Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.43 pair #433314528

details

property	value
status	complete
benchmark	ex6.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n070.star.cs.uiowa.edu
space	Frederiksen_Others

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	1.82806 seconds
cpu usage	3.93307
user time	3.73407
system time	0.199001
max virtual memory	1.865646E7
max residence set size	297336.0

stage attributes

key	value
certification-result	CERTIFIED
output-size	5073
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>g</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>g</name><arg><var>x</var></arg><arg><funapp><name>S</name><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><var>y</var></arg><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>S</name><arg><var>y</var></arg></funapp></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>g</name><arg><funapp><name>0</name></funapp></arg><arg><var>x2</var></arg></funapp></lhs><rhs><var>x2</var></rhs></rule><rule><lhs><funapp><name>f</name><arg><var>x1</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>g</name><arg><var>x1</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule></rules></trs><strategy><innermost/></strategy></trsInput><runtimeComplexity><signature><symbol><name>S</name><arity>1</arity></symbol><symbol><name>0</name><arity>0</arity></symbol></signature><signature><symbol><name>g</name><arity>2</arity></symbol><symbol><name>f</name><arity>2</arity></symbol></signature></runtimeComplexity><polynomial>1</polynomial></complexityInput></input><cpfVersion>2.1</cpfVersion><proof><complexityProof><bounds><type><match/></type><bound>2</bound><finalStates><state>0</state></finalStates><treeAutomaton><finalStates><state>0</state><state>1</state><state>2</state></finalStates><transitions><transition><lhs><name>S</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>g</name><height>0</height><state>0</state><state>0</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>f</name><height>0</height><state>0</state><state>0</state></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>S</name><height>1</height><state>0</state></lhs><rhs><state>3</state></rhs></transition><transition><lhs><name>g</name><height>1</height><state>0</state><state>3</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>S</name><height>1</height><state>0</state></lhs><rhs><state>4</state></rhs></transition><transition><lhs><name>f</name><height>1</height><state>4</state><state>0</state></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>0</name><height>1</height></lhs><rhs><state>5</state></rhs></transition><transition><lhs><name>g</name><height>1</height><state>0</state><state>5</state></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>S</name><height>1</height><state>3</state></lhs><rhs><state>3</state></rhs></transition><transition><lhs><name>S</name><height>1</height><state>5</state></lhs><rhs><state>3</state></rhs></transition><transition><lhs><name>g</name><height>1</height><state>0</state><state>3</state></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>S</name><height>1</height><state>4</state></lhs><rhs><state>4</state></rhs></transition><transition><lhs><name>g</name><height>1</height><state>4</state><state>5</state></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>S</name><height>2</height><state>5</state></lhs><rhs><state>6</state></rhs></transition><transition><lhs><name>g</name><height>2</height><state>0</state><state>6</state></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>g</name><height>2</height><state>4</state><state>6</state></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>S</name><height>1</height><state>6</state></lhs><rhs><state>3</state></rhs></transition><transition><lhs><name>S</name><height>2</height><state>6</state></lhs><rhs><state>6</state></rhs></transition><transition><lhs><state>0</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><state>3</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><state>3</state></lhs><rhs><state>2</state></rhs></transition><transition><lhs><state>5</state></lhs><rhs><state>2</state></rhs></transition><transition><lhs><state>6</state></lhs><rhs><state>2</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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