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Runti Compl Inner Rewri certi 34749 pair #381907172
details
property
value
status
complete
benchmark
inssort.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n072.star.cs.uiowa.edu
space
Frederiksen_Others
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rci_cert
runtime (wallclock)
143.094583035 seconds
cpu usage
631.68548166
max memory
4.64384E8
stage attributes
key
value
certification-result
CERTIFIED
output-size
49515
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>insert</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>insert[Ite]</name><arg><funapp><name><</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>r</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>inssort</name><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>isort</name><arg><var>xs</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isort</name><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>isort</name><arg><var>xs</var></arg><arg><funapp><name>insert</name><arg><var>x</var></arg><arg><var>r</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isort</name><arg><funapp><name>Nil</name></funapp></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>Nil</name></funapp></rhs></rule></rules></trs><strategy><innermost/></strategy><relativeRules><rules><rule><lhs><funapp><name><</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name><</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>True</name></funapp></rhs></rule><rule><lhs><funapp><name><</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><</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>insert[Ite]</name><arg><funapp><name>False</name></funapp></arg><arg><var>x'</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>Cons</name><arg><var>x</var></arg><arg><funapp><name>insert</name><arg><var>x'</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>insert[Ite]</name><arg><funapp><name>True</name></funapp></arg><arg><var>x</var></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>r</var></arg></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><</name><arity>2</arity></symbol><symbol><name>insert</name><arity>2</arity></symbol><symbol><name>insert[Ite]</name><arity>3</arity></symbol><symbol><name>inssort</name><arity>1</arity></symbol><symbol><name>isort</name><arity>2</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>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret><interpret><name><</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>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>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>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>True</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret><interpret><name>insert</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>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>insert[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>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>inssort</name><arity>1</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>1</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></sum></polynomial></interpret><interpret><name>isort</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>8</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>inssort</name><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>isort</name><arg><var>xs</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name><</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name><</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>True</name></funapp></rhs></rule><rule><lhs><funapp><name><</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><</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>insert</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>insert[Ite]</name><arg><funapp><name><</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>r</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>insert[Ite]</name><arg><funapp><name>False</name></funapp></arg><arg><var>x'</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>Cons</name><arg><var>x</var></arg><arg><funapp><name>insert</name><arg><var>x'</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>insert[Ite]</name><arg><funapp><name>True</name></funapp></arg><arg><var>x</var></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>r</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>inssort</name><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>isort</name><arg><var>xs</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isort</name><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>isort</name><arg><var>xs</var></arg><arg><funapp><name>insert</name><arg><var>x</var></arg><arg><var>r</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isort</name><arg><funapp><name>Nil</name></funapp></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>Nil</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>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>2</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret><interpret><name><</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>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>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>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>True</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret><interpret><name>insert</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>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>insert[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>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><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>inssort</name><arity>1</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>9</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>isort</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>9</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></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>isort</name><arg><funapp><name>Nil</name></funapp></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>Nil</name></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name><</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name><</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>True</name></funapp></rhs></rule><rule><lhs><funapp><name><</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><</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>insert</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>insert[Ite]</name><arg><funapp><name><</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>r</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>insert[Ite]</name><arg><funapp><name>False</name></funapp></arg><arg><var>x'</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>Cons</name><arg><var>x</var></arg><arg><funapp><name>insert</name><arg><var>x'</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>insert[Ite]</name><arg><funapp><name>True</name></funapp></arg><arg><var>x</var></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>r</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>inssort</name><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>isort</name><arg><var>xs</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isort</name><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>isort</name><arg><var>xs</var></arg><arg><funapp><name>insert</name><arg><var>x</var></arg><arg><var>r</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isort</name><arg><funapp><name>Nil</name></funapp></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>Nil</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>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret><interpret><name><</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>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>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>insert</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>6</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>insert[Ite]</name><arity>3</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>6</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>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>inssort</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>11</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isort</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>11</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></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>isort</name><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>isort</name><arg><var>xs</var></arg><arg><funapp><name>insert</name><arg><var>x</var></arg><arg><var>r</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name><</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name><</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>True</name></funapp></rhs></rule><rule><lhs><funapp><name><</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><</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>insert</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>insert[Ite]</name><arg><funapp><name><</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>r</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>insert[Ite]</name><arg><funapp><name>False</name></funapp></arg><arg><var>x'</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>Cons</name><arg><var>x</var></arg><arg><funapp><name>insert</name><arg><var>x'</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>insert[Ite]</name><arg><funapp><name>True</name></funapp></arg><arg><var>x</var></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>r</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>inssort</name><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>isort</name><arg><var>xs</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isort</name><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>isort</name><arg><var>xs</var></arg><arg><funapp><name>insert</name><arg><var>x</var></arg><arg><var>r</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isort</name><arg><funapp><name>Nil</name></funapp></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>Nil</name></funapp></rhs></rule></rules></usableRules><complexityProof><dtTransformation><strictDTs><ruleWithDT><rule><lhs><funapp><name>insert</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>insert[Ite]</name><arg><funapp><name><</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>r</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>insert</name></sharp><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>c1</name><arg><funapp><sharp><name>insert[Ite]</name></sharp><arg><funapp><name><</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>r</var></arg></funapp></arg><arg><funapp><sharp><name><</name></sharp><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule></ruleWithDT></strictDTs><weakDTs><ruleWithDT><rule><lhs><funapp><name><</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name><</name></sharp><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c2</name></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name><</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>True</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name><</name></sharp><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>S</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c3</name></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name><</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><</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name><</name></sharp><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>c4</name><arg><funapp><sharp><name><</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name>insert[Ite]</name><arg><funapp><name>False</name></funapp></arg><arg><var>x'</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>Cons</name><arg><var>x</var></arg><arg><funapp><name>insert</name><arg><var>x'</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>insert[Ite]</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><var>x'</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c5</name><arg><funapp><sharp><name>insert</name></sharp><arg><var>x'</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name>insert[Ite]</name><arg><funapp><name>True</name></funapp></arg><arg><var>x</var></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>r</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>insert[Ite]</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><var>x</var></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>c6</name></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name>inssort</name><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>isort</name><arg><var>xs</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>inssort</name></sharp><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>c7</name><arg><funapp><sharp><name>isort</name></sharp><arg><var>xs</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name>isort</name><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>isort</name><arg><var>xs</var></arg><arg><funapp><name>insert</name><arg><var>x</var></arg><arg><var>r</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isort</name></sharp><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>c8</name><arg><funapp><sharp><name>isort</name></sharp><arg><var>xs</var></arg><arg><funapp><name>insert</name><arg><var>x</var></arg><arg><var>r</var></arg></funapp></arg></funapp></arg><arg><funapp><sharp><name>insert</name></sharp><arg><var>x</var></arg><arg><var>r</var></arg></funapp></arg></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name>isort</name><arg><funapp><name>Nil</name></funapp></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>Nil</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isort</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>c9</name></funapp></rhs></rule></ruleWithDT></weakDTs><innermostLhss><funapp><sharp><name>insert</name></sharp><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>r</var></arg></funapp><funapp><sharp><name><</name></sharp><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp><funapp><sharp><name><</name></sharp><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>S</name><arg><var>y</var></arg></funapp></arg></funapp><funapp><sharp><name><</name></sharp><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><funapp><sharp><name>insert[Ite]</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><var>x'</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp><funapp><sharp><name>insert[Ite]</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><var>x</var></arg><arg><var>r</var></arg></funapp><funapp><sharp><name>inssort</name></sharp><arg><var>xs</var></arg></funapp><funapp><sharp><name>isort</name></sharp><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>r</var></arg></funapp><funapp><sharp><name>isort</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><var>r</var></arg></funapp></innermostLhss><complexityProof><usableRules><nonUsableRules><rules><rule><lhs><funapp><name>inssort</name><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>isort</name><arg><var>xs</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isort</name><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>isort</name><arg><var>xs</var></arg><arg><funapp><name>insert</name><arg><var>x</var></arg><arg><var>r</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isort</name><arg><funapp><name>Nil</name></funapp></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>Nil</name></funapp></rhs></rule></rules></nonUsableRules><complexityProof><ruleShifting><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>2</degree></polynomial></type><interpret><name>0</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name><</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>Cons</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</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><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></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>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>True</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>insert</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>insert[Ite]</name><arity>3</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>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>inssort</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isort</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>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name><</name></sharp><arity>2</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><sharp><name>insert</name></sharp><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>insert[Ite]</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</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>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>inssort</name></sharp><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</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></sum></polynomial></interpret><interpret><sharp><name>isort</name></sharp><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></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>c1</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>c2</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>c3</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>c4</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>c5</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>c6</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>c7</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>c8</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>c9</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><sharp><name>insert</name></sharp><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>c1</name><arg><funapp><sharp><name>insert[Ite]</name></sharp><arg><funapp><name><</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>r</var></arg></funapp></arg><arg><funapp><sharp><name><</name></sharp><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name><</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name><</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>True</name></funapp></rhs></rule><rule><lhs><funapp><name><</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><</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>insert</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>insert[Ite]</name><arg><funapp><name><</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>r</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>insert[Ite]</name><arg><funapp><name>False</name></funapp></arg><arg><var>x'</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>Cons</name><arg><var>x</var></arg><arg><funapp><name>insert</name><arg><var>x'</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>insert[Ite]</name><arg><funapp><name>True</name></funapp></arg><arg><var>x</var></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>r</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name><</name></sharp><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c2</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name><</name></sharp><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>S</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c3</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name><</name></sharp><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>c4</name><arg><funapp><sharp><name><</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>insert</name></sharp><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>c1</name><arg><funapp><sharp><name>insert[Ite]</name></sharp><arg><funapp><name><</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>r</var></arg></funapp></arg><arg><funapp><sharp><name><</name></sharp><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>insert[Ite]</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><var>x'</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c5</name><arg><funapp><sharp><name>insert</name></sharp><arg><var>x'</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>insert[Ite]</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><var>x</var></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>c6</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>inssort</name></sharp><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>c7</name><arg><funapp><sharp><name>isort</name></sharp><arg><var>xs</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isort</name></sharp><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>c8</name><arg><funapp><sharp><name>isort</name></sharp><arg><var>xs</var></arg><arg><funapp><name>insert</name><arg><var>x</var></arg><arg><var>r</var></arg></funapp></arg></funapp></arg><arg><funapp><sharp><name>insert</name></sharp><arg><var>x</var></arg><arg><var>r</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isort</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><var>r</var></arg></funapp></lhs><rhs><funapp><name>c9</name></funapp></rhs></rule></rules></usableRules><complexityProof><rIsEmpty/></complexityProof></ruleShifting></complexityProof></usableRules></complexityProof></dtTransformation></complexityProof></ruleShifting></complexityProof></ruleShifting></complexityProof></ruleShifting></complexityProof></proof><origin><proofOrigin><tool><name>TcT</name><version/></tool></proofOrigin></origin></certificationProblem>
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