/export/starexec/sandbox2/solver/bin/starexec_run_tct_rci_cert /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


WORST_CASE(?,O(n^1))
<?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>divp</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>=</name><arg><funapp><name>rem</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>prime</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>prime</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>prime</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>prime1</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>prime1</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>prime1</name><arg><var>x</var></arg><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>prime1</name><arg><var>x</var></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>not</name><arg><funapp><name>divp</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><funapp><name>prime1</name><arg><var>x</var></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><strategy><innermost/></strategy><relativeRules><rules/></relativeRules></trsInput><runtimeComplexity><signature><symbol><name>0</name><arity>0</arity></symbol><symbol><name>=</name><arity>2</arity></symbol><symbol><name>and</name><arity>2</arity></symbol><symbol><name>false</name><arity>0</arity></symbol><symbol><name>not</name><arity>1</arity></symbol><symbol><name>rem</name><arity>2</arity></symbol><symbol><name>s</name><arity>1</arity></symbol><symbol><name>true</name><arity>0</arity></symbol></signature><signature><symbol><name>divp</name><arity>2</arity></symbol><symbol><name>prime</name><arity>1</arity></symbol><symbol><name>prime1</name><arity>2</arity></symbol></signature></runtimeComplexity><polynomial>1</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>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>and</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>divp</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>false</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret><interpret><name>not</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>prime</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>2</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>prime1</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>rem</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>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>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></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>prime</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>prime</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>prime</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>prime1</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>divp</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>=</name><arg><funapp><name>rem</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>prime</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>prime</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>prime</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>prime1</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>prime1</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>prime1</name><arg><var>x</var></arg><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>prime1</name><arg><var>x</var></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>not</name><arg><funapp><name>divp</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><funapp><name>prime1</name><arg><var>x</var></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg></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>and</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>divp</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>false</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret><interpret><name>not</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>prime</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>8</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>prime1</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>8</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>rem</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>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>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>4</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>prime1</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>prime1</name><arg><var>x</var></arg><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>divp</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>=</name><arg><funapp><name>rem</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>prime</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>prime</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>prime</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>prime1</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>prime1</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>prime1</name><arg><var>x</var></arg><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>prime1</name><arg><var>x</var></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>not</name><arg><funapp><name>divp</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><funapp><name>prime1</name><arg><var>x</var></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg></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>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>and</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>divp</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>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>false</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret><interpret><name>not</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>prime</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>8</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>prime1</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>4</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>4</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>rem</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>s</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>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>8</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>divp</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>=</name><arg><funapp><name>rem</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>prime1</name><arg><var>x</var></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>not</name><arg><funapp><name>divp</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><funapp><name>prime1</name><arg><var>x</var></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>divp</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>=</name><arg><funapp><name>rem</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>prime</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>prime</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>prime</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>prime1</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>prime1</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>prime1</name><arg><var>x</var></arg><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>prime1</name><arg><var>x</var></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>not</name><arg><funapp><name>divp</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><funapp><name>prime1</name><arg><var>x</var></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><complexityProof><rIsEmpty/></complexityProof></ruleShifting></complexityProof></ruleShifting></complexityProof></ruleShifting></complexityProof></proof><origin><proofOrigin><tool><name>TcT</name><version/></tool></proofOrigin></origin></certificationProblem>