details

property	value
status	complete
benchmark	85079.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	61.6568 seconds
cpu usage	239.183
user time	231.851
system time	7.33241
max virtual memory	3.7622008E7
max residence set size	1.215718E7

stage attributes

key	value
certification-result	CERTIFIED
starexec-result	CERTIFIED YES
certification-time	4.88
bare-result	YES

output

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napp></lhs><rhs><funapp><name>2</name><arg><funapp><name>4</name><arg><funapp><name>1</name><arg><funapp><name>3</name><arg><funapp><name>3</name><arg><funapp><name>5</name><arg><funapp><name>0</name><arg><funapp><name>2</name><arg><funapp><name>0</name><arg><funapp><name>3</name><arg><funapp><name>3</name><arg><funapp><name>5</name><arg><funapp><name>3</name><arg><funapp><name>0</name><arg><funapp><name>1</name><arg><funapp><name>4</name><arg><funapp><name>5</name><arg><funapp><name>0</name><arg><funapp><name>2</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>1</name><arg><funapp><name>0</name><arg><funapp><name>0</name><arg><funapp><name>4</name><arg><funapp><name>4</name><arg><funapp><name>4</name><arg><funapp><name>1</name><arg><funapp><name>3</name><arg><funapp><name>2</name><arg><funapp><name>4</name><arg><funapp><name>5</name><arg><funapp><name>1</name><arg><funapp><name>2</name><arg><funapp><name>5</name><arg><funapp><name>3</name><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><funapp><name>2</name><arg><funapp><name>2</name><arg><funapp><name>5</name><arg><funapp><name>2</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>4</name><arg><funapp><name>5</name><arg><funapp><name>1</name><arg><funapp><name>3</name><arg><funapp><name>5</name><arg><funapp><name>4</name><arg><funapp><name>2</name><arg><funapp><name>4</name><arg><funapp><name>4</name><arg><funapp><name>4</name><arg><funapp><name>5</name><arg><funapp><name>0</name><arg><funapp><name>2</name><arg><funapp><name>2</name><arg><funapp><name>1</name><arg><funapp><name>1</name><arg><funapp><name>1</name><arg><funapp><name>1</name><arg><funapp><name>3</name><arg><funapp><name>4</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>3</name><arg><funapp><name>4</name><arg><funapp><name>4</name><arg><funapp><name>4</name><arg><funapp><name>2</name><arg><funapp><name>1</name><arg><funapp><name>5</name><arg><funapp><name>3</name><arg><funapp><name>1</name><arg><funapp><name>4</name><arg><funapp><name>1</name><arg><funapp><name>5</name><arg><funapp><name>3</name><arg><funapp><name>5</name><arg><funapp><name>3</name><arg><funapp><name>3</name><arg><funapp><name>0</name><arg><funapp><name>2</name><arg><funapp><name>1</name><arg><funapp><name>3</name><arg><funapp><name>1</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>3</name><arg><funapp><name>4</name><arg><funapp><name>3</name><arg><funapp><name>0</name><arg><funapp><name>3</name><arg><funapp><name>3</name><arg><funapp><name>4</name><arg><funapp><name>4</name><arg><funapp><name>3</name><arg><funapp><name>4</name><arg><funapp><name>0</name><arg><funapp><name>1</name><arg><funapp><name>4</name><arg><funapp><name>0</name><arg><funapp><name>1</name><arg><funapp><name>5</name><arg><funapp><name>1</name><arg><funapp><name>5</name><arg><funapp><name>4</name><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>5</name><arg><funapp><name>2</name><arg><funapp><name>1</name><arg><funapp><name>2</name><arg><funapp><name>2</name><arg><funapp><name>4</name><arg><funapp><name>5</name><arg><funapp><name>2</name><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><funapp><name>3</name><arg><funapp><name>3</name><arg><funapp><name>1</name><arg><funapp><name>0</name><arg><funapp><name>3</name><arg><funapp><name>4</name><arg><funapp><name>1</name><arg><funapp><name>0</name><arg><funapp><name>0</name><arg><funapp><name>3</name><arg><funapp><name>2</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>5</name><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><funapp><name>2</name><arg><funapp><name>4</name><arg><funapp><name>0</name><arg><funapp><name>2</name><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><funapp><name>1</name><arg><funapp><name>4</name><arg><funapp><name>3</name><arg><funapp><name>2</name><arg><funapp><name>1</name><arg><funapp><name>2</name><arg><funapp><name>1</name><arg><funapp><name>2</name><arg><funapp><name>5</name><arg><funapp><name>5</name><arg><funapp><name>2</name><arg><funapp><name>4</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>0</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>2</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>3</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>4</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>5</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>0</name><arg><funapp><name>1</name><arg><funapp><name>2</name><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>4</name><arg><funapp><name>1</name><arg><funapp><name>4</name><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>1</name><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><funapp><name>5</name><arg><funapp><name>3</name><arg><funapp><name>0</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>1</name><arg><funapp><name>4</name><arg><funapp><name>3</name><arg><funapp><name>5</name><arg><funapp><name>1</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>2</name><arg><funapp><name>1</name><arg><funapp><name>3</name><arg><funapp><name>5</name><arg><funapp><name>0</name><arg><funapp><name>0</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>4</name><arg><funapp><name>4</name><arg><funapp><name>2</name><arg><funapp><name>4</name><arg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1</name><arg><funapp><name>3</name><arg><funapp><name>0</name><arg><funapp><name>1</name><arg><funapp><name>3</name><arg><funapp><name>1</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>2</name><arg><funapp><name>1</name><arg><funapp><name>3</name><arg><funapp><name>5</name><arg><funapp><name>0</name><arg><funapp><name>0</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>4</name><arg><funapp><name>4</name><arg><funapp><name>2</name><arg><funapp><name>4</name><arg><funapp><name>5</name><arg><funapp><name>0</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>2</name><arg><funapp><name>2</name><arg><funapp><name>5</name><arg><funapp><name>1</name><arg><funapp><name>3</name><arg><funapp><name>4</name><arg><funapp><name>5</name><arg><funapp><name>3</name><arg><funapp><name>1</name><arg><funapp><name>4</name><arg><funapp><name>1</name><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><funapp><name>4</name><arg><funapp><name>2</name><arg><funapp><name>2</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>2</name><arg><funapp><name>5</name><arg><funapp><name>2</name><arg><funapp><name>0</name><arg><funapp><name>4</name><arg><funapp><name>2</name><arg><funapp><name>4</name><arg><funapp><name>4</name><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><funapp><name>4</name><arg><funapp><name>0</name><arg><funapp><name>0</name><arg><funapp><name>4</name><arg><funapp><name>3</name><arg><funapp><name>2</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>2</name><arg><funapp><name>0</name><arg><funapp><name>1</name><arg><funapp><name>3</name><arg><funapp><name>1</name><arg><funapp><name>2</name><arg><funapp><name>5</name><arg><funapp><name>4</name><arg><funapp><name>3</name><arg><funapp><name>4</name><arg><funapp><name>4</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>2</name><arg><funapp><name>1</name><arg><funapp><name>2</name><arg><funapp><name>4</name><arg><funapp><name>4</name><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><funapp><name>4</name><arg><funapp><name>2</name><arg><funapp><name>4</name><arg><funapp><name>4</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>4</name><arg><funapp><name>1</name><arg><funapp><name>5</name><arg><funapp><name>1</name><arg><funapp><name>2</name><arg><funapp><name>4</name><arg><funapp><name>1</name><arg><funapp><name>4</name><arg><funapp><name>1</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>4</name><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><funapp><name>1</name><arg><funapp><name>3</name><arg><funapp><name>0</name><arg><funapp><name>1</name><arg><funapp><name>3</name><arg><funapp><name>1</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>4</name><arg><funapp><name>3</name><arg><funapp><name>5</name><arg><funapp><name>1</name><arg><funapp><name>5</name><arg><funapp><name>1</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>4</name><arg><funapp><name>0</name><arg><funapp><name>2</name><arg><funapp><name>4</name><arg><funapp><name>5</name><arg><funapp><name>4</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>4</name><arg><funapp><name>1</name><arg><funapp><name>0</name><arg><funapp><name>5</name><arg><funapp><name>3</name><arg><funapp><name>4</name><arg><funapp><name>3</name><arg><funapp><name>5</name><arg><funapp><name>4</name><arg><funapp><name>1</name><arg><funapp><name>1</name><arg><var>x1</var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/funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><redPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>5</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>4</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>5</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>3</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>2</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>5</name></sharp><arg><funapp><name>4</name><arg><funapp><name>5</name><arg><funapp><name>3</name><arg><funapp><name>0</name><arg><funapp><name>3</name><arg><funapp><name>3</name><arg><funapp><name>3</name><arg><funapp><name>1</name><arg><funapp><name>2</name><arg><funapp><name>0</name><arg><funapp><name>0</name><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><funapp><name>3</name><arg><funapp><name>2</name><arg><funapp><name>0</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>5</name></sharp><arg><funapp><name>2</name><arg><funapp><name>0</name><arg><funapp><name>1</name><arg><funapp><name>4</name><arg><funapp><name>2</name><arg><funapp><name>4</name><arg><funapp><name>1</name><arg><funapp><name>2</name><arg><funapp><name>0</name><arg><funapp><name>0</name><arg><funapp><name>4</name><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><funapp><name>1</name><arg><funapp><name>2</name><arg><funapp><name>2</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><dpProof><redPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>5</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>4</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>5</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>3</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>2</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules/></dps><dpProof><p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</arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>2</name><arg><funapp><name>5</name><arg><funapp><name>2</name><arg><funapp><name>0</name><arg><funapp><name>4</name><arg><funapp><name>2</name><arg><funapp><name>4</name><arg><funapp><name>4</name><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><funapp><name>4</name><arg><funapp><name>0</name><arg><funapp><name>0</name><arg><funapp><name>4</name><arg><funapp><name>3</name><arg><funapp><name>2</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>2</name><arg><funapp><name>0</name><arg><funapp><name>1</name><arg><funapp><name>3</name><arg><funapp><name>1</name><arg><funapp><name>2</name><arg><funapp><name>5</name><arg><funapp><name>4</name><arg><funapp><name>3</name><arg><funapp><name>4</name><arg><funapp><name>4</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>2</name><arg><funapp><name>1</name><arg><funapp><name>2</name><arg><funapp><name>4</name><arg><funapp><name>4</name><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><funapp><name>4</name><arg><funapp><name>2</name><arg><funapp><name>4</name><arg><funapp><name>4</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>4</name><arg><funapp><name>1</name><arg><funapp><name>5</name><arg><funapp><name>1</name><arg><funapp><name>2</name><arg><funapp><name>4</name><arg><funapp><name>1</name><arg><funapp><name>4</name><arg><funapp><name>1</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>4</name><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><funapp><name>1</name><arg><funapp><name>3</name><arg><funapp><name>0</name><arg><funapp><name>1</name><arg><funapp><name>3</name><arg><funapp><name>1</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>4</name><arg><funapp><name>3</name><arg><funapp><name>5</name><arg><funapp><name>1</name><arg><funapp><name>5</name><arg><funapp><name>1</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>4</name><arg><funapp><name>0</name><arg><funapp><name>2</name><arg><funapp><name>4</name><arg><funapp><name>5</name><arg><funapp><name>4</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>4</name><arg><funapp><name>1</name><arg><funapp><name>0</name><arg><funapp><name>5</name><arg><funapp><name>3</name><arg><funapp><name>4</name><arg><funapp><name>3</name><arg><funapp><name>5</name><arg><funapp><name>4</name><arg><funapp><name>1</name><arg><funapp><name>1</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>4</name><arg><funapp><name>4</name><arg><funapp><name>4</name><arg><funapp><name>3</name><arg><funapp><name>3</name><arg><funapp><name>2</name><arg><funapp><name>0</name><arg><funapp><name>2</name><arg><funapp><name>4</name><arg><funapp><name>5</name><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>4</name><arg><funapp><name>3</name><arg><funapp><name>0</name><arg><funapp><name>3</name><arg><funapp><name>2</name><arg><funapp><name>4</name><arg><funapp><name>5</name><arg><funapp><name>0</name><arg><funapp><name>2</name><arg><funapp><name>5</name><arg><funapp><name>0</name><arg><funapp><name>0</name><arg><funapp><name>4</name><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><funapp><name>1</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>4</name><arg><funapp><name>4</name><arg><funapp><name>4</name><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><funapp><name>3</name><arg><funapp><name>4</name><arg><funapp><name>5</name><arg><funapp><name>0</name><arg><funapp><name>5</name><arg><funapp><name>2</name><arg><funapp><name>2</name><arg><funapp><name>1</name><arg><funapp><name>2</name><arg><funapp><name>0</name><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>5</name><arg><funapp><name>4</name><arg><funapp><name>5</name><arg><funapp><name>3</name><arg><funapp><name>0</name><arg><funapp><name>3</name><arg><funapp><name>3</name><arg><funapp><name>3</name><arg><funapp><name>1</name><arg><funapp><name>2</name><arg><funapp><name>0</name><arg><funapp><name>0</name><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><funapp><name>3</name><arg><funapp><name>2</name><arg><funapp><name>0</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>5</name><arg><funapp><name>2</name><arg><funapp><name>0</name><arg><funapp><name>1</name><arg><funapp><name>4</name><arg><funapp><name>2</name><arg><funapp><name>4</name><arg><funapp><name>1</name><arg><funapp><name>2</name><arg><funapp><name>0</name><arg><funapp><name>0</name><arg><funapp><name>4</name><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><funapp><name>1</name><arg><funapp><name>2</name><arg><funapp><name>2</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>5</name><arg><funapp><name>3</name><arg><funapp><name>3</name><arg><funapp><name>5</name><arg><funapp><name>3</name><arg><funapp><name>4</name><arg><funapp><name>0</name><arg><funapp><name>5</name><arg><funapp><name>0</name><arg><funapp><name>2</name><arg><funapp><name>4</name><arg><funapp><name>0</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>5</name><arg><funapp><name>5</name><arg><funapp><name>3</name><arg><funapp><name>2</name><arg><funapp><name>5</name><arg><funapp><name>4</name><arg><funapp><name>4</name><arg><funapp><name>2</name><arg><funapp><name>1</name><arg><funapp><name>1</name><arg><funapp><name>1</name><arg><funapp><name>3</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>5</name><arg><funapp><name>2</name><arg><funapp><name>1</name><arg><funapp><name>2</name><arg><funapp><name>2</name><arg><funapp><name>4</name><arg><funapp><name>5</name><arg><funapp><name>2</name><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><funapp><name>3</name><arg><funapp><name>3</name><arg><funapp><name>1</name><arg><funapp><name>0</name><arg><funapp><name>3</name><arg><funapp><name>4</name><arg><funapp><name>1</name><arg><funapp><name>0</name><arg><funapp><name>0</name><arg><funapp><name>3</name><arg><funapp><name>2</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>5</name><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><funapp><name>2</name><arg><funapp><name>4</name><arg><funapp><name>0</name><arg><funapp><name>2</name><arg><funapp><name>2</name><arg><funapp><name>3</name><arg><funapp><name>1</name><arg><funapp><name>4</name><arg><funapp><name>3</name><arg><funapp><name>2</name><arg><funapp><name>1</name><arg><funapp><name>2</name><arg><funapp><name>1</name><arg><funapp><name>2</name><arg><funapp><name>5</name><arg><funapp><name>5</name><arg><funapp><name>2</name><arg><funapp><name>4</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><redPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>3</name></sharp><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>-1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></sum></polynomial></interpret><interpret><name>4</name><arity>1</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></sum></polynomial></interpret><interpret><name>3</name><arity>1</arity><polynomial><coefficient><integer>-2</integer></coefficient></polynomial></interpret><interpret><name>2</name><arity>1</arity><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></interpret><interpret><name>1</name><arity>1</arity><polynomial><coefficient><integer>1</integer></coefficient></polynomial></interpret><interpret><name>5</name><arity>1</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>0</name><arity>1</arity><polynomial><coefficient><integer>1</integer></coefficient></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules/></dps><dpProof><pIsEmpty/></dpProof></redPairProc></dpProof></redPairUrProc></dpProof></component></depGraphProc></dpProof></redPairProc></dpProof></dpTrans></trsTerminationProof></ruleRemoval></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

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