Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.43 pair #433313991

details
property	value
status	complete
benchmark	flatten.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n092.star.cs.uiowa.edu
space	hoca
run statistics
property	value
solver	AProVE
configuration	certified
runtime (wallclock)	4.34449 seconds
cpu usage	13.412
user time	12.9035
system time	0.508433
max virtual memory	3.7366928E7
max residence set size	1089656.0
stage attributes
key	value
certification-result	CERTIFIED
output-size	13574
starexec-result	WORST_CASE(?,O(n^1))
certification-time	0.1
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>walk#1</name><arg><funapp><name>Leaf</name><arg><var>x2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons_x</name><arg><var>x2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>walk#1</name><arg><funapp><name>Node</name><arg><var>x5</var></arg><arg><var>x3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>comp_f_g</name><arg><funapp><name>walk#1</name><arg><var>x5</var></arg></funapp></arg><arg><funapp><name>walk#1</name><arg><var>x3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>comp_f_g#1</name><arg><funapp><name>comp_f_g</name><arg><var>x4</var></arg><arg><var>x5</var></arg></funapp></arg><arg><funapp><name>comp_f_g</name><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><name>comp_f_g#1</name><arg><var>x4</var></arg><arg><var>x5</var></arg><arg><funapp><name>comp_f_g#1</name><arg><var>x2</var></arg><arg><var>x3</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>comp_f_g#1</name><arg><funapp><name>comp_f_g</name><arg><var>x7</var></arg><arg><var>x9</var></arg></funapp></arg><arg><funapp><name>cons_x</name><arg><var>x2</var></arg></funapp></arg><arg><var>x4</var></arg></funapp></lhs><rhs><funapp><name>comp_f_g#1</name><arg><var>x7</var></arg><arg><var>x9</var></arg><arg><funapp><name>Cons</name><arg><var>x2</var></arg><arg><var>x4</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>comp_f_g#1</name><arg><funapp><name>cons_x</name><arg><var>x2</var></arg></funapp></arg><arg><funapp><name>comp_f_g</name><arg><var>x5</var></arg><arg><var>x7</var></arg></funapp></arg><arg><var>x3</var></arg></funapp></lhs><rhs><funapp><name>Cons</name><arg><var>x2</var></arg><arg><funapp><name>comp_f_g#1</name><arg><var>x5</var></arg><arg><var>x7</var></arg><arg><var>x3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>comp_f_g#1</name><arg><funapp><name>cons_x</name><arg><var>x5</var></arg></funapp></arg><arg><funapp><name>cons_x</name><arg><var>x2</var></arg></funapp></arg><arg><var>x4</var></arg></funapp></lhs><rhs><funapp><name>Cons</name><arg><var>x5</var></arg><arg><funapp><name>Cons</name><arg><var>x2</var></arg><arg><var>x4</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>main</name><arg><funapp><name>Leaf</name><arg><var>x4</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>Cons</name><arg><var>x4</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>main</name><arg><funapp><name>Node</name><arg><var>x9</var></arg><arg><var>x5</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>comp_f_g#1</name><arg><funapp><name>walk#1</name><arg><var>x9</var></arg></funapp></arg><arg><funapp><name>walk#1</name><arg><var>x5</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></rhs></rule></rules></trs><strategy><innermost/></strategy></trsInput><runtimeComplexity><signature><symbol><name>Leaf</name><arity>1</arity></symbol><symbol><name>cons_x</name><arity>1</arity></symbol><symbol><name>Node</name><arity>2</arity></symbol><symbol><name>comp_f_g</name><arity>2</arity></symbol><symbol><name>Cons</name><arity>2</arity></symbol><symbol><name>Nil</name><arity>0</arity></symbol></signature><signature><symbol><name>walk#1</name><arity>1</arity></symbol><symbol><name>comp_f_g#1</name><arity>3</arity></symbol><symbol><name>main</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>Leaf</name><height>0</height><state>0</state></lhs><rhs><state>0</state></rhs></transition><transition><lhs><name>cons_x</name><height>0</height><state>0</state></lhs><rhs><state>0</state></rhs></transition><transition><lhs><name>Node</name><height>0</height><state>0</state><state>0</state></lhs><rhs><state>0</state></rhs></transition><transition><lhs><name>comp_f_g</name><height>0</height><state>0</state><state>0</state></lhs><rhs><state>0</state></rhs></transition><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>walk#1</name><height>0</height><state>0</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>comp_f_g#1</name><height>0</height><state>0</state><state>0</state><state>0</state></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>main</name><height>0</height><state>0</state></lhs><rhs><state>3</state></rhs></transition><transition><lhs><name>cons_x</name><height>1</height><state>0</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>walk#1</name><height>1</height><state>0</state></lhs><rhs><state>4</state></rhs></transition><transition><lhs><name>walk#1</name><height>1</height><state>0</state></lhs><rhs><state>5</state></rhs></transition><transition><lhs><name>comp_f_g</name><height>1</height><state>4</state><state>5</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>comp_f_g#1</name><height>1</height><state>0</state><state>0</state><state>0</state></lhs><rhs><state>6</state></rhs></transition><transition><lhs><name>comp_f_g#1</name><height>1</height><state>0</state><state>0</state><state>6</state></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>Cons</name><height>1</height><state>0</state><state>0</state></lhs><rhs><state>7</state></rhs></transition><transition><lhs><name>comp_f_g#1</name><height>1</height><state>0</state><state>0</state><state>7</state></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>comp_f_g#1</name><height>1</height><state>0</state><state>0</state><state>0</state></lhs><rhs><state>8</state></rhs></transition><transition><lhs><name>Cons</name><height>1</height><state>0</state><state>8</state></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>Cons</name><height>1</height><state>0</state><state>0</state></lhs><rhs><state>9</state></rhs></transition><transition><lhs><name>Cons</name><height>1</height><state>0</state><state>9</state></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>Nil</name><height>1</height></lhs><rhs><state>10</state></rhs></transition><transition><lhs><name>Cons</name><height>1</height><state>0</state><state>10</state></lhs><rhs><state>3</state></rhs></transition><transition><lhs><name>walk#1</name><height>1</height><state>0</state></lhs><rhs><state>11</state></rhs></transition><transition><lhs><name>walk#1</name><height>1</height><state>0</state></lhs><rhs><state>12</state></rhs></transition><transition><lhs><name>Nil</name><height>1</height></lhs><rhs><state>13</state></rhs></transition><transition><lhs><name>comp_f_g#1</name><height>1</height><state>11</state><state>12</state><state>13</state></lhs><rhs><state>3</state></rhs></transition><transition><lhs><name>cons_x</name><height>1</height><state>0</state></lhs><rhs><state>4</state></rhs></transition><transition><lhs><name>cons_x</name><height>1</height><state>0</state></lhs><rhs><state>5</state></rhs></transition><transition><lhs><name>cons_x</name><height>1</height><state>0</state></lhs><rhs><state>11</state></rhs></transition><transition><lhs><name>cons_x</name><height>1</height><state>0</state></lhs><rhs><state>12</state></rhs></transition><transition><lhs><name>comp_f_g</name><height>1</height><state>4</state><state>5</state></lhs><rhs><state>4</state></rhs></transition><transition><lhs><name>comp_f_g</name><height>1</height><state>4</state><state>5</state></lhs><rhs><state>5</state></rhs></transition><transition><lhs><name>comp_f_g</name><height>1</height><state>4</state><state>5</state></lhs><rhs><state>11</state></rhs></transition><transition><lhs><name>comp_f_g</name><height>1</height><state>4</state><state>5</state></lhs><rhs><state>12</state></rhs></transition><transition><lhs><name>comp_f_g#1</name><height>1</height><state>0</state><state>0</state><state>6</state></lhs><rhs><state>6</state></rhs></transition><transition><lhs><name>comp_f_g#1</name><height>1</height><state>0</state><state>0</state><state>7</state></lhs><rhs><state>6</state></rhs></transition><transition><lhs><name>comp_f_g#1</name><height>1</height><state>0</state><state>0</state><state>6</state></lhs><rhs><state>8</state></rhs></transition><transition><lhs><name>Cons</name><height>1</height><state>0</state><state>6</state></lhs><rhs><state>7</state></rhs></transition><transition><lhs><name>Cons</name><height>1</height><state>0</state><state>7</state></lhs><rhs><state>7</state></rhs></transition><transition><lhs><name>comp_f_g#1</name><height>1</height><state>0</state><state>0</state><state>7</state></lhs><rhs><state>8</state></rhs></transition><transition><lhs><name>Cons</name><height>1</height><state>0</state><state>8</state></lhs><rhs><state>6</state></rhs></transition><transition><lhs><name>Cons</name><height>1</height><state>0</state><state>8</state></lhs><rhs><state>8</state></rhs></transition><transition><lhs><name>Cons</name><height>1</height><state>0</state><state>6</state></lhs><rhs><state>9</state></rhs></transition><transition><lhs><name>Cons</name><height>1</height><state>0</state><state>7</state></lhs><rhs><state>9</state></rhs></transition><transition><lhs><name>Cons</name><height>1</height><state>0</state><state>9</state></lhs><rhs><state>6</state></rhs></transition><transition><lhs><name>Cons</name><height>1</height><state>0</state><state>9</state></lhs><rhs><state>8</state></rhs></transition><transition><lhs><name>comp_f_g#1</name><height>2</height><state>4</state><state>5</state><state>13</state></lhs><rhs><state>14</state></rhs></transition><transition><lhs><name>comp_f_g#1</name><height>2</height><state>4</state><state>5</state><state>14</state></lhs><rhs><state>3</state></rhs></transition><transition><lhs><name>Cons</name><height>2</height><state>0</state><state>13</state></lhs><rhs><state>15</state></rhs></transition><transition><lhs><name>comp_f_g#1</name><height>2</height><state>4</state><state>5</state><state>15</state></lhs><rhs><state>3</state></rhs></transition><transition><lhs><name>comp_f_g#1</name><height>2</height><state>4</state><state>5</state><state>13</state></lhs><rhs><state>16</state></rhs></transition><transition><lhs><name>Cons</name><height>2</height><state>0</state><state>16</state></lhs><rhs><state>3</state></rhs></transition><transition><lhs><name>Cons</name><height>2</height><state>0</state><state>13</state></lhs><rhs><state>17</state></rhs></transition><transition><lhs><name>Cons</name><height>2</height><state>0</state><state>17</state></lhs><rhs><state>3</state></rhs></transition><transition><lhs><name>comp_f_g#1</name><height>2</height><state>4</state><state>5</state><state>14</state></lhs><rhs><state>14</state></rhs></transition><transition><lhs><name>comp_f_g#1</name><height>2</height><state>4</state><state>5</state><state>15</state></lhs><rhs><state>14</state></rhs></transition><transition><lhs><name>comp_f_g#1</name><height>2</height><state>4</state><state>5</state><state>14</state></lhs><rhs><state>16</state></rhs></transition><transition><lhs><name>Cons</name><height>2</height><state>0</state><state>14</state></lhs><rhs><state>15</state></rhs></transition><transition><lhs><name>Cons</name><height>2</height><state>0</state><state>15</state></lhs><rhs><state>15</state></rhs></transition><transition><lhs><name>comp_f_g#1</name><height>2</height><state>4</state><state>5</state><state>15</state></lhs><rhs><state>16</state></rhs></transition><transition><lhs><name>Cons</name><height>2</height><state>0</state><state>16</state></lhs><rhs><state>14</state></rhs></transition><transition><lhs><name>Cons</name><height>2</height><state>0</state><state>16</state></lhs><rhs><state>16</state></rhs></transition><transition><lhs><name>Cons</name><height>2</height><state>0</state><state>14</state></lhs><rhs><state>17</state></rhs></transition><transition><lhs><name>Cons</name><height>2</height><state>0</state><state>15</state></lhs><rhs><state>17</state></rhs></transition><transition><lhs><name>Cons</name><height>2</height><state>0</state><state>17</state></lhs><rhs><state>14</state></rhs></transition><transition><lhs><name>Cons</name><height>2</height><state>0</state><state>17</state></lhs><rhs><state>16</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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