details

property	value
status	complete
benchmark	Liveness_WRS.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n112.star.cs.uiowa.edu
space	AProVE_04

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	2.62501811981 seconds
cpu usage	7.224434095
max memory	4.80055296E8

stage attributes

key	value
certification-result	CERTIFIED
output-size	66866
starexec-result	YES
certification-time	0.0

output

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oefficient><vector><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mat</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>2</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><vector><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>f</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>X</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>y</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>2</integer></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>no</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>2</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><vector><coefficient><integer>2</integer></coefficient></vector></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>2</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><vector><coefficient><integer>2</integer></coefficient></vector></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules/></dps><dpProof><pIsEmpty/></dpProof></redPairProc></dpProof></monoRedPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>tp</name></sharp><arg><funapp><name>mark</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>chk</name></sharp><arg><funapp><name>mat</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>X</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>chk</name></sharp><arg><funapp><name>no</name><arg><funapp><name>f</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>chk</name></sharp><arg><funapp><name>mat</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>X</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>x</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><interpret><name>mat</name><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><name>f</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>y</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>c</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>no</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>X</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>chk</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>chk</name></sharp><arg><funapp><name>no</name><arg><funapp><name>f</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>chk</name></sharp><arg><funapp><name>mat</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>X</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>mat</name><arg><funapp><name>f</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>f</name><arg><funapp><name>y</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>mat</name><arg><var>x</var></arg><arg><funapp><name>y</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mat</name><arg><funapp><name>f</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>c</name></funapp></arg></funapp></lhs><rhs><funapp><name>no</name><arg><funapp><name>c</name></funapp></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>mat</name><arg><funapp><name>f</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>f</name><arg><funapp><name>y</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>mat</name><arg><var>x</var></arg><arg><funapp><name>y</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mat</name><arg><funapp><name>f</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>c</name></funapp></arg></funapp></lhs><rhs><funapp><name>no</name><arg><funapp><name>c</name></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><switchInnermostProc><wcrProof><joinableCriticalPairsBFS>20</joinableCriticalPairsBFS></wcrProof><dpProof><monoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>mat</name><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>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>f</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>y</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><int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><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>X</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>tp</name></sharp><arg><funapp><name>mark</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mat</name></sharp><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>X</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>mat</name></sharp><arg><funapp><name>f</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>f</name><arg><funapp><name>y</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mat</name></sharp><arg><var>x</var></arg><arg><funapp><name>y</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>chk</name></sharp><arg><funapp><name>no</name><arg><funapp><name>c</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>c</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>chk</name></sharp><arg><funapp><name>no</name><arg><funapp><name>f</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>chk</name><arg><funapp><name>mat</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>X</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>chk</name></sharp><arg><funapp><name>no</name><arg><funapp><name>f</name><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>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>X</name></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><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>chk</name></sharp><arg><funapp><name>no</name><arg><funapp><name>f</name><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>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>X</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>chk</name></sharp><arg><funapp><name>no</name><arg><funapp><name>f</name><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>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>X</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>chk</name></sharp><arg><funapp><name>no</name><arg><funapp><name>f</name><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>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>X</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>chk</name></sharp><arg><funapp><name>no</name><arg><funapp><name>f</name><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>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>X</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>chk</name></sharp><arg><funapp><name>no</name><arg><funapp><name>f</name><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>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>X</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>chk</name></sharp><arg><funapp><name>no</name><arg><funapp><name>f</name><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>f</name><arg><funapp><name>f</name><arg><funapp><name>X</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>chk</name></sharp><arg><funapp><name>no</name><arg><funapp><name>f</name><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>f</name><arg><funapp><name>X</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>chk</name></sharp><arg><funapp><name>no</name><arg><funapp><name>f</name><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>X</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>chk</name></sharp><arg><funapp><name>no</name><arg><funapp><name>f</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>X</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>mat</name></sharp><arg><funapp><name>f</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>f</name><arg><funapp><name>y</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>mat</name><arg><var>x</var></arg><arg><funapp><name>y</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>tp</name></sharp><arg><funapp><name>mark</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>X</name></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><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>tp</name></sharp><arg><funapp><name>mark</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>X</name></funapp></arg></funapp></arg></funapp></arg></funap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rg></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>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>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>no</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>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><interpret><sharp><name>f</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>f</name></sharp><arg><funapp><name>active</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>f</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>f</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>active</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>no</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>mark</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>x</var></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>f</name><arg><funapp><name>active</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>active</name><arg><funapp><name>f</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>no</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>no</name><arg><funapp><name>f</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>mark</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>f</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>f</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>f</name><arg><funapp><name>active</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>active</name><arg><funapp><name>f</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>no</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>no</name><arg><funapp><name>f</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>mark</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>f</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>f</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><monoRedPairProc><orderingConstraintProof><redPair><knuthBendixOrder><w0>1</w0><precedenceWeight><precedenceWeightEntry><name>f</name><arity>1</arity><precedence>4</precedence><weight>2</weight></precedenceWeightEntry><precedenceWeightEntry><name>active</name><arity>1</arity><precedence>3</precedence><weight>3</weight></precedenceWeightEntry><precedenceWeightEntry><name>no</name><arity>1</arity><precedence>0</precedence><weight>1</weight></precedenceWeightEntry><precedenceWeightEntry><name>mark</name><arity>1</arity><precedence>2</precedence><weight>1</weight></precedenceWeightEntry><precedenceWeightEntry><sharp><name>f</name></sharp><arity>1</arity><precedence>1</precedence><weight>1</weight></precedenceWeightEntry><precedenceWeightEntry><sharp><name>active</name></sharp><arity>1</arity><precedence>5</precedence><weight>1</weight></precedenceWeightEntry></precedenceWeight></knuthBendixOrder></redPair></orderingConstraintProof><dps><rules/></dps><trs><rules/></trs><dpProof><pIsEmpty/></dpProof></monoRedPairProc></dpProof></monoRedPairUrProc></dpProof></component></depGraphProc></dpProof></dpTrans></trsTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (13 real / 0 unknown / 0 assumptions / 13 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 Stand certi 70678