details

property	value
status	complete
benchmark	overlap.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n040.star.cs.uiowa.edu
space	Frederiksen_Glenstrup

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rci_cert
runtime (wallclock)	5.09080600739 seconds
cpu usage	20.925406517
max memory	3.58719488E8

stage attributes

key	value
certification-result	CERTIFIED
output-size	59849
starexec-result	WORST_CASE(?,O(n^2))
certification-time	0.0

output

/export/starexec/sandbox/solver/bin/starexec_run_tct_rci_cert /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?,O(n^2)) <?xml version="1.0" encoding="UTF-8"?> <?xml-stylesheet type="text/xsl" href="cpfHTML.xsl"?> <certificationProblem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="cpf.xsd"><input><complexityInput><trsInput><trs><rules><rule><lhs><funapp><name>goal</name><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>overlap</name><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>member</name><arg><var>x</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>member</name><arg><var>x&apos;</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>member[Ite][True][Ite]</name><arg><funapp><name>!EQ</name><arg><var>x</var></arg><arg><var>x&apos;</var></arg></funapp></arg><arg><var>x&apos;</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>notEmpty</name><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><name>notEmpty</name><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>overlap</name><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>overlap[Ite][True][Ite]</name><arg><funapp><name>member</name><arg><var>x</var></arg><arg><var>ys</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>overlap</name><arg><funapp><name>Nil</name></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule></rules></trs><strategy><innermost/></strategy><relativeRules><rules><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>S</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>S</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>!EQ</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>member[Ite][True][Ite]</name><arg><funapp><name>False</name></funapp></arg><arg><var>x&apos;</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>member</name><arg><var>x&apos;</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>member[Ite][True][Ite]</name><arg><funapp><name>True</name></funapp></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><name>overlap[Ite][True][Ite]</name><arg><funapp><name>False</name></funapp></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>overlap</name><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>overlap[Ite][True][Ite]</name><arg><funapp><name>True</name></funapp></arg><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule></rules></relativeRules></trsInput><runtimeComplexity><signature><symbol><name>0</name><arity>0</arity></symbol><symbol><name>Cons</name><arity>2</arity></symbol><symbol><name>False</name><arity>0</arity></symbol><symbol><name>Nil</name><arity>0</arity></symbol><symbol><name>S</name><arity>1</arity></symbol><symbol><name>True</name><arity>0</arity></symbol></signature><signature><symbol><name>!EQ</name><arity>2</arity></symbol><symbol><name>goal</name><arity>2</arity></symbol><symbol><name>member</name><arity>2</arity></symbol><symbol><name>member[Ite][True][Ite]</name><arity>3</arity></symbol><symbol><name>notEmpty</name><arity>1</arity></symbol><symbol><name>overlap</name><arity>2</arity></symbol><symbol><name>overlap[Ite][True][Ite]</name><arity>3</arity></symbol></signature></runtimeComplexity><polynomial>2</polynomial></complexityInput></input><cpfVersion>2.2</cpfVersion><proof><complexityProof><ruleShifting><orderingConstraintProof><redPair><interpretation><type><matrixInterpretation><domain><naturals/></domain><dimension>1</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><name>!EQ</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret><interpret><name>Cons</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>False</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret><interpret><name>Nil</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret><interpret><name>S</name><arity>1</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>True</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret><interpret><name>goal</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>8</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>15</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>14</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>member</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>member[Ite][True][Ite]</name><arity>3</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>4</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>notEmpty</name><arity>1</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>overlap</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>15</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>14</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>overlap[Ite][True][Ite]</name><arity>3</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>2</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>15</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>14</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>goal</name><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>overlap</name><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>S</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>S</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>!EQ</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>goal</name><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>overlap</name><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>member</name><arg><var>x</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>member</name><arg><var>x&apos;</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>member[Ite][True][Ite]</name><arg><funapp><name>!EQ</name><arg><var>x</var></arg><arg><var>x&apos;</var></arg></funapp></arg><arg><var>x&apos;</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>member[Ite][True][Ite]</name><arg><funapp><name>False</name></funapp></arg><arg><var>x&apos;</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>member</name><arg><var>x&apos;</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>member[Ite][True][Ite]</name><arg><funapp><name>True</name></funapp></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><name>notEmpty</name><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><name>notEmpty</name><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>overlap</name><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>overlap[Ite][True][Ite]</name><arg><funapp><name>member</name><arg><var>x</var></arg><arg><var>ys</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>overlap</name><arg><funapp><name>Nil</name></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>overlap[Ite][True][Ite]</name><arg><funapp><name>False</name></funapp></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>overlap</name><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>overlap[Ite][True][Ite]</name><arg><funapp><name>True</name></funapp></arg><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule></rules></usableRules><complexityProof><ruleShifting><orderingConstraintProof><redPair><interpretation><type><matrixInterpretation><domain><naturals/></domain><dimension>1</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><name>!EQ</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret><interpret><name>Cons</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>False</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret><interpret><name>Nil</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret><interpret><name>S</name><arity>1</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>4</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>True</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret><interpret><name>goal</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>3</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>member</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>member[Ite][True][Ite]</name><arity>3</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>4</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>notEmpty</name><arity>1</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>12</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>overlap</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>overlap[Ite][True][Ite]</name><arity>3</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>notEmpty</name><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><name>notEmpty</name><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>overlap</name><arg><funapp><name>Nil</name></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>S</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>S</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>!EQ</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>goal</name><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>overlap</name><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>member</name><arg><var>x</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>member</name><arg><var>x&apos;</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>member[Ite][True][Ite]</name><arg><funapp><name>!EQ</name><arg><var>x</var></arg><arg><var>x&apos;</var></arg></funapp></arg><arg><var>x&apos;</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>member[Ite][True][Ite]</name><arg><funapp><name>False</name></funapp></arg><arg><var>x&apos;</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>member</name><arg><var>x&apos;</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>member[Ite][True][Ite]</name><arg><funapp><name>True</name></funapp></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><name>notEmpty</name><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><name>notEmpty</name><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>overlap</name><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>overlap[Ite][True][Ite]</name><arg><funapp><name>member</name><arg><var>x</var></arg><arg><var>ys</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>overlap</name><arg><funapp><name>Nil</name></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>overlap[Ite][True][Ite]</name><arg><funapp><name>False</name></funapp></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>overlap</name><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>overlap[Ite][True][Ite]</name><arg><funapp><name>True</name></funapp></arg><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule></rules></usableRules><complexityProof><ruleShifting><orderingConstraintProof><redPair><interpretation><type><matrixInterpretation><domain><naturals/></domain><dimension>1</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><name>!EQ</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret><interpret><name>Cons</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>False</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret><interpret><name>Nil</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret><interpret><name>S</name><arity>1</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>2</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>True</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret><interpret><name>goal</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>11</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>9</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>9</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>member</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>member[Ite][True][Ite]</name><arity>3</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>4</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>notEmpty</name><arity>1</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>13</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>overlap</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>8</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>8</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>8</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>overlap[Ite][True][Ite]</name><arity>3</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>8</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>8</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>8</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>overlap</name><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>overlap[Ite][True][Ite]</name><arg><funapp><name>member</name><arg><var>x</var></arg><arg><var>ys</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>S</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>S</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>!EQ</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>goal</name><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>overlap</name><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>member</name><arg><var>x</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>member</name><arg><var>x&apos;</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>member[Ite][True][Ite]</name><arg><funapp><name>!EQ</name><arg><var>x</var></arg><arg><var>x&apos;</var></arg></funapp></arg><arg><var>x&apos;</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>member[Ite][True][Ite]</name><arg><funapp><name>False</name></funapp></arg><arg><var>x&apos;</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>member</name><arg><var>x&apos;</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>member[Ite][True][Ite]</name><arg><funapp><name>True</name></funapp></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><name>notEmpty</name><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><name>notEmpty</name><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>overlap</name><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>overlap[Ite][True][Ite]</name><arg><funapp><name>member</name><arg><var>x</var></arg><arg><var>ys</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>overlap</name><arg><funapp><name>Nil</name></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>overlap[Ite][True][Ite]</name><arg><funapp><name>False</name></funapp></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>overlap</name><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>overlap[Ite][True][Ite]</name><arg><funapp><name>True</name></funapp></arg><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule></rules></usableRules><complexityProof><ruleShifting><orderingConstraintProof><redPair><interpretation><type><matrixInterpretation><domain><naturals/></domain><dimension>1</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><name>!EQ</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>2</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret><interpret><name>Cons</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>2</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>False</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret><interpret><name>Nil</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>2</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret><interpret><name>S</name><arity>1</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>8</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>True</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret><interpret><name>goal</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>10</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>10</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>2</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>member</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>member[Ite][True][Ite]</name><arity>3</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>4</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>notEmpty</name><arity>1</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>5</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>6</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>overlap</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>3</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>8</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>overlap[Ite][True][Ite]</name><arity>3</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>8</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>member</name><arg><var>x</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>S</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>S</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>!EQ</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>goal</name><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>overlap</name><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>member</name><arg><var>x</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>member</name><arg><var>x&apos;</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>member[Ite][True][Ite]</name><arg><funapp><name>!EQ</name><arg><var>x</var></arg><arg><var>x&apos;</var></arg></funapp></arg><arg><var>x&apos;</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>member[Ite][True][Ite]</name><arg><funapp><name>False</name></funapp></arg><arg><var>x&apos;</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>member</name><arg><var>x&apos;</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>member[Ite][True][Ite]</name><arg><funapp><name>True</name></funapp></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><name>notEmpty</name><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><name>notEmpty</name><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>overlap</name><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>overlap[Ite][True][Ite]</name><arg><funapp><name>member</name><arg><var>x</var></arg><arg><var>ys</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>overlap</name><arg><funapp><name>Nil</name></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>overlap[Ite][True][Ite]</name><arg><funapp><name>False</name></funapp></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>overlap</name><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>overlap[Ite][True][Ite]</name><arg><funapp><name>True</name></funapp></arg><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule></rules></usableRules><complexityProof><ruleShifting><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>2</degree></polynomial></type><interpret><name>!EQ</name><arity>2</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>0</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>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>False</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>Nil</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>S</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>True</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>goal</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</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>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>7</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>member</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>member[Ite][True][Ite]</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>notEmpty</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>overlap</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>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>7</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>overlap[Ite][True][Ite]</name><arity>3</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><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>member</name><arg><var>x&apos;</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>member[Ite][True][Ite]</name><arg><funapp><name>!EQ</name><arg><var>x</var></arg><arg><var>x&apos;</var></arg></funapp></arg><arg><var>x&apos;</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>S</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>S</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>!EQ</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>goal</name><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>overlap</name><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>member</name><arg><var>x</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>member</name><arg><var>x&apos;</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>member[Ite][True][Ite]</name><arg><funapp><name>!EQ</name><arg><var>x</var></arg><arg><var>x&apos;</var></arg></funapp></arg><arg><var>x&apos;</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>member[Ite][True][Ite]</name><arg><funapp><name>False</name></funapp></arg><arg><var>x&apos;</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>member</name><arg><var>x&apos;</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>member[Ite][True][Ite]</name><arg><funapp><name>True</name></funapp></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><name>notEmpty</name><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><name>notEmpty</name><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>overlap</name><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>overlap[Ite][True][Ite]</name><arg><funapp><name>member</name><arg><var>x</var></arg><arg><var>ys</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>overlap</name><arg><funapp><name>Nil</name></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>overlap[Ite][True][Ite]</name><arg><funapp><name>False</name></funapp></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>overlap</name><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>overlap[Ite][True][Ite]</name><arg><funapp><name>True</name></funapp></arg><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule></rules></usableRules><complexityProof><rIsEmpty/></complexityProof></ruleShifting></complexityProof></ruleShifting></complexityProof></ruleShifting></complexityProof></ruleShifting></complexityProof></ruleShifting></complexityProof></proof><origin><proofOrigin><tool><name>TcT</name><version/></tool></proofOrigin></origin></certificationProblem> 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