details

property	value
status	complete
benchmark	Ex5_DLMMU04_FR.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	10.2943 seconds
cpu usage	25.9948
user time	25.0368
system time	0.958024
max virtual memory	3.6817824E7
max residence set size	2022176.0

stage attributes

key	value
certification-result	CERTIFIED
starexec-result	CERTIFIED NO
certification-time	0.81
bare-result	NO

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" 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X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>zip</name><arg><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__repItems</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>repItems</name><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></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><trsNonterminationProof><ruleRemoval><trs><rules><rule><lhs><funapp><name>pairNs</name></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>n__incr</name><arg><funapp><name>n__oddNs</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>oddNs</name></funapp></lhs><rhs><funapp><name>incr</name><arg><funapp><name>pairNs</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>incr</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>n__incr</name><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>take</name><arg><funapp><name>0</name></funapp></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>take</name><arg><funapp><name>s</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><var>X</var></arg><arg><funapp><name>n__take</name><arg><var>N</var></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>zip</name><arg><funapp><name>nil</name></funapp></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>zip</name><arg><var>X</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>zip</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>Y</var></arg><arg><var>YS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>pair</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>n__zip</name><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>YS</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>repItems</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>repItems</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><var>X</var></arg><arg><funapp><name>n__cons</name><arg><var>X</var></arg><arg><funapp><name>n__repItems</name><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>incr</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__incr</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>oddNs</name></funapp></lhs><rhs><funapp><name>n__oddNs</name></funapp></rhs></rule><rule><lhs><funapp><name>take</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>n__take</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>zip</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>n__zip</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>n__cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>repItems</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__repItems</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__incr</name><arg><var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name>s</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>n__incr</name><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>take</name><arg><funapp><name>s</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><var>X</var></arg><arg><funapp><name>n__take</name><arg><var>N</var></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>zip</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>Y</var></arg><arg><var>YS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>pair</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>n__zip</name><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>YS</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>repItems</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><var>X</var></arg><arg><funapp><name>n__cons</name><arg><var>X</var></arg><arg><funapp><name>n__repItems</name><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>incr</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__incr</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>oddNs</name></funapp></lhs><rhs><funapp><name>n__oddNs</name></funapp></rhs></rule><rule><lhs><funapp><name>take</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>n__take</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>zip</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>n__zip</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>n__cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>repItems</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__repItems</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>incr</name><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__oddNs</name></funapp></arg></funapp></lhs><rhs><funapp><name>oddNs</name></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__take</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>take</name><arg><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__zip</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>zip</name><arg><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__repItems</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>repItems</name><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></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><dpNonterminationProof><dpRuleRemoval><dps><rules><rule><lhs><funapp><sharp><name>oddNs</name></sharp></funapp></lhs><rhs><funapp><sharp><name>incr</name></sharp><arg><funapp><name>pairNs</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>incr</name></sharp><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>incr</name></sharp><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__incr</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__oddNs</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>oddNs</name></sharp></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__zip</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>zip</name></sharp><arg><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>zip</name></sharp><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>Y</var></arg><arg><var>YS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__zip</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__zip</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>zip</name></sharp><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>Y</var></arg><arg><var>YS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>YS</var></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>pairNs</name></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>n__incr</name><arg><funapp><name>n__oddNs</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>oddNs</name></funapp></lhs><rhs><funapp><name>incr</name><arg><funapp><name>pairNs</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>incr</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>n__incr</name><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>take</name><arg><funapp><name>s</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><var>X</var></arg><arg><funapp><name>n__take</name><arg><var>N</var></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>zip</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>Y</var></arg><arg><var>YS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>pair</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>n__zip</name><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>YS</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>repItems</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><var>X</var></arg><arg><funapp><name>n__cons</name><arg><var>X</var></arg><arg><funapp><name>n__repItems</name><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>incr</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__incr</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>oddNs</name></funapp></lhs><rhs><funapp><name>n__oddNs</name></funapp></rhs></rule><rule><lhs><funapp><name>take</name><arg><var>X1</var></arg><arg><var>X2</v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p><name>n__incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>incr</name></sharp><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__incr</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__oddNs</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>oddNs</name></sharp></funapp></rhs></rule><rule><lhs><funapp><sharp><name>oddNs</name></sharp></funapp></lhs><rhs><funapp><sharp><name>incr</name></sharp><arg><funapp><name>pairNs</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>pairNs</name></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>n__incr</name><arg><funapp><name>n__oddNs</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>oddNs</name></funapp></lhs><rhs><funapp><name>incr</name><arg><funapp><name>pairNs</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>incr</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>n__incr</name><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>take</name><arg><funapp><name>s</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><var>X</var></arg><arg><funapp><name>n__take</name><arg><var>N</var></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>zip</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>Y</var></arg><arg><var>YS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>pair</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>n__zip</name><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>YS</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>repItems</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><var>X</var></arg><arg><funapp><name>n__cons</name><arg><var>X</var></arg><arg><funapp><name>n__repItems</name><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>incr</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__incr</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>oddNs</name></funapp></lhs><rhs><funapp><name>n__oddNs</name></funapp></rhs></rule><rule><lhs><funapp><name>take</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>n__take</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>zip</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>n__zip</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>n__cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>repItems</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__repItems</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>incr</name><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__oddNs</name></funapp></arg></funapp></lhs><rhs><funapp><name>oddNs</name></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__take</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>take</name><arg><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>a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var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>n__cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>repItems</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__repItems</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>incr</name><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__oddNs</name></funapp></arg></funapp></lhs><rhs><funapp><name>oddNs</name></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__take</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>take</name><arg><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__zip</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>zip</name><arg><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__repItems</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>repItems</name><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></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><dpNonterminationProof><dpRuleRemoval><dps><rules><rule><lhs><funapp><sharp><name>incr</name></sharp><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__incr</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__oddNs</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>oddNs</name></sharp></funapp></rhs></rule><rule><lhs><funapp><sharp><name>oddNs</name></sharp></funapp></lhs><rhs><funapp><sharp><name>incr</name></sharp><arg><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>n__incr</name><arg><funapp><name>n__oddNs</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__incr</name><arg><funapp><name>n__incr</name><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>incr</name></sharp><arg><funapp><name>incr</name><arg><funapp><name>activate</name><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__incr</name><arg><funapp><name>n__oddNs</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>incr</name></sharp><arg><funapp><name>oddNs</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__incr</name><arg><funapp><name>n__cons</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>incr</name></sharp><arg><funapp><name>cons</name><arg><funapp><name>activate</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__incr</name><arg><var>x0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>incr</name></sharp><arg><var>x0</var></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>pairNs</name></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>n__incr</name><arg><funapp><name>n__oddNs</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>oddNs</name></funapp></lhs><rhs><funapp><name>incr</name><arg><funapp><name>pairNs</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>incr</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>n__incr</name><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>take</name><arg><funapp><name>s</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><var>X</var></arg><arg><funapp><name>n__take</name><arg><var>N</var></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>zip</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>Y</var></arg><arg><var>YS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>pair</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>n__zip</name><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>YS</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>repItems</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><var>X</var></arg><arg><funapp><name>n__cons</name><arg><var>X</var></arg><arg><funapp><name>n__repItems</name><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>incr</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__incr</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>oddNs</name></funapp></lhs><rhs><funapp><name>n__oddNs</name></funapp></rhs></rule><rule><lhs><funapp><name>take</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>n__take</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>zip</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>n__zip</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>n__cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>repItems</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__repItems</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>incr</name><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__oddNs</name></funapp></arg></funapp></lhs><rhs><funapp><name>oddNs</name></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__take</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>take</name><arg><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__zip</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>zip</name><arg><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__repItems</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>repItems</name><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></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><dpNonterminationProof><loop><rewriteSequence><startTerm><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__incr</name><arg><funapp><name>n__oddNs</name></funapp></arg></funapp></arg></funapp></startTerm><rewriteStep><positionInTerm/><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__incr</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><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__oddNs</name></funapp></arg></funapp></rewriteStep><rewriteStep><positionInTerm/><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__oddNs</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>oddNs</name></sharp></funapp></rhs></rule><funapp><sharp><name>oddNs</name></sharp></funapp></rewriteStep><rewriteStep><positionInTerm/><rule><lhs><funapp><sharp><name>oddNs</name></sharp></funapp></lhs><rhs><funapp><sharp><name>incr</name></sharp><arg><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>n__incr</name><arg><funapp><name>n__oddNs</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><funapp><sharp><name>incr</name></sharp><arg><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>n__incr</name><arg><funapp><name>n__oddNs</name></funapp></arg></funapp></arg></funapp></arg></funapp></rewriteStep><rewriteStep><positionInTerm/><rule><lhs><funapp><sharp><name>incr</name></sharp><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__incr</name><arg><funapp><name>n__oddNs</name></funapp></arg></funapp></arg></funapp></rewriteStep></rewriteSequence><substitution/><box/></loop></dpNonterminationProof></dpRuleRemoval></dpNonterminationProof></dpRuleRemoval></dpNonterminationProof></dpRuleRemoval></dpNonterminationProof></narrowingProc></dpNonterminationProof></dpRuleRemoval></dpNonterminationProof></narrowingProc></dpNonterminationProof></dpRuleRemoval></dpNonterminationProof></dpRuleRemoval></dpNonterminationProof></dpRuleRemoval></dpNonterminationProof></dpRuleRemoval></dpNonterminationProof></dpRuleRemoval></dpNonterminationProof></dpTrans></trsNonterminationProof></ruleRemoval></trsNonterminationProof></ruleRemoval></trsNonterminationProof></ruleRemoval></trsNonterminationProof></ruleRemoval></trsNonterminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (17 real / 0 unknown / 0 assumptions / 17 total proof steps)</strategy><url>http://aprove.informatik.rwth-aachen.de</url></tool><toolUser><firstName>John</firstName><lastName>Doe</lastName></toolUser></proofOrigin><inputOrigin/></origin></certificationProblem> popout

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all output return to TRS Standard Certified