details

property	value
status	complete
benchmark	Ex26_Luc03b_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n137.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	3.00307 seconds
cpu usage	8.53044
user time	8.19308
system time	0.337361
max virtual memory	1.859278E7
max residence set size	541796.0

stage attributes

key	value
certification-result	CERTIFIED
starexec-result	CERTIFIED YES
certification-time	0.29
bare-result	YES

output

<?xml version="1.0" encoding="UTF-8" standalone="no"?><?xml-stylesheet type="text/xsl" href="cpfHTML.xsl"?><certificationProblem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="cpf.xsd"><input><trsInput><trs><rules><rule><lhs><funapp><name>terms</name><arg><var>N</var></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>recip</name><arg><funapp><name>sqr</name><arg><var>N</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__terms</name><arg><funapp><name>s</name><arg><var>N</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>sqr</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>sqr</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>n__add</name><arg><funapp><name>sqr</name><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>dbl</name><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>dbl</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>dbl</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>n__s</name><arg><funapp><name>n__dbl</name><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>add</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>n__add</name><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>first</name><arg><funapp><name>0</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>first</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>Y</var></arg><arg><var>Z</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><var>Y</var></arg><arg><funapp><name>n__first</name><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>Z</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>terms</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__terms</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>add</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>n__add</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>s</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__s</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>dbl</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__dbl</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>first</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>n__first</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__terms</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>terms</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__add</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>add</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__dbl</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>dbl</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__first</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>first</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><name>terms</name></sharp><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>sqr</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>terms</name></sharp><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sqr</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><funapp><name>n__add</name><arg><funapp><name>sqr</name><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>dbl</name><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sqr</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>sqr</name></sharp><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sqr</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sqr</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>dbl</name></sharp><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dbl</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><funapp><name>n__s</name><arg><funapp><name>n__dbl</name><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dbl</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>add</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><funapp><name>n__add</name><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>add</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>first</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>Y</var></arg><arg><var>Z</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>first</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>Y</var></arg><arg><var>Z</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>Z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__terms</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>terms</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__add</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>add</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__dbl</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>dbl</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__first</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>first</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>sqr</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>sqr</name></sharp><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sqr</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__terms</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>terms</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>terms</name></sharp><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>sqr</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sqr</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>dbl</name></sharp><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dbl</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__add</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>add</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>add</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__dbl</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>dbl</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__first</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>first</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>first</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>Y</var></arg><arg><var>Z</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>first</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>Y</var></arg><arg><var>Z</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>Z</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><redPairProc><orderingConstraintProof><redPair><interpretation><type><matrixInterpretation><domain><arctic><domain><naturals/></domain></arctic></domain><dimension>1</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><sharp><name>sqr</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></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>s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><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>activate</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><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><sharp><name>activate</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></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>n__terms</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><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><sharp><name>terms</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></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><sharp><name>dbl</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></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>n__add</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><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><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>add</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></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><polynomial><product><polynomial><coefficient><vector><coefficient><minusInfinity/></coefficient></vector></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>n__dbl</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><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>n__first</name><arity>2</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>5</integer></coefficient></vector></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>first</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><vector><coefficient><integer>4</integer></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>cons</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><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><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>terms</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><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>add</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><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><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>n__s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><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>dbl</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><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>first</name><arity>2</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>5</integer></coefficient></vector></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>sqr</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><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>0</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>recip</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><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>nil</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>4</integer></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>sqr</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>sqr</name></sharp><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sqr</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__terms</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>terms</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>terms</name></sharp><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>sqr</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sqr</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>dbl</name></sharp><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dbl</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__add</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>add</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>add</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__dbl</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>dbl</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>first</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>Y</var></arg><arg><var>Z</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>first</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>Y</var></arg><arg><var>Z</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>Z</var></arg></funapp></rhs></rule></rules></dps><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>first</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>Y</var></arg><arg><var>Z</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>first</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>Y</var></arg><arg><var>Z</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>Z</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>sqr</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__terms</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>terms</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>terms</name></sharp><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>sqr</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sqr</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>sqr</name></sharp><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sqr</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>dbl</name></sharp><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dbl</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__add</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>add</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>add</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__dbl</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>dbl</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><redPairProc><orderingConstraintProof><redPair><pathOrder><statusPrecedence><statusPrecedenceEntry><sharp><name>sqr</name></sharp><arity>1</arity><precedence>1</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>s</name><arity>1</arity><precedence>2</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><sharp><name>activate</name></sharp><arity>1</arity><precedence>1</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><sharp><name>terms</name></sharp><arity>1</arity><precedence>1</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>n__add</name><arity>2</arity><precedence>3</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>n__dbl</name><arity>1</arity><precedence>5</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>add</name><arity>2</arity><precedence>3</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>n__s</name><arity>1</arity><precedence>2</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>dbl</name><arity>1</arity><precedence>5</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>n__first</name><arity>2</arity><precedence>6</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>first</name><arity>2</arity><precedence>6</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>sqr</name><arity>1</arity><precedence>5</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>0</name><arity>0</arity><precedence>4</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>cons</name><arity>2</arity><precedence>0</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>nil</name><arity>0</arity><precedence>6</precedence><mul/></statusPrecedenceEntry></statusPrecedence><argumentFilter><argumentFilterEntry><sharp><name>sqr</name></sharp><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>s</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><sharp><name>activate</name></sharp><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>n__terms</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><sharp><name>terms</name></sharp><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>activate</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><sharp><name>dbl</name></sharp><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>n__add</name><arity>2</arity><nonCollapsing><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><sharp><name>add</name></sharp><arity>2</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>n__dbl</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>terms</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>add</name><arity>2</arity><nonCollapsing><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>n__s</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>dbl</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>n__first</name><arity>2</arity><nonCollapsing><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>first</name><arity>2</arity><nonCollapsing><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>sqr</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>0</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>cons</name><arity>2</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>recip</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>nil</name><arity>0</arity><nonCollapsing/></argumentFilterEntry></argumentFilter></pathOrder></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__terms</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>terms</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>terms</name></sharp><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>sqr</name></sharp><arg><var>N</var></arg></funapp></rhs></rule></rules></dps><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__terms</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>terms</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>terms</name></sharp><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>sqr</name></sharp><arg><var>N</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></redPairProc></dpProof></component></depGraphProc></dpProof></redPairProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>terms</name></sharp><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><var>N</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>sqr</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><funapp><name>n__add</name><arg><funapp><name>sqr</name><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>dbl</name><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>dbl</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><funapp><name>n__s</name><arg><funapp><name>n__dbl</name><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>add</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><funapp><name>n__add</name><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></dpTrans></trsTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (6 real / 0 unknown / 0 assumptions / 6 total proof steps)</strategy><url>http://aprove.informatik.rwth-aachen.de</url></tool><toolUser><firstName>John</firstName><lastName>Doe</lastName></toolUser></proofOrigin><inputOrigin/></origin></certificationProblem> popout

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all output return to TRS Standard Certified