details

property	value
status	complete
benchmark	teparla2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	Secret_05_TRS

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	2.74058 seconds
cpu usage	7.49184
user time	7.15111
system time	0.34073
max virtual memory	1.8725108E7
max residence set size	497768.0

stage attributes

key	value
certification-result	CERTIFIED
starexec-result	CERTIFIED YES
certification-time	0.50
bare-result	YES

output

<?xml version="1.0" encoding="UTF-8" standalone="no"?><?xml-stylesheet type="text/xsl" href="cpfHTML.xsl"?><certificationProblem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" 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e><numberLabel/></labeledSymbol></funapp></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>f</name></sharp><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>y</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>f</name></sharp><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>y</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg></funapp></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>y</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg></funapp></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>y</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><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<arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></rhs></rule></rules></trs><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>f</name></sharp><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>y</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>f</name></sharp><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg></funapp></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>f</name></sharp><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>y</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>f</name></sharp><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg></funapp></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><monoRedPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><int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erLabel/></labeledSymbol></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg></funapp></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>f</name></sharp><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>y</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>f</name></sharp><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg></funapp></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>f</name></sharp><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>y</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>f</name></sharp><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg></funapp></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><monoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>a</name><numberLabel/></labeledSymbol><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><sharp><name>f</name></sharp><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>f</name></sharp><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>y</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>f</name></sharp><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg></funapp></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></rhs></rule></rules></trs><dpProof><monoRedPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><labeledSymbol><sharp><name>f</name></sharp><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>a</name><numberLabel/></labeledSymbol><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>f</name></sharp><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>y</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>f</name></sharp><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg></funapp></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules/></trs><usableRules><rules/></usableRules><dpProof><redPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><labeledSymbol><sharp><name>f</name></sharp><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>a</name><numberLabel/></labeledSymbol><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules/></dps><dpProof><pIsEmpty/></dpProof></redPairProc></dpProof></monoRedPairUrProc></dpProof></monoRedPairProc></dpProof></component></depGraphProc></dpProof></monoRedPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>f</name></sharp><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>y</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>f</name></sharp><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>f</name></sharp><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>y</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>f</name></sharp><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>f</name></sharp><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>y</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>f</name></sharp><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg></funapp></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>f</name></sharp><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>y</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>f</name></sharp><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg></funapp></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>f</name></sharp><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>y</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>f</name></sharp><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>f</name></sharp><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>y</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x</var></arg><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>f</name></sharp><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></semlabProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><var>y</var></arg><arg><funapp><name>f</name><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>a</name></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><funapp><name>a</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>x</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><var>y</var></arg><arg><funapp><name>f</name><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>a</name></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>x</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><var>x</var></arg><arg><funapp><name>f</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><var>x</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><funapp><name>a</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><var>x</var></arg><arg><funapp><name>f</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><var>x</var></arg><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><funapp><name>a</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><var>x</var></arg><arg><funapp><name>f</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>x</var></arg><arg><funapp><name>a</name></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: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (10 real / 0 unknown / 0 assumptions / 10 total proof steps)</strategy><url>http://aprove.informatik.rwth-aachen.de</url></tool><toolUser><firstName>John</firstName><lastName>Doe</lastName></toolUser></proofOrigin><inputOrigin/></origin></certificationProblem> popout

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all output return to TRS Standard Certified