details

property	value
status	complete
benchmark	LengthOfFiniteLists_nokinds_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n007.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	2.32393407822 seconds
cpu usage	6.149824297
max memory	4.40344576E8

stage attributes

key	value
certification-result	CERTIFIED
output-size	73197
starexec-result	YES
certification-time	0.2

output

/export/starexec/sandbox/solver/bin/starexec_run_certified /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- 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" xsi:noNamespaceSchemaLocation="cpf.xsd"><input><trsInput><trs><rules><rule><lhs><funapp><name>a__zeros</name></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>zeros</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>L</var></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>a__length</name><arg><funapp><name>mark</name><arg><var>L</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__and</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>length</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__isNatList</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNatIList</name><arg><var>V</var></arg></funapp></lhs><rhs><funapp><name>a__isNatList</name><arg><var>V</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNatIList</name><arg><funapp><name>zeros</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>a__isNatIList</name><arg><funapp><name>cons</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__and</name><arg><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isNatIList</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNatList</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>a__isNatList</name><arg><funapp><name>cons</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__and</name><arg><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isNatList</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__length</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>a__length</name><arg><funapp><name>cons</name><arg><var>N</var></arg><arg><var>L</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__U11</name><arg><funapp><name>a__and</name><arg><funapp><name>a__isNatList</name><arg><var>L</var></arg></funapp></arg><arg><funapp><name>isNat</name><arg><var>N</var></arg></funapp></arg></funapp></arg><arg><var>L</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>zeros</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__zeros</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__U11</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>length</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__length</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__and</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>isNat</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__isNat</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>isNatList</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__isNatList</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>isNatIList</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__isNatIList</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>a__zeros</name></funapp></lhs><rhs><funapp><name>zeros</name></funapp></rhs></rule><rule><lhs><funapp><name>a__U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__length</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>length</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>isNat</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNatList</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>isNatList</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNatIList</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>isNatIList</name><arg><var>X</var></arg></funapp></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>a__zeros</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>cons</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>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>zeros</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a__U11</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>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>s</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__length</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>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>a__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>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>a__isNat</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>length</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__isNatList</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__isNatIList</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>isNatIList</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>nil</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isNatList</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>isNat</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>U11</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>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>a__zeros</name></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>zeros</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>L</var></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>a__length</name><arg><funapp><name>mark</name><arg><var>L</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__and</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>length</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__isNatList</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNatIList</name><arg><var>V</var></arg></funapp></lhs><rhs><funapp><name>a__isNatList</name><arg><var>V</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNatIList</name><arg><funapp><name>zeros</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>a__isNatIList</name><arg><funapp><name>cons</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__and</name><arg><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isNatIList</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNatList</name><arg><funapp><name>cons</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__and</name><arg><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isNatList</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__length</name><arg><funapp><name>cons</name><arg><var>N</var></arg><arg><var>L</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__U11</name><arg><funapp><name>a__and</name><arg><funapp><name>a__isNatList</name><arg><var>L</var></arg></funapp></arg><arg><funapp><name>isNat</name><arg><var>N</var></arg></funapp></arg></funapp></arg><arg><var>L</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>zeros</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__zeros</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__U11</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>length</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__length</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__and</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>isNat</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__isNat</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>isNatList</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__isNatList</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>isNatIList</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__isNatIList</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>a__zeros</name></funapp></lhs><rhs><funapp><name>zeros</name></funapp></rhs></rule><rule><lhs><funapp><name>a__U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__length</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>length</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>isNat</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNatList</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>isNatList</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNatIList</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>isNatIList</name><arg><var>X</var></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>a__zeros</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>cons</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>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>zeros</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a__U11</name><arity>2</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><polynomial><product><polynomial><coefficient><integer>2</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>s</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__length</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>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>a__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>a__isNat</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>length</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>a__isNatList</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__isNatIList</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>isNatIList</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>isNatList</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>isNat</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>U11</name><arity>2</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><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>nil</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>a__zeros</name></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>zeros</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>L</var></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>a__length</name><arg><funapp><name>mark</name><arg><var>L</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__and</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNatIList</name><arg><var>V</var></arg></funapp></lhs><rhs><funapp><name>a__isNatList</name><arg><var>V</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNatIList</name><arg><funapp><name>zeros</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>a__isNatIList</name><arg><funapp><name>cons</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__and</name><arg><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isNatIList</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNatList</name><arg><funapp><name>cons</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__and</name><arg><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isNatList</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__length</name><arg><funapp><name>cons</name><arg><var>N</var></arg><arg><var>L</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__U11</name><arg><funapp><name>a__and</name><arg><funapp><name>a__isNatList</name><arg><var>L</var></arg></funapp></arg><arg><funapp><name>isNat</name><arg><var>N</var></arg></funapp></arg></funapp></arg><arg><var>L</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>zeros</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__zeros</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__U11</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>length</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__length</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__and</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>isNat</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__isNat</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>isNatList</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__isNatList</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>isNatIList</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__isNatIList</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>a__zeros</name></funapp></lhs><rhs><funapp><name>zeros</name></funapp></rhs></rule><rule><lhs><funapp><name>a__U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__length</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>length</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>isNat</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNatList</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>isNatList</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNatIList</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>isNatIList</name><arg><var>X</var></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>a__zeros</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>cons</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>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>zeros</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a__U11</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>s</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__length</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>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>a__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>a__isNat</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__isNatIList</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>a__isNatList</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>isNatIList</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>isNatList</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>isNat</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>U11</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>length</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>nil</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>a__zeros</name></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>zeros</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>L</var></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>a__length</name><arg><funapp><name>mark</name><arg><var>L</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__and</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNatIList</name><arg><funapp><name>cons</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__and</name><arg><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isNatIList</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNatList</name><arg><funapp><name>cons</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__and</name><arg><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isNatList</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__length</name><arg><funapp><name>cons</name><arg><var>N</var></arg><arg><var>L</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__U11</name><arg><funapp><name>a__and</name><arg><funapp><name>a__isNatList</name><arg><var>L</var></arg></funapp></arg><arg><funapp><name>isNat</name><arg><var>N</var></arg></funapp></arg></funapp></arg><arg><var>L</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>zeros</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__zeros</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__U11</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>length</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__length</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__and</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>isNat</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__isNat</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>isNatList</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__isNatList</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>isNatIList</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__isNatIList</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>a__zeros</name></funapp></lhs><rhs><funapp><name>zeros</name></funapp></rhs></rule><rule><lhs><funapp><name>a__U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__length</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>length</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>isNat</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNatList</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>isNatList</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNatIList</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>isNatIList</name><arg><var>X</var></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>a__zeros</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>cons</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>zeros</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a__U11</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>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>s</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__length</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mark</name><arity>1</arity><polynomial><sum><polynomial><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>a__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>a__isNat</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__isNatIList</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>isNatIList</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>a__isNatList</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>isNatList</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>isNat</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>U11</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>length</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>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>nil</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>a__zeros</name></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>zeros</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>L</var></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>a__length</name><arg><funapp><name>mark</name><arg><var>L</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__and</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNatList</name><arg><funapp><name>cons</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__and</name><arg><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isNatList</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__length</name><arg><funapp><name>cons</name><arg><var>N</var></arg><arg><var>L</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__U11</name><arg><funapp><name>a__and</name><arg><funapp><name>a__isNatList</name><arg><var>L</var></arg></funapp></arg><arg><funapp><name>isNat</name><arg><var>N</var></arg></funapp></arg></funapp></arg><arg><var>L</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>zeros</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__zeros</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__U11</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>length</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__length</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__and</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__length</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>length</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>isNat</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNatList</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>isNatList</name><arg><var>X</var></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>a__zeros</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>cons</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>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>zeros</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a__U11</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>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>s</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__length</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>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>a__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>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>a__isNat</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>a__isNatList</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>isNatList</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>isNat</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>U11</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>length</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>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>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>a__zeros</name></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>zeros</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>L</var></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>a__length</name><arg><funapp><name>mark</name><arg><var>L</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNatList</name><arg><funapp><name>cons</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__and</name><arg><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isNatList</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__length</name><arg><funapp><name>cons</name><arg><var>N</var></arg><arg><var>L</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__U11</name><arg><funapp><name>a__and</name><arg><funapp><name>a__isNatList</name><arg><var>L</var></arg></funapp></arg><arg><funapp><name>isNat</name><arg><var>N</var></arg></funapp></arg></funapp></arg><arg><var>L</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>zeros</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__zeros</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__U11</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>length</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__length</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__and</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__length</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>length</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>a__zeros</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>cons</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>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>zeros</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a__U11</name><arity>2</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><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>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>s</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__length</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mark</name><arity>1</arity><polynomial><sum><polynomial><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>a__isNat</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>a__isNatList</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__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>isNatList</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>isNat</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>U11</name><arity>2</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><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>length</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>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></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>a__zeros</name></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>zeros</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>L</var></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>a__length</name><arg><funapp><name>mark</name><arg><var>L</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>zeros</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__zeros</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__U11</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>length</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__length</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__and</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__length</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>length</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><knuthBendixOrder><w0>1</w0><precedenceWeight><precedenceWeightEntry><name>a__zeros</name><arity>0</arity><precedence>12</precedence><weight>3</weight></precedenceWeightEntry><precedenceWeightEntry><name>0</name><arity>0</arity><precedence>9</precedence><weight>1</weight></precedenceWeightEntry><precedenceWeightEntry><name>zeros</name><arity>0</arity><precedence>1</precedence><weight>1</weight></precedenceWeightEntry><precedenceWeightEntry><name>tt</name><arity>0</arity><precedence>2</precedence><weight>5</weight></precedenceWeightEntry><precedenceWeightEntry><name>s</name><arity>1</arity><precedence>0</precedence><weight>1</weight></precedenceWeightEntry><precedenceWeightEntry><name>a__length</name><arity>1</arity><precedence>10</precedence><weight>1</weight></precedenceWeightEntry><precedenceWeightEntry><name>mark</name><arity>1</arity><precedence>13</precedence><weight>2</weight></precedenceWeightEntry><precedenceWeightEntry><name>a__isNat</name><arity>1</arity><precedence>3</precedence><weight>4</weight></precedenceWeightEntry><precedenceWeightEntry><name>length</name><arity>1</arity><precedence>5</precedence><weight>1</weight></precedenceWeightEntry><precedenceWeightEntry><name>cons</name><arity>2</arity><precedence>11</precedence><weight>0</weight></precedenceWeightEntry><precedenceWeightEntry><name>a__U11</name><arity>2</arity><precedence>6</precedence><weight>0</weight></precedenceWeightEntry><precedenceWeightEntry><name>U11</name><arity>2</arity><precedence>4</precedence><weight>0</weight></precedenceWeightEntry><precedenceWeightEntry><name>and</name><arity>2</arity><precedence>7</precedence><weight>0</weight></precedenceWeightEntry><precedenceWeightEntry><name>a__and</name><arity>2</arity><precedence>8</precedence><weight>0</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></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (8 real / 0 unknown / 0 assumptions / 8 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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