details

property	value
status	complete
benchmark	nonterm.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n146.star.cs.uiowa.edu
space	AProVE_06

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	2.33197 seconds
cpu usage	5.8167
user time	5.59133
system time	0.225363
max virtual memory	3.6817824E7
max residence set size	350536.0

stage attributes

key	value
certification-result	CERTIFIED
starexec-result	CERTIFIED NO
certification-time	0.26
bare-result	NO

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" xsi:noNamespaceSchemaLocation="cpf.xsd"><input><trsInput><trs><rules><rule><lhs><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>id</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>id</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>id</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>id</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsNonterminationProof><innermostLhssIncrease><innermostLhss><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x1</var></arg></funapp><funapp><name>id</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>id</name><arg><funapp><name>0</name></funapp></arg></funapp></innermostLhss><trsNonterminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>id</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>id</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>id</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>id</name></sharp><arg><var>x</var></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpNonterminationProof><dpRuleRemoval><dps><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>id</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>id</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>id</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>id</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>id</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule></rules></trs><dpNonterminationProof><dpRuleRemoval><dps><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>id</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>id</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>id</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>id</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule></rules></trs><dpNonterminationProof><innermostLhssRemovalProc><innermostLhss><funapp><name>id</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>id</name><arg><funapp><name>0</name></funapp></arg></funapp></innermostLhss><dpNonterminationProof><rewritingProc><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>id</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>1</position></positionInTerm><rule><lhs><funapp><name>id</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>id</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>id</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>id</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rhs></rule><usableRules><rules><rule><lhs><funapp><name>id</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>id</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>id</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule></rules></usableRules><dpNonterminationProof><rewritingProc><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>id</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>1</position><position>1</position></positionInTerm><rule><lhs><funapp><name>id</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>id</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>id</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>id</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rhs></rule><usableRules><rules><rule><lhs><funapp><name>id</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>id</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>id</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule></rules></usableRules><dpNonterminationProof><rewritingProc><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>id</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>1</position><position>1</position><position>1</position></positionInTerm><rule><lhs><funapp><name>id</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>id</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>id</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>id</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rhs></rule><usableRules><rules><rule><lhs><funapp><name>id</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>id</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>id</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule></rules></usableRules><dpNonterminationProof><rewritingProc><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>id</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>1</position><position>1</position><position>1</position><position>1</position></positionInTerm><rule><lhs><funapp><name>id</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>id</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>id</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>id</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rhs></rule><usableRules><rules><rule><lhs><funapp><name>id</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>id</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>id</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule></rules></usableRules><dpNonterminationProof><rewritingProc><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>id</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>1</position><position>1</position><position>1</position><position>1</position><position>1</position></positionInTerm><rule><lhs><funapp><name>id</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>id</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>id</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>id</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rhs></rule><usableRules><rules><rule><lhs><funapp><name>id</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>id</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>id</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule></rules></usableRules><dpNonterminationProof><rewritingProc><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>id</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>1</position><position>1</position><position>1</position><position>1</position><position>1</position><position>1</position></positionInTerm><rule><lhs><funapp><name>id</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>id</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>id</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>id</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rhs></rule><usableRules><rules><rule><lhs><funapp><name>id</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>id</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>id</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule></rules></usableRules><dpNonterminationProof><rewritingProc><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>id</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>1</position><position>1</position><position>1</position><position>1</position><position>1</position><position>1</position><position>1</position></positionInTerm><rule><lhs><funapp><name>id</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>id</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>id</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>id</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rhs></rule><usableRules><rules><rule><lhs><funapp><name>id</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>id</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>id</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule></rules></usableRules><dpNonterminationProof><rewritingProc><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>id</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>1</position><position>1</position><position>1</position><position>1</position><position>1</position><position>1</position><position>1</position><position>1</position></positionInTerm><rule><lhs><funapp><name>id</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>id</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>id</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>id</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rhs></rule><usableRules><rules><rule><lhs><funapp><name>id</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>id</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>id</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule></rules></usableRules><dpNonterminationProof><switchFullStrategyProc><wcrProof><joinableCriticalPairsBFS>0</joinableCriticalPairsBFS></wcrProof><dpNonterminationProof><loop><rewriteSequence><startTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></startTerm><rewriteStep><positionInTerm/><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>id</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rhs></rule><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>id</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><var>y</var></arg></funapp></rewriteStep></rewriteSequence><substitution><substEntry><var>x</var><funapp><name>id</name><arg><var>x</var></arg></funapp></substEntry><substEntry><var>y</var><var>y</var></substEntry></substitution><box/></loop></dpNonterminationProof></switchFullStrategyProc></dpNonterminationProof></rewritingProc></dpNonterminationProof></rewritingProc></dpNonterminationProof></rewritingProc></dpNonterminationProof></rewritingProc></dpNonterminationProof></rewritingProc></dpNonterminationProof></rewritingProc></dpNonterminationProof></rewritingProc></dpNonterminationProof></rewritingProc></dpNonterminationProof></innermostLhssRemovalProc></dpNonterminationProof></dpRuleRemoval></dpNonterminationProof></dpRuleRemoval></dpNonterminationProof></dpTrans></trsNonterminationProof></innermostLhssIncrease></trsNonterminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (15 real / 0 unknown / 0 assumptions / 15 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