Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.43 pair #433314198

details

property	value
status	complete
benchmark	Ex26_Luc03b_L.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n153.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	1.89135 seconds
cpu usage	3.81138
user time	3.60812
system time	0.203254
max virtual memory	1.865566E7
max residence set size	291684.0

stage attributes

key	value
certification-result	CERTIFIED
output-size	5711
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>terms</name><arg><var>N</var></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>recip</name><arg><funapp><name>sqr</name><arg><var>N</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>sqr</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>sqr</name><arg><funapp><name>s</name></funapp></arg></funapp></lhs><rhs><funapp><name>s</name></funapp></rhs></rule><rule><lhs><funapp><name>dbl</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>dbl</name><arg><funapp><name>s</name></funapp></arg></funapp></lhs><rhs><funapp><name>s</name></funapp></rhs></rule><rule><lhs><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>add</name><arg><funapp><name>s</name></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>s</name></funapp></rhs></rule><rule><lhs><funapp><name>first</name><arg><funapp><name>0</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>first</name><arg><funapp><name>s</name></funapp></arg><arg><funapp><name>cons</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><var>Y</var></arg></funapp></rhs></rule></rules></trs><strategy><innermost/></strategy></trsInput><runtimeComplexity><signature><symbol><name>cons</name><arity>1</arity></symbol><symbol><name>recip</name><arity>1</arity></symbol><symbol><name>0</name><arity>0</arity></symbol><symbol><name>s</name><arity>0</arity></symbol><symbol><name>nil</name><arity>0</arity></symbol></signature><signature><symbol><name>terms</name><arity>1</arity></symbol><symbol><name>sqr</name><arity>1</arity></symbol><symbol><name>dbl</name><arity>1</arity></symbol><symbol><name>add</name><arity>2</arity></symbol><symbol><name>first</name><arity>2</arity></symbol></signature></runtimeComplexity><polynomial>1</polynomial></complexityInput></input><cpfVersion>2.1</cpfVersion><proof><complexityProof><bounds><type><match/></type><bound>1</bound><finalStates><state>0</state></finalStates><treeAutomaton><finalStates><state>0</state><state>1</state><state>2</state><state>3</state><state>4</state><state>5</state></finalStates><transitions><transition><lhs><name>cons</name><height>0</height><state>0</state></lhs><rhs><state>0</state></rhs></transition><transition><lhs><name>recip</name><height>0</height><state>0</state></lhs><rhs><state>0</state></rhs></transition><transition><lhs><name>0</name><height>0</height></lhs><rhs><state>0</state></rhs></transition><transition><lhs><name>s</name><height>0</height></lhs><rhs><state>0</state></rhs></transition><transition><lhs><name>nil</name><height>0</height></lhs><rhs><state>0</state></rhs></transition><transition><lhs><name>terms</name><height>0</height><state>0</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>sqr</name><height>0</height><state>0</state></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>dbl</name><height>0</height><state>0</state></lhs><rhs><state>3</state></rhs></transition><transition><lhs><name>add</name><height>0</height><state>0</state><state>0</state></lhs><rhs><state>4</state></rhs></transition><transition><lhs><name>first</name><height>0</height><state>0</state><state>0</state></lhs><rhs><state>5</state></rhs></transition><transition><lhs><name>sqr</name><height>1</height><state>0</state></lhs><rhs><state>7</state></rhs></transition><transition><lhs><name>recip</name><height>1</height><state>7</state></lhs><rhs><state>6</state></rhs></transition><transition><lhs><name>cons</name><height>1</height><state>6</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>0</name><height>1</height></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>s</name><height>1</height></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>0</name><height>1</height></lhs><rhs><state>3</state></rhs></transition><transition><lhs><name>s</name><height>1</height></lhs><rhs><state>3</state></rhs></transition><transition><lhs><name>s</name><height>1</height></lhs><rhs><state>4</state></rhs></transition><transition><lhs><name>nil</name><height>1</height></lhs><rhs><state>5</state></rhs></transition><transition><lhs><name>cons</name><height>1</height><state>0</state></lhs><rhs><state>5</state></rhs></transition><transition><lhs><name>0</name><height>1</height></lhs><rhs><state>7</state></rhs></transition><transition><lhs><name>s</name><height>1</height></lhs><rhs><state>7</state></rhs></transition><transition><lhs><state>0</state></lhs><rhs><state>4</state></rhs></transition></transitions></treeAutomaton></bounds></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 % (1 real / 0 unknown / 0 assumptions / 1 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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actions all output return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.43