details

property	value
status	complete
benchmark	PALINDROME_nokinds_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n101.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	3.04979 seconds
cpu usage	8.38208
user time	7.96815
system time	0.413926
max virtual memory	1.8590028E7
max residence set size	645600.0

stage attributes

key	value
certification-result	CERTIFIED
output-size	130542
starexec-result	YES
certification-time	0.4

output

YES <?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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></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>i</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>i</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>o</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>o</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>u</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>u</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>__</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isList</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isList</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNeList</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isNeList</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isQid</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isQid</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNePal</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isNePal</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isPal</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isPal</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><strategy><innermost/></strategy></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>active</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>__</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mark</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>nil</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isList</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isNeList</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isQid</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isNePal</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isPal</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>a</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>e</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>i</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>o</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>u</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>proper</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>ok</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>top</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>active</name><arg><funapp><name>__</name><arg><funapp><name>__</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>Z</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>__</name><arg><var>X</var></arg><arg><funapp><name>__</name><arg><var>Y</var></arg><arg><var>Z</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>__</name><arg><var>X</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>__</name><arg><funapp><name>nil</name></funapp></arg><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>and</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>isList</name><arg><var>V</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>isNeList</name><arg><var>V</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>isList</name><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>tt</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>isList</name><arg><funapp><name>__</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>and</name><arg><funapp><name>isList</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isList</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>isNeList</name><arg><var>V</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>isQid</name><arg><var>V</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>isNeList</name><arg><funapp><name>__</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>and</name><arg><funapp><name>isList</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isNeList</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>isNeList</name><arg><funapp><name>__</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>and</name><arg><funapp><name>isNeList</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isList</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>isNePal</name><arg><var>V</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>isQid</name><arg><var>V</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>isNePal</name><arg><funapp><name>__</name><arg><var>I</var></arg><arg><funapp><name>__</name><arg><var>P</var></arg><arg><var>I</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>and</name><arg><funapp><name>isQid</name><arg><var>I</var></arg></funapp></arg><arg><funapp><name>isPal</name><arg><var>P</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>isPal</name><arg><var>V</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>isNePal</name><arg><var>V</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>isPal</name><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>tt</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>isQid</name><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>tt</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>isQid</name><arg><funapp><name>i</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>tt</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>isQid</name><arg><funapp><name>o</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>tt</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>isQid</name><arg><funapp><name>u</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>tt</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>__</name><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>__</name><arg><var>X1</var></arg><arg><funapp><name>active</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>__</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>__</name><arg><var>X1</var></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>__</name><arg><funapp><name>proper</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napp><name>top</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>active</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>__</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mark</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>nil</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isList</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isNeList</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isQid</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isNePal</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isPal</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>a</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>i</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>o</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>u</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>proper</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>ok</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>e</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>top</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomi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me>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isList</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isList</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNeList</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isNeList</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isQid</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isQid</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNePal</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isNePal</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isPal</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isPal</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>active</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>__</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mark</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>nil</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isList</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isNeList</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isQid</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isNePal</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isPal</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>proper</name><arity>1</arity><polynomial><sum><polynomial><product><polyno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e><rule><lhs><funapp><name>and</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isList</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isList</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNeList</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isNeList</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isQid</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isQid</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNePal</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isNePal</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isPal</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isPal</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>active</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>__</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mark</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isList</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isNeList</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isQid</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isNePal</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isPal</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>proper</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>nil</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>ok</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>e</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>i</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>o</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>u</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>top</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>active</name><arg><funapp><name>__</name><arg><funapp><name>__</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>Z</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>__</name><arg><var>X</var></arg><arg><funapp><name>__</name><arg><var>Y</var></arg><arg><var>Z</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>isList</name><arg><var>V</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>isNeList</name><arg><var>V</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>isList</name><arg><funapp><name>__</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>and</name><arg><funapp><name>isList</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isList</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>isNeList</name><arg><var>V</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>isQid</name><arg><var>V</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>isNeList</name><arg><funapp><name>__</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>and</name><arg><funapp><name>isList</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isNeList</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>isNeList</name><arg><funapp><name>__</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>and</name><arg><funapp><name>isNeList</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isList</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>isNePal</name><arg><funapp><name>__</name><arg><var>I</var></arg><arg><funapp><name>__</name><arg><var>P</var></arg><arg><var>I</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>and</name><arg><funapp><name>isQid</name><arg><var>I</var></arg></funapp></arg><arg><funapp><name>isPal</name><arg><var>P</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>isPal</name><arg><var>V</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>isNePal</name><arg><var>V</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>__</name><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>__</name><arg><var>X1</var></arg><arg><funapp><name>active</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>__</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>__</name><arg><var>X1</var></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>__</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>nil</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>tt</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isList</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isList</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isNeList</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNeList</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isQid</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isQid</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isNePal</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNePal</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isPal</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isPal</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>a</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>a</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>e</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>e</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>i</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>i</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>o</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>o</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>u</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>u</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>__</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isList</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isList</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNeList</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isNeList</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isQid</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isQid</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNePal</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isNePal</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isPal</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isPal</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>active</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>__</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mark</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isList</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isNeList</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isQid</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isNePal</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isPal</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>proper</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>nil</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>ok</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>e</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>i</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>o</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>u</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>top</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>active</name><arg><funapp><name>isNeList</name><arg><var>V</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>isQid</name><arg><var>V</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>__</name><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>__</name><arg><var>X1</var></arg><arg><funapp><name>active</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>__</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>__</name><arg><var>X1</var></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>__</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>nil</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>tt</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isList</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isList</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isNeList</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNeList</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isQid</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isQid</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isNePal</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNePal</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isPal</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isPal</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>a</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>a</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>e</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>e</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>i</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>i</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>o</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>o</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>u</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>u</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>__</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isList</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isList</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNeList</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isNeList</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isQid</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isQid</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNePal</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isNePal</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isPal</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isPal</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>active</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isNeList</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mark</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isQid</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>__</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>proper</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>nil</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>ok</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isList</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isNePal</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isPal</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>a</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>e</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>i</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>o</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>u</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>top</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>active</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>__</name><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>__</name><arg><var>X1</var></arg><arg><funapp><name>active</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>__</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>__</name><arg><var>X1</var></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>__</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>nil</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>tt</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isList</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isList</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isNeList</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNeList</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isQid</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isQid</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isNePal</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNePal</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isPal</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isPal</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>a</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>a</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>e</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>e</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>i</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>i</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>o</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>o</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>u</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>u</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>__</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isList</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isList</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNeList</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isNeList</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isQid</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isQid</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNePal</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isNePal</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isPal</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isPal</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>active</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>__</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mark</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>proper</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>nil</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>ok</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isList</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isNeList</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isQid</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isNePal</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isPal</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>a</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>e</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>i</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>o</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>u</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>top</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>active</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>__</name><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>__</name><arg><var>X1</var></arg><arg><funapp><name>active</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>__</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>nil</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>tt</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isList</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isList</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isNeList</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNeList</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isQid</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isQid</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isNePal</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNePal</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isPal</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isPal</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>a</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>a</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>e</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>e</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>i</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>i</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>o</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>o</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>u</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>u</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>__</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isList</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isList</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNeList</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isNeList</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isQid</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isQid</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNePal</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isNePal</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isPal</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isPal</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>active</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>__</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>proper</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>nil</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>ok</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isList</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isNeList</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isQid</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isNePal</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isPal</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>a</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>e</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>i</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>o</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>u</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>top</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>proper</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>__</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>nil</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>tt</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isList</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isList</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isNeList</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNeList</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isQid</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isQid</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isNePal</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNePal</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isPal</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isPal</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>a</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>a</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>e</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>e</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>i</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>i</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>o</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>o</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>u</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>u</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>__</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>__</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isList</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isList</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNeList</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isNeList</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isQid</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isQid</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNePal</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isNePal</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isPal</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isPal</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>proper</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>__</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>nil</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>ok</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isList</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isNeList</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isQid</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isNePal</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isPal</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>a</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>e</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>i</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>o</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>u</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>proper</name><arg><funapp><name>isNeList</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNeList</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isQid</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isQid</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isNePal</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNePal</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isPal</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isPal</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNeList</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isNeList</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isQid</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isQid</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><knuthBendixOrder><w0>1</w0><precedenceWeight><precedenceWeightEntry><name>proper</name><arity>1</arity><precedence>5</precedence><weight>3</weight></precedenceWeightEntry><precedenceWeightEntry><name>isNeList</name><arity>1</arity><precedence>3</precedence><weight>2</weight></precedenceWeightEntry><precedenceWeightEntry><name>isQid</name><arity>1</arity><precedence>4</precedence><weight>2</weight></precedenceWeightEntry><precedenceWeightEntry><name>isNePal</name><arity>1</arity><precedence>0</precedence><weight>1</weight></precedenceWeightEntry><precedenceWeightEntry><name>isPal</name><arity>1</arity><precedence>1</precedence><weight>1</weight></precedenceWeightEntry><precedenceWeightEntry><name>ok</name><arity>1</arity><precedence>2</precedence><weight>1</weight></precedenceWeightEntry></precedenceWeight></knuthBendixOrder></redPair></orderingConstraintProof><trs><rules/></trs><trsTerminationProof><rIsEmpty/></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (11 real / 0 unknown / 0 assumptions / 11 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_Innermost Certified 2019-04-01 06.48