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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.43 pair #433314491
details
property
value
status
complete
benchmark
decrease.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n016.star.cs.uiowa.edu
space
Frederiksen_Glenstrup
run statistics
property
value
solver
AProVE
configuration
certified
runtime (wallclock)
1.88023 seconds
cpu usage
4.03683
user time
3.83752
system time
0.199309
max virtual memory
1.8788788E7
max residence set size
305268.0
stage attributes
key
value
certification-result
CERTIFIED
output-size
8670
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>decrease</name><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>decrease</name><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>decrease</name><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>number42</name><arg><funapp><name>Nil</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>number42</name><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>goal</name><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>decrease</name><arg><var>x</var></arg></funapp></rhs></rule></rules></trs><strategy><innermost/></strategy></trsInput><runtimeComplexity><signature><symbol><name>Cons</name><arity>2</arity></symbol><symbol><name>Nil</name><arity>0</arity></symbol></signature><signature><symbol><name>decrease</name><arity>1</arity></symbol><symbol><name>number42</name><arity>1</arity></symbol><symbol><name>goal</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>0</state></finalStates><treeAutomaton><finalStates><state>0</state><state>1</state><state>2</state><state>3</state></finalStates><transitions><transition><lhs><name>Cons</name><height>0</height><state>0</state><state>0</state></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>decrease</name><height>0</height><state>0</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>number42</name><height>0</height><state>0</state></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>goal</name><height>0</height><state>0</state></lhs><rhs><state>3</state></rhs></transition><transition><lhs><name>decrease</name><height>1</height><state>0</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>Nil</name><height>1</height></lhs><rhs><state>4</state></rhs></transition><transition><lhs><name>number42</name><height>1</height><state>4</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>Nil</name><height>1</height></lhs><rhs><state>5</state></rhs></transition><transition><lhs><name>Nil</name><height>1</height></lhs><rhs><state>8</state></rhs></transition><transition><lhs><name>Cons</name><height>1</height><state>5</state><state>8</state></lhs><rhs><state>7</state></rhs></transition><transition><lhs><name>Cons</name><height>1</height><state>5</state><state>7</state></lhs><rhs><state>6</state></rhs></transition><transition><lhs><name>Cons</name><height>1</height><state>5</state><state>6</state></lhs><rhs><state>6</state></rhs></transition><transition><lhs><name>Cons</name><height>1</height><state>5</state><state>6</state></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>decrease</name><height>1</height><state>0</state></lhs><rhs><state>3</state></rhs></transition><transition><lhs><name>number42</name><height>1</height><state>4</state></lhs><rhs><state>3</state></rhs></transition><transition><lhs><name>Nil</name><height>2</height></lhs><rhs><state>9</state></rhs></transition><transition><lhs><name>Nil</name><height>2</height></lhs><rhs><state>12</state></rhs></transition><transition><lhs><name>Cons</name><height>2</height><state>9</state><state>12</state></lhs><rhs><state>11</state></rhs></transition><transition><lhs><name>Cons</name><height>2</height><state>9</state><state>11</state></lhs><rhs><state>10</state></rhs></transition><transition><lhs><name>Cons</name><height>2</height><state>9</state><state>10</state></lhs><rhs><state>10</state></rhs></transition><transition><lhs><name>Cons</name><height>2</height><state>9</state><state>10</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>Cons</name><height>2</height><state>9</state><state>10</state></lhs><rhs><state>3</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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