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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.43 pair #433314254
details
property
value
status
complete
benchmark
2.37.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n127.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
certified
runtime (wallclock)
1.75772 seconds
cpu usage
3.84373
user time
3.68485
system time
0.158876
max virtual memory
1.865462E7
max residence set size
239108.0
stage attributes
key
value
certification-result
CERTIFIED
output-size
6225
starexec-result
WORST_CASE(?,O(n^1))
certification-time
0.0
output
WORST_CASE(?, O(n^1)) <?xml version="1.0" encoding="UTF-8" standalone="no"?><?xml-stylesheet type="text/xsl" href="cpfHTML.xsl"?><certificationProblem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="cpf.xsd"><input><complexityInput><trsInput><trs><rules><rule><lhs><funapp><name>and</name><arg><funapp><name>not</name><arg><funapp><name>not</name><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><var>y</var></arg><arg><funapp><name>not</name><arg><var>z</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>y</var></arg><arg><funapp><name>band</name><arg><var>x</var></arg><arg><var>z</var></arg></funapp></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></trs><strategy><innermost/></strategy></trsInput><runtimeComplexity><signature><symbol><name>not</name><arity>1</arity></symbol><symbol><name>band</name><arity>2</arity></symbol></signature><signature><symbol><name>and</name><arity>3</arity></symbol></signature></runtimeComplexity><polynomial>1</polynomial></complexityInput></input><cpfVersion>2.1</cpfVersion><proof><complexityProof><dtTransformation><strictDTs><ruleWithDT><rule><lhs><funapp><name>and</name><arg><funapp><name>not</name><arg><funapp><name>not</name><arg><var>z0</var></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg><arg><funapp><name>not</name><arg><var>z2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>z1</var></arg><arg><funapp><name>band</name><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z0</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>not</name><arg><funapp><name>not</name><arg><var>z0</var></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg><arg><funapp><name>not</name><arg><var>z2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><sharp><name>and</name></sharp><arg><var>z1</var></arg><arg><funapp><name>band</name><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z0</var></arg></funapp></arg></funapp></rhs></rule></ruleWithDT></strictDTs><weakDTs/><innermostLhss><funapp><sharp><name>and</name></sharp><arg><funapp><name>not</name><arg><funapp><name>not</name><arg><var>z0</var></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg><arg><funapp><name>not</name><arg><var>z2</var></arg></funapp></arg></funapp></innermostLhss><complexityProof><usableRules><nonUsableRules><rules><rule><lhs><funapp><name>and</name><arg><funapp><name>not</name><arg><funapp><name>not</name><arg><var>z0</var></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg><arg><funapp><name>not</name><arg><var>z2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>z1</var></arg><arg><funapp><name>band</name><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z0</var></arg></funapp></rhs></rule></rules></nonUsableRules><complexityProof><ruleShifting><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>c</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>and</name></sharp><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>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>not</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>band</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>not</name><arg><funapp><name>not</name><arg><var>z0</var></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg><arg><funapp><name>not</name><arg><var>z2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><sharp><name>and</name></sharp><arg><var>z1</var></arg><arg><funapp><name>band</name><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z0</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>not</name><arg><funapp><name>not</name><arg><var>z0</var></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg><arg><funapp><name>not</name><arg><var>z2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><sharp><name>and</name></sharp><arg><var>z1</var></arg><arg><funapp><name>band</name><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z0</var></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><complexityProof><rIsEmpty/></complexityProof></ruleShifting></complexityProof></usableRules></complexityProof></dtTransformation></complexityProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (4 real / 0 unknown / 0 assumptions / 4 total proof steps)</strategy><url>http://aprove.informatik.rwth-aachen.de</url></tool><toolUser><firstName>John</firstName><lastName>Doe</lastName></toolUser></proofOrigin><inputOrigin/></origin></certificationProblem>
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