details

property	value
status	complete
benchmark	Ex9_Luc06_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n062.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE21
configuration	certified
runtime (wallclock)	22.0679278374 seconds
cpu usage	52.461025994
max memory	2.389397504E9

stage attributes

key	value
certification-result	CERTIFIED
starexec-result	YES
certification-time	0.31

output

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<arg><funapp><name>f</name><arg><var>X</var></arg><arg><funapp><name>b</name></funapp></arg><arg><funapp><name>b</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>b</name></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>a</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><var>X1</var></arg><arg><funapp><name>active</name><arg><var>X2</var></arg></funapp></arg><arg><var>X3</var></arg></funapp></rhs></rule></rules></usableRules><dpProof><narrowingProc><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><positionInTerm><position>1</position></positionInTerm><narrowings><rules><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>f</name><arg><funapp><name>a</name></funapp></arg><arg><var>x0</var></arg><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><funapp><name>b</name></funapp></arg><arg><funapp><name>b</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>b</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><funapp><name>active</name><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule></rules></narrowings><dpProof><narrowingProc><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><positionInTerm><position>1</position></positionInTerm><narrowings><rules><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>f</name><arg><funapp><name>proper</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><funapp><name>b</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>b</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></narrowings><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>f</name><arg><funapp><name>proper</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>f</name><arg><funapp><name>a</name></funapp></arg><arg><var>x0</var></arg><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><funapp><name>b</name></funapp></arg><arg><funapp><name>b</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><funapp><name>active</name><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><redPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>top</name></sharp><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>f</name><arity>3</arity><polynomial><sum><polynomial><variable>1</variable></polynomial><polynomial><variable>3</variable></polynomial></sum></polynomial></interpret><interpret><name>proper</name><arity>1</arity><polynomial><variable>1</variable></polynomial></interpret><interpret><name>a</name><arity>0</arity><polynomial><coefficient><integer>1</integer></coefficient></polynomial></interpret><interpret><name>ok</name><arity>1</arity><polynomial><variable>1</variable></polynomial></interpret><interpret><name>b</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>mark</name><arity>1</arity><polynomial><variable>1</variable></polynomial></interpret><interpret><name>active</name><arity>1</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>f</name><arg><funapp><name>proper</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><funapp><name>active</name><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>proper</name><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>a</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>a</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>b</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>b</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><var>X1</var></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg><arg><var>X3</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><redPairProc><orderingConstraintProof><redPair><interpretation><type><matrixInterpretation><domain><integers/></domain><dimension>2</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><sharp><name>top</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mark</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>f</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>2</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>proper</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>ok</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>active</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>a</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>3</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>b</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><funapp><name>active</name><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><dpProof><monoRedPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>active</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>f</name><arity>3</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><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>a</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>mark</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>b</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>ok</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><sharp><name>top</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></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><funapp><name>active</name><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>active</name><arg><funapp><name>f</name><arg><funapp><name>a</name></funapp></arg><arg><var>X</var></arg><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>f</name><arg><var>X</var></arg><arg><funapp><name>b</name></funapp></arg><arg><funapp><name>b</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>b</name></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>a</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><var>X1</var></arg><arg><funapp><name>active</name><arg><var>X2</var></arg></funapp></arg><arg><var>X3</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><var>X1</var></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg><arg><var>X3</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>active</name><arg><funapp><name>f</name><arg><funapp><name>a</name></funapp></arg><arg><var>X</var></arg><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>f</name><arg><var>X</var></arg><arg><funapp><name>b</name></funapp></arg><arg><funapp><name>b</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>b</name></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>a</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><var>X1</var></arg><arg><funapp><name>active</name><arg><var>X2</var></arg></funapp></arg><arg><var>X3</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><var>X1</var></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg><arg><var>X3</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><monoRedPairProc><orderingConstraintProof><redPair><knuthBendixOrder><w0>1</w0><precedenceWeight><precedenceWeightEntry><name>a</name><arity>0</arity><precedence>6</precedence><weight>4</weight></precedenceWeightEntry><precedenceWeightEntry><name>b</name><arity>0</arity><precedence>1</precedence><weight>3</weight></precedenceWeightEntry><precedenceWeightEntry><name>active</name><arity>1</arity><precedence>4</precedence><weight>2</weight></precedenceWeightEntry><precedenceWeightEntry><name>mark</name><arity>1</arity><precedence>0</precedence><weight>1</weight></precedenceWeightEntry><precedenceWeightEntry><name>ok</name><arity>1</arity><precedence>2</precedence><weight>3</weight></precedenceWeightEntry><precedenceWeightEntry><sharp><name>top</name></sharp><arity>1</arity><precedence>5</precedence><weight>1</weight></precedenceWeightEntry><precedenceWeightEntry><name>f</name><arity>3</arity><precedence>3</precedence><weight>0</weight></precedenceWeightEntry></precedenceWeight></knuthBendixOrder></redPair></orderingConstraintProof><dps><rules/></dps><trs><rules/></trs><dpProof><pIsEmpty/></dpProof></monoRedPairProc></dpProof></monoRedPairUrProc></dpProof></redPairProc></dpProof></redPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><funapp><name>b</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>b</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>b</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><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>top</name></sharp><arg><funapp><name>mark</name><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></narrowingProc></dpProof></narrowingProc></dpProof></monoRedPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>active</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>proper</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>active</name></sharp><arg><var>X2</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><monoRedPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>f</name><arity>3</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><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>active</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></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>active</name></sharp><arg><var>X2</var></arg></funapp></rhs></rule></rules></dps><trs><rules/></trs><usableRules><rules/></usableRules><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>active</name></sharp><arg><var>X2</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></monoRedPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>proper</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>proper</name></sharp><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>proper</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>proper</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>proper</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>proper</name></sharp><arg><var>X3</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><monoRedPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>f</name><arity>3</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><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>proper</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></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>proper</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>proper</name></sharp><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>proper</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>proper</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>proper</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>proper</name></sharp><arg><var>X3</var></arg></funapp></rhs></rule></rules></dps><trs><rules/></trs><usableRules><rules/></usableRules><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>proper</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>proper</name></sharp><arg><var>X2</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>proper</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>proper</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>proper</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>proper</name></sharp><arg><var>X3</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></monoRedPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>f</name><arg><funapp><name>a</name></funapp></arg><arg><var>X</var></arg><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>X</var></arg><arg><funapp><name>b</name></funapp></arg><arg><funapp><name>b</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>X1</var></arg><arg><funapp><name>active</name><arg><var>X2</var></arg></funapp></arg><arg><var>X3</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>proper</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X3</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><var>X1</var></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg><arg><var>X3</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><monoRedPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>ok</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>mark</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><sharp><name>f</name></sharp><arity>3</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><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><var>X1</var></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg><arg><var>X3</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></rhs></rule></rules></dps><trs><rules/></trs><usableRules><rules/></usableRules><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge><edge><position>2</position><strict>true</strict><position>2</position></edge><edge><position>3</position><strict>true</strict><position>3</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>f</name></sharp><arg><var>X1</var></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg><arg><var>X3</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></rhs></rule><edge><position>1</position><strict>false</strict><position>1</position></edge><edge><position>2</position><strict>true</strict><position>2</position></edge><edge><position>3</position><strict>false</strict><position>3</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></monoRedPairUrProc></dpProof></component></depGraphProc></dpProof></dpTrans></trsTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished </version><strategy>Statistics for single proof: 100.00 % (17 real / 0 unknown / 0 assumptions / 17 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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