</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>shuff</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>if</name><arg><funapp><name>null</name><arg><var>x</var></arg></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>app</name><arg><var>y</var></arg><arg><funapp><name>add</name><arg><funapp><name>head</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>if</name><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>z</var></arg></funapp></lhs><rhs><var>y</var></rhs></rule><rule><lhs><funapp><name>if</name><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>shuff</name><arg><funapp><name>reverse</name><arg><funapp><name>tail</name><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><var>z</var></arg></funapp></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><switchInnermost><wcrProof><joinableCriticalPairsBFS>10</joinableCriticalPairsBFS></wcrProof><trsTerminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reverse</name></sharp><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>reverse</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>add</name><arg><var>n</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reverse</name></sharp><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>reverse</name></sharp><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>shuffle</name></sharp><arg><var>x</var></arg></funapp></lhs><rhs><funapp><sharp><name>shuff</name></sharp><arg><var>x</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>shuff</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>null</name><arg><var>x</var></arg></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>app</name><arg><var>y</var></arg><arg><funapp><name>add</name><arg><funapp><name>head</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>shuff</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>null</name></sharp><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>shuff</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><var>y</var></arg><arg><funapp><name>add</name><arg><funapp><name>head</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>shuff</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>head</name></sharp><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>shuff</name></sharp><arg><funapp><name>reverse</name><arg><funapp><name>tail</name><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>reverse</name></sharp><arg><funapp><name>tail</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>tail</name></sharp><arg><var>x</var></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>shuffle</name></sharp><arg><var>x</var></arg></funapp></lhs><rhs><funapp><sharp><name>shuff</name></sharp><arg><var>x</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>shuff</name></sharp><arg><funapp><name>reverse</name><arg><funapp><name>tail</name><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>shuff</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>null</name><arg><var>x</var></arg></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>app</name><arg><var>y</var></arg><arg><funapp><name>add</name><arg><funapp><name>head</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>null</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>null</name><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>head</name><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>n</var></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>nil</name></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>y</var></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>add</name><arg><var>n</var></arg><arg><funapp><name>app</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>tail</name><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>tail</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>reverse</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>reverse</name><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>reverse</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>add</name><arg><var>n</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>null</name><arg><funapp><name>nil</name></funapp></arg></funapp><funapp><name>null</name><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>tail</name><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>tail</name><arg><funapp><name>nil</name></funapp></arg></funapp><funapp><name>head</name><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>app</name><arg><funapp><name>nil</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>app</name><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp><funapp><name>reverse</name><arg><funapp><name>nil</name></funapp></arg></funapp><funapp><name>reverse</name><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></innermostLhss><dpProof><narrowingProc><rule><lhs><funapp><sharp><name>shuff</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>null</name><arg><var>x</var></arg></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>app</name><arg><var>y</var></arg><arg><funapp><name>add</name><arg><funapp><name>head</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><positionInTerm><position>1</position></positionInTerm><narrowings><rules><rule><lhs><funapp><sharp><name>shuff</name></sharp><arg><funapp><name>nil</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>nil</name></funapp></arg><arg><var>y1</var></arg><arg><funapp><name>app</name><arg><var>y1</var></arg><arg><funapp><name>add</name><arg><funapp><name>head</name><arg><funapp><name>nil</name></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>shuff</name></sharp><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg><arg><funapp><name>app</name><arg><var>y1</var></arg><arg><funapp><name>add</name><arg><funapp><name>head</name><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></narrowings><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>shuff</name></sharp><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg><arg><funapp><name>app</name><arg><var>y1</var></arg><arg><funapp><name>add</name><arg><funapp><name>head</name><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>shuff</name></sharp><arg><funapp><name>reverse</name><arg><funapp><name>tail</name><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><var>z</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>tail</name><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>tail</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>reverse</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>reverse</name><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>reverse</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>add</name><arg><var>n</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>nil</name></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>y</var></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>add</name><arg><var>n</var></arg><arg><funapp><name>app</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>head</name><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>n</var></rhs></rule></rules></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>tail</name><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>tail</name><arg><funapp><name>nil</name></funapp></arg></funapp><funapp><name>head</name><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>app</name><arg><funapp><name>nil</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>app</name><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp><funapp><name>reverse</name><arg><funapp><name>nil</name></funapp></arg></funapp><funapp><name>reverse</name><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></innermostLhss><dpProof><rewritingProc><rule><lhs><funapp><sharp><name>shuff</name></sharp><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg><arg><funapp><name>app</name><arg><var>y1</var></arg><arg><funapp><name>add</name><arg><funapp><name>head</name><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>4</position><position>2</position><position>1</position></positionInTerm><rule><lhs><funapp><name>head</name><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>n</var></rhs></rule><funapp><sharp><name>if</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg><arg><funapp><name>app</name><arg><var>y1</var></arg><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>shuff</name></sharp><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg><arg><funapp><name>app</name><arg><var>y1</var></arg><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><usableRules><rules><rule><lhs><funapp><name>head</name><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>n</var></rhs></rule></rules></usableRules><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>app</name><arg><funapp><name>nil</name></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>y</var></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>add</name><arg><var>n</var></arg><arg><funapp><name>app</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>tail</name><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>tail</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>reverse</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>reverse</name><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>reverse</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>add</name><arg><var>n</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>tail</name><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>tail</name><arg><funapp><name>nil</name></funapp></arg></funapp><funapp><name>app</name><arg><funapp><name>nil</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>app</name><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp><funapp><name>reverse</name><arg><funapp><name>nil</name></funapp></arg></funapp><funapp><name>reverse</name><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></innermostLhss><dpProof><narrowingProc><rule><lhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>shuff</name></sharp><arg><funapp><name>reverse</name><arg><funapp><name>tail</name><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><var>z</var></arg></funapp></rhs></rule><positionInTerm><position>1</position></positionInTerm><narrowings><rules><rule><lhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>y2</var></arg></funapp></lhs><rhs><funapp><sharp><name>shuff</name></sharp><arg><funapp><name>reverse</name><arg><var>x1</var></arg></funapp></arg><arg><var>y2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>nil</name></funapp></arg><arg><var>y1</var></arg><arg><var>y2</var></arg></funapp></lhs><rhs><funapp><sharp><name>shuff</name></sharp><arg><funapp><name>reverse</name><arg><funapp><name>nil</name></funapp></arg></funapp></arg><arg><var>y2</var></arg></funapp></rhs></rule></rules></narrowings><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>y2</var></arg></funapp></lhs><rhs><funapp><sharp><name>shuff</name></sharp><arg><funapp><name>reverse</name><arg><var>x1</var></arg></funapp></arg><arg><var>y2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>shuff</name></sharp><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg><arg><funapp><name>app</name><arg><var>y1</var></arg><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>app</name><arg><funapp><name>nil</name></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>y</var></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>add</name><arg><var>n</var></arg><arg><funapp><name>app</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>reverse</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>reverse</name><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>reverse</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>add</name><arg><var>n</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>app</name><arg><funapp><name>nil</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>app</name><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp><funapp><name>reverse</name><arg><funapp><name>nil</name></funapp></arg></funapp><funapp><name>reverse</name><arg><funapp><name>add</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></innermostLhss><dpProof><redPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>shuff</name></sharp><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>reverse</name><arity>1</arity><polynomial><variable>1</variable></polynomial></interpret><interpret><name>nil</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>add</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></sum></polynomial></interpret><interpret><name>app</name><arity>2</arity><polynomial><sum><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></sum></polynomial></interpret><interpret><sharp><name>if</name></sharp><arity>4</arity><polynomial><sum><polynomial><coefficient><integer>-2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>false</name><arity>0</arity><polynomial><coefficient><integer>1</integer></coefficient></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules/></dps><dpProof><pIsEmpty/></dpProof></redPairProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>nil</name></funapp></arg><arg><var>y1</var></arg><arg><var>y2</var></arg></funapp></lhs><rhs><funapp><sharp><name>shuff</name></sharp><arg><funapp><name>reverse</name><arg><funapp><name>nil</name></funapp></arg></funapp></arg><arg><var>y2</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></narrowingProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></rewritingProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>shuff</name></sharp><arg><funapp><name>nil</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>nil</name></funapp></arg><arg><var>y1</var></arg><arg><funapp><name>app</name><arg><var>y1</var></arg><arg><funapp><name>add</name><arg><funapp><name>head</name><arg><funapp><name>nil</name></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></narrowingProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>reverse</name></sharp><arg><funapp><name>tail</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>reverse</name></sharp><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>reverse</name></sharp><arg><var>x</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>reverse</name></sharp><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>reverse</name></sharp><arg><var>x</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>reverse</name></sharp><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>reverse</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>add</name><arg><var>n</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>shuff</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><var>y</var></arg><arg><funapp><name>add</name><arg><funapp><name>head</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>app</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>app</name></sharp><arg><funapp><name>add</name><arg><var>n</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>app</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>shuff</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>null</name></sharp><arg><var>x</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>shuff</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>head</name></sharp><arg><var>x</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>tail</name></sharp><arg><var>x</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></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 % (24 real / 0 unknown / 0 assumptions / 24 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

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to TRS Standard Certified