details

property	value
status	complete
benchmark	264033.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n074.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	6.91173005104 seconds
cpu usage	23.874846848
max memory	3.064180736E9

stage attributes

key	value
certification-result	CERTIFIED
output-size	1020139
starexec-result	YES
certification-time	2.3

output

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napp></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>0</name><arg><funapp><name>1</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></lhs><rhs><funapp><name>1</name><arg><funapp><name>0</name><arg><funapp><name>2</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></rhs></rule><rule><lhs><funapp><name>2</name><arg><funapp><name>2</name><arg><funapp><name>0</name><arg><funapp><name>1</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></lhs><rhs><funapp><name>2</name><arg><funapp><name>0</name><arg><funapp><name>1</name><arg><funapp><name>2</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></rhs></rule><rule><lhs><funapp><name>0</name><arg><funapp><name>2</name><arg><funapp><name>0</name><arg><funapp><name>1</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></lhs><rhs><funapp><name>0</name><arg><funapp><name>0</name><arg><funapp><name>1</name><arg><funapp><name>2</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></rhs></rule><rule><lhs><funapp><name>1</name><arg><funapp><name>2</name><arg><funapp><name>0</name><arg><funapp><name>1</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></lhs><rhs><funapp><name>1</name><arg><funapp><name>0</name><arg><funapp><name>1</name><arg><funapp><name>2</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></rhs></rule><rule><lhs><funapp><name>2</name><arg><funapp><name>2</name><arg><funapp><name>0</name><arg><funapp><name>2</name><arg><funapp><name>1</name><arg><funapp><name>2</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>2</name><arg><funapp><name>0</name><arg><funapp><name>1</name><arg><funapp><name>2</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></rhs></rule><rule><lhs><funapp><name>0</name><arg><funapp><name>2</name><arg><funapp><name>0</name><arg><funapp><name>2</name><arg><funapp><name>1</name><arg><funapp><name>2</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>0</name><arg><funapp><name>1</name><arg><funapp><name>2</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></rhs></rule><rule><lhs><funapp><name>1</name><arg><funapp><name>2</name><arg><funapp><name>0</name><arg><funapp><name>2</name><arg><funapp><name>1</name><arg><funapp><name>2</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>0</name><arg><funapp><name>1</name><arg><funapp><name>2</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></rhs></rule></rules></trs><trsTerminationProof><semlab><model><rootLabeling/></model><trs><rules><rule><lhs><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>2</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>2</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>2</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>2</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>2</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>2</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>2</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>2</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>2</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>2</name><symbolLab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<labeledSymbol><name>2</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>1</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>1</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>1</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>1</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>1</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>1</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><p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>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>2</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>2</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>2</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>1</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><labeledSymbol><name>2</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><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><labeledSymbol><name>0</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><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><labeledSymbol><name>2</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><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><labeledSymbol><name>1</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><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><labeledSymbol><name>0</name><symbolLabel><name>1</name></symbolLabel></labeledSymbol><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><labeledSymbol><name>1</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><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><labeledSymbol><name>0</name><symbolLabel><name>0</name></symbolLabel></labeledSymbol><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><labeledSymbol><name>2</name><symbolLabel><name>2</name></symbolLabel></labeledSymbol><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><trs><rules/></trs><trsTerminationProof><rIsEmpty/></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></semlab></trsTerminationProof></flatContextClosure></trsTerminationProof></stringReversal></trsTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (10 real / 0 unknown / 0 assumptions / 10 total proof steps)</strategy><url>http://aprove.informatik.rwth-aachen.de</url></tool><toolUser><firstName>John</firstName><lastName>Doe</lastName></toolUser></proofOrigin><inputOrigin/></origin></certificationProblem> popout

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