Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.43 pair #433314145

details

property	value
status	complete
benchmark	Ex23_Luc06_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n084.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	2.05429 seconds
cpu usage	4.70207
user time	4.46746
system time	0.23461
max virtual memory	1.8657468E7
max residence set size	342396.0

stage attributes

key	value
certification-result	CERTIFIED
output-size	6734
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>a__f</name><arg><funapp><name>f</name><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>f</name><arg><funapp><name>g</name><arg><funapp><name>f</name><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>f</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__f</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>a</name></funapp></arg></funapp></lhs><rhs><funapp><name>a</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>c</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>g</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>g</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__f</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>f</name><arg><var>X</var></arg></funapp></rhs></rule></rules></trs><strategy><innermost/></strategy></trsInput><runtimeComplexity><signature><symbol><name>f</name><arity>1</arity></symbol><symbol><name>a</name><arity>0</arity></symbol><symbol><name>c</name><arity>1</arity></symbol><symbol><name>g</name><arity>1</arity></symbol></signature><signature><symbol><name>a__f</name><arity>1</arity></symbol><symbol><name>mark</name><arity>1</arity></symbol></signature></runtimeComplexity><polynomial>1</polynomial></complexityInput></input><cpfVersion>2.1</cpfVersion><proof><complexityProof><bounds><type><match/></type><bound>2</bound><finalStates><state>2</state></finalStates><treeAutomaton><finalStates><state>1</state><state>2</state></finalStates><transitions><transition><lhs><name>a__f</name><height>0</height><state>2</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>mark</name><height>0</height><state>2</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>f</name><height>1</height><state>2</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>a</name><height>1</height></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>c</name><height>1</height><state>2</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>c</name><height>1</height><state>3</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>a__f</name><height>1</height><state>7</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>f</name><height>2</height><state>7</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>g</name><height>1</height><state>8</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>c</name><height>2</height><state>9</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>f</name><height>0</height><state>2</state></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>a</name><height>0</height></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>c</name><height>0</height><state>2</state></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>g</name><height>0</height><state>2</state></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>f</name><height>1</height><state>4</state></lhs><rhs><state>3</state></rhs></transition><transition><lhs><name>g</name><height>1</height><state>5</state></lhs><rhs><state>4</state></rhs></transition><transition><lhs><name>f</name><height>1</height><state>6</state></lhs><rhs><state>5</state></rhs></transition><transition><lhs><name>a</name><height>1</height></lhs><rhs><state>6</state></rhs></transition><transition><lhs><name>mark</name><height>1</height><state>2</state></lhs><rhs><state>7</state></rhs></transition><transition><lhs><name>a</name><height>1</height></lhs><rhs><state>7</state></rhs></transition><transition><lhs><name>c</name><height>1</height><state>2</state></lhs><rhs><state>7</state></rhs></transition><transition><lhs><name>a__f</name><height>1</height><state>7</state></lhs><rhs><state>7</state></rhs></transition><transition><lhs><name>f</name><height>2</height><state>7</state></lhs><rhs><state>7</state></rhs></transition><transition><lhs><name>g</name><height>1</height><state>8</state></lhs><rhs><state>7</state></rhs></transition><transition><lhs><name>c</name><height>2</height><state>9</state></lhs><rhs><state>7</state></rhs></transition><transition><lhs><name>mark</name><height>1</height><state>2</state></lhs><rhs><state>8</state></rhs></transition><transition><lhs><name>a</name><height>1</height></lhs><rhs><state>8</state></rhs></transition><transition><lhs><name>c</name><height>1</height><state>2</state></lhs><rhs><state>8</state></rhs></transition><transition><lhs><name>a__f</name><height>1</height><state>7</state></lhs><rhs><state>8</state></rhs></transition><transition><lhs><name>f</name><height>2</height><state>7</state></lhs><rhs><state>8</state></rhs></transition><transition><lhs><name>g</name><height>1</height><state>8</state></lhs><rhs><state>8</state></rhs></transition><transition><lhs><name>c</name><height>2</height><state>9</state></lhs><rhs><state>8</state></rhs></transition><transition><lhs><name>f</name><height>2</height><state>10</state></lhs><rhs><state>9</state></rhs></transition><transition><lhs><name>g</name><height>2</height><state>11</state></lhs><rhs><state>10</state></rhs></transition><transition><lhs><name>f</name><height>2</height><state>12</state></lhs><rhs><state>11</state></rhs></transition><transition><lhs><name>a</name><height>2</height></lhs><rhs><state>12</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