details

property	value
status	complete
benchmark	10.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n146.star.cs.uiowa.edu
space	Various_04

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2_cert
runtime (wallclock)	6.34397 seconds
cpu usage	20.9807
user time	19.5933
system time	1.38737
max virtual memory	2493664.0
max residence set size	134232.0

stage attributes

key	value
certification-result	CERTIFIED
starexec-result	CERTIFIED YES
certification-time	0.23
bare-result	YES

output

<?xml version="1.0"?> <?xml-stylesheet type="text/xsl" href="cpfHTML.xsl"?><certificationProblem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="cpf.xsd"><input><trsInput><trs><rules><rule><lhs><funapp><name>+</name><arg><funapp><name>0</name></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>y</var></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>++</name><arg><funapp><name>nil</name></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><var>ys</var></rhs></rule><rule><lhs><funapp><name>++</name><arg><funapp><name>:</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>:</name><arg><var>x</var></arg><arg><funapp><name>++</name><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>sum</name><arg><funapp><name>:</name><arg><var>x</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>:</name><arg><var>x</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>sum</name><arg><funapp><name>:</name><arg><var>x</var></arg><arg><funapp><name>:</name><arg><var>y</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>sum</name><arg><funapp><name>:</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>sum</name><arg><funapp><name>++</name><arg><var>xs</var></arg><arg><funapp><name>:</name><arg><var>x</var></arg><arg><funapp><name>:</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>sum</name><arg><funapp><name>++</name><arg><var>xs</var></arg><arg><funapp><name>sum</name><arg><funapp><name>:</name><arg><var>x</var></arg><arg><funapp><name>:</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>quot</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>quot</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>quot</name><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>length</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>length</name><arg><funapp><name>:</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>length</name><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>hd</name><arg><funapp><name>:</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>avg</name><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>quot</name><arg><funapp><name>hd</name><arg><funapp><name>sum</name><arg><var>xs</var></arg></funapp></arg></funapp></arg><arg><funapp><name>length</name><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><name>+</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>+</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>++</name></sharp><arg><funapp><name>:</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><sharp><name>++</name></sharp><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>:</name><arg><var>x</var></arg><arg><funapp><name>:</name><arg><var>y</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>+</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>:</name><arg><var>x</var></arg><arg><funapp><name>:</name><arg><var>y</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>:</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>++</name><arg><var>xs</var></arg><arg><funapp><name>:</name><arg><var>x</var></arg><arg><funapp><name>:</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>:</name><arg><var>x</var></arg><arg><funapp><name>:</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>++</name><arg><var>xs</var></arg><arg><funapp><name>:</name><arg><var>x</var></arg><arg><funapp><name>:</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>++</name></sharp><arg><var>xs</var></arg><arg><funapp><name>sum</name><arg><funapp><name>:</name><arg><var>x</var></arg><arg><funapp><name>:</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>++</name><arg><var>xs</var></arg><arg><funapp><name>:</name><arg><var>x</var></arg><arg><funapp><name>:</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>++</name><arg><var>xs</var></arg><arg><funapp><name>sum</name><arg><funapp><name>:</name><arg><var>x</var></arg><arg><funapp><name>:</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>-</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>-</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>quot</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>-</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>quot</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>quot</name></sharp><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>length</name></sharp><arg><funapp><name>:</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>length</name></sharp><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>avg</name></sharp><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>length</name></sharp><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>avg</name></sharp><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>sum</name></sharp><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>avg</name></sharp><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>hd</name></sharp><arg><funapp><name>sum</name><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>avg</name></sharp><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>quot</name></sharp><arg><funapp><name>hd</name><arg><funapp><name>sum</name><arg><var>xs</var></arg></funapp></arg></funapp></arg><arg><funapp><name>length</name><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>avg</name></sharp><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>sum</name></sharp><arg><var>xs</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs><forwardArc>1</forwardArc><forwardArc>2</forwardArc><forwardArc>3</forwardArc><forwardArc>4</forwardArc><forwardArc>6</forwardArc></arcs></component><component><dps><rules><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>++</name><arg><var>xs</var></arg><arg><funapp><name>:</name><arg><var>x</var></arg><arg><funapp><name>:</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>++</name><arg><var>xs</var></arg><arg><funapp><name>sum</name><arg><funapp><name>:</name><arg><var>x</var></arg><arg><funapp><name>:</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><arcs><forwardArc>1</forwardArc><forwardArc>2</forwardArc><forwardArc>3</forwardArc><forwardArc>5</forwardArc></arcs><dpProof><redPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>++</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>6</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>+</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>nil</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>:</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>sum</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>6</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>sum</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules/></dps><usableRules><rules><rule><lhs><funapp><name>sum</name><arg><funapp><name>:</name><arg><var>x</var></arg><arg><funapp><name>:</name><arg><var>y</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>sum</name><arg><funapp><name>:</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>sum</name><arg><funapp><name>:</name><arg><var>x</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>:</name><arg><var>x</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>++</name><arg><funapp><name>nil</name></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><var>ys</var></rhs></rule><rule><lhs><funapp><name>++</name><arg><funapp><name>:</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><name>:</name><arg><var>x</var></arg><arg><funapp><name>++</name><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><pIsEmpty/></dpProof></redPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>++</name><arg><var>xs</var></arg><arg><funapp><name>:</name><arg><var>x</var></arg><arg><funapp><name>:</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>:</name><arg><var>x</var></arg><arg><funapp><name>:</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs><forwardArc>1</forwardArc><forwardArc>2</forwardArc></arcs></component><component><dps><rules><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>:</name><arg><var>x</var></arg><arg><funapp><name>:</name><arg><var>y</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>:</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><arcs><forwardArc>1</forwardArc></arcs><dpProof><subtermProc><multisetArgumentFilter><multisetArgumentFilterEntry><sharp><name>sum</name></sharp><arity>1</arity><status><position>1</position></status></multisetArgumentFilterEntry><multisetArgumentFilterEntry><name>-</name><arity>2</arity><status><position>1</position></status></multisetArgumentFilterEntry><multisetArgumentFilterEntry><name>:</name><arity>2</arity><status><position>1</position><position>2</position><position>2</position></status></multisetArgumentFilterEntry><multisetArgumentFilterEntry><name>s</name><arity>1</arity><status><position>1</position></status></multisetArgumentFilterEntry><multisetArgumentFilterEntry><name>+</name><arity>2</arity><status><position>2</position><position>2</position></status></multisetArgumentFilterEntry></multisetArgumentFilter><dps><rules><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>:</name><arg><var>x</var></arg><arg><funapp><name>:</name><arg><var>y</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>:</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><dpProof><pIsEmpty/></dpProof></subtermProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>:</name><arg><var>x</var></arg><arg><funapp><name>:</name><arg><var>y</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>+</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs><forwardArc>1</forwardArc></arcs></component><component><dps><rules><rule><lhs><funapp><sharp><name>+</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>+</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><arcs/><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>+</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>+</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><edge><position>2</position><strict>false</strict><position>2</position></edge><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>++</name><arg><var>xs</var></arg><arg><funapp><name>:</name><arg><var>x</var></arg><arg><funapp><name>:</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>++</name></sharp><arg><var>xs</var></arg><arg><funapp><name>sum</name><arg><funapp><name>:</name><arg><var>x</var></arg><arg><funapp><name>:</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs><forwardArc>1</forwardArc></arcs></component><component><dps><rules><rule><lhs><funapp><sharp><name>++</name></sharp><arg><funapp><name>:</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><sharp><name>++</name></sharp><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><arcs/><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>++</name></sharp><arg><funapp><name>:</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><sharp><name>++</name></sharp><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></rhs></rule><edge><position>2</position><strict>false</strict><position>2</position></edge><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>avg</name></sharp><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>quot</name></sharp><arg><funapp><name>hd</name><arg><funapp><name>sum</name><arg><var>xs</var></arg></funapp></arg></funapp></arg><arg><funapp><name>length</name><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs><forwardArc>1</forwardArc><forwardArc>2</forwardArc></arcs></component><component><dps><rules><rule><lhs><funapp><sharp><name>quot</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>quot</name></sharp><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><arcs><forwardArc>1</forwardArc></arcs><dpProof><subtermProc><multisetArgumentFilter><multisetArgumentFilterEntry><sharp><name>quot</name></sharp><arity>2</arity><status><position>1</position></status></multisetArgumentFilterEntry><multisetArgumentFilterEntry><name>-</name><arity>2</arity><status><position>1</position></status></multisetArgumentFilterEntry></multisetArgumentFilter><dps><rules><rule><lhs><funapp><sharp><name>quot</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>quot</name></sharp><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><dpProof><pIsEmpty/></dpProof></subtermProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>quot</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>-</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs><forwardArc>1</forwardArc></arcs></component><component><dps><rules><rule><lhs><funapp><sharp><name>-</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>-</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><arcs/><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>-</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>-</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><edge><position>2</position><strict>true</strict><position>2</position></edge><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>avg</name></sharp><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>length</name></sharp><arg><var>xs</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs><forwardArc>1</forwardArc></arcs></component><component><dps><rules><rule><lhs><funapp><sharp><name>length</name></sharp><arg><funapp><name>:</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>length</name></sharp><arg><var>xs</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><arcs/><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>length</name></sharp><arg><funapp><name>:</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>length</name></sharp><arg><var>xs</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>avg</name></sharp><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>hd</name></sharp><arg><funapp><name>sum</name><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs/></component></depGraphProc></dpProof></dpTrans></trsTerminationProof></proof><origin><proofOrigin><tool><name>ttt2</name><version>ttt2 1.20 [hg: unknown]</version><strategy>((if standard then var else fail) | con | (if srs then ((sleep -t 25?;rlab;(((( (if srs then arctic -dim 1 -ib 4 -ob 5 else fail) || (if srs then arctic -dim 2 -ib 2 -ob 3 else fail) || (if srs then arctic -dim 3 -ib 1 -ob 2 else fail) || (if srs then arctic -dim 3 -ib 2 -ob 2 else fail) || matrix -dim 1 -ib 5 -ob 8 || matrix -dim 2 -ib 3 -ob 4 || matrix -dim 3 -ib 2 -ob 3 || matrix -dim 3 -ib 1 -ob 2 || matrix -dim 4 -ib 1 -ob 2 || matrix -dim 5 -ib 1 -ob 1 || kbo -ib 3 -ob 4 || wpo -msum -ib 3 -ob 4 -cpf || fail)[5]*);((dp;(edg -gtcap -nl[1.0]?;(sccs | ((sc || sc -rec -defs || sc -mulex -defs) || sct || {ur?;( (wpo -cpf -dp -ur -sum -ib 3 -ob 3 [3] | wpo -cpf -dp -ur -pol -ib 3 -ob 3 [3] | wpo -cpf -dp -ur -max -ib 3 -ob 3 [3] | wpo -cpf -dp -ur -msum -ib 3 -ob 3 [4] | wpo -cpf -dp -ur -mat -dim 2 -ib 3 -ob 3 [5] | wpo -cpf -dp -ur -mat -dim 3 -ib 3 -ob 3 [5] | wpo -cpf -dp -ur -ib 3 -ob 3 [9] | fail ) || matrix -dp -ur -dim 1 -ib 3 -ob 5 || matrix -dp -ur -dim 1 -ib 3 -ob 8 -rat 2 -db 1 || matrix -dp -ur -dim 1 -ib 4 -ob 10 -rat 4 -db 1 || matrix -dp -ur -dim 2 -ib 2 -ob 3 || matrix -dp -ur -dim 2 -ib 3 -ob 4 -rat 2 -db 0 || matrix -dp -ur -dim 3 -ib 1 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 -rat 2 -db 0 || matrix -dp -ur -dim 4 -ib 1 -ob 2 || lpo -ur -af || (arctic -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || (arctic -bz -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -bz -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -bz -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -bz -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || fail) } restore) )*[29])) || (bounds -cert || fail;(bounds -rfc -qc))))! || (( unfold || fail)*[7])!)[299])! || ((((( (if srs then arctic -dim 1 -ib 4 -ob 5 else fail) || (if srs then arctic -dim 2 -ib 2 -ob 3 else fail) || (if srs then arctic -dim 3 -ib 1 -ob 2 else fail) || (if srs then arctic -dim 3 -ib 2 -ob 2 else fail) || matrix -dim 1 -ib 5 -ob 8 || matrix -dim 2 -ib 3 -ob 4 || matrix -dim 3 -ib 2 -ob 3 || matrix -dim 3 -ib 1 -ob 2 || matrix -dim 4 -ib 1 -ob 2 || matrix -dim 5 -ib 1 -ob 1 || kbo -ib 3 -ob 4 || wpo -msum -ib 3 -ob 4 -cpf || fail)[5]*);((dp;(edg -gtcap -nl[1.0]?;(sccs | ((sc || sc -rec -defs || sc -mulex -defs) || sct || {ur?;( (wpo -cpf -dp -ur -sum -ib 3 -ob 3 [3] | wpo -cpf -dp -ur -pol -ib 3 -ob 3 [3] | wpo -cpf -dp -ur -max -ib 3 -ob 3 [3] | wpo -cpf -dp -ur -msum -ib 3 -ob 3 [4] | wpo -cpf -dp -ur -mat -dim 2 -ib 3 -ob 3 [5] | wpo -cpf -dp -ur -mat -dim 3 -ib 3 -ob 3 [5] | wpo -cpf -dp -ur -ib 3 -ob 3 [9] | fail ) || matrix -dp -ur -dim 1 -ib 3 -ob 5 || matrix -dp -ur -dim 1 -ib 3 -ob 8 -rat 2 -db 1 || matrix -dp -ur -dim 1 -ib 4 -ob 10 -rat 4 -db 1 || matrix -dp -ur -dim 2 -ib 2 -ob 3 || matrix -dp -ur -dim 2 -ib 3 -ob 4 -rat 2 -db 0 || matrix -dp -ur -dim 3 -ib 1 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 -rat 2 -db 0 || matrix -dp -ur -dim 4 -ib 1 -ob 2 || lpo -ur -af || (arctic -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || (arctic -bz -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -bz -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -bz -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -bz -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || fail) } restore) )*[29])) || (bounds -cert || fail;(bounds -rfc -qc))))! || (( unfold || fail)*[7])!)[299])! || (rev?;((( (if srs then arctic -dim 1 -ib 4 -ob 5 else fail) || (if srs then arctic -dim 2 -ib 2 -ob 3 else fail) || (if srs then arctic -dim 3 -ib 1 -ob 2 else fail) || (if srs then arctic -dim 3 -ib 2 -ob 2 else fail) || matrix -dim 1 -ib 5 -ob 8 || matrix -dim 2 -ib 3 -ob 4 || matrix -dim 3 -ib 2 -ob 3 || matrix -dim 3 -ib 1 -ob 2 || matrix -dim 4 -ib 1 -ob 2 || matrix -dim 5 -ib 1 -ob 1 || kbo -ib 3 -ob 4 || wpo -msum -ib 3 -ob 4 -cpf || fail)[5]*);((dp;(edg -gtcap -nl[1.0]?;(sccs | ((sc || sc -rec -defs || sc -mulex -defs) || sct || {ur?;( (wpo -cpf -dp -ur -sum -ib 3 -ob 3 [3] | wpo -cpf -dp -ur -pol -ib 3 -ob 3 [3] | wpo -cpf -dp -ur -max -ib 3 -ob 3 [3] | wpo -cpf -dp -ur -msum -ib 3 -ob 3 [4] | wpo -cpf -dp -ur -mat -dim 2 -ib 3 -ob 3 [5] | wpo -cpf -dp -ur -mat -dim 3 -ib 3 -ob 3 [5] | wpo -cpf -dp -ur -ib 3 -ob 3 [9] | fail ) || matrix -dp -ur -dim 1 -ib 3 -ob 5 || matrix -dp -ur -dim 1 -ib 3 -ob 8 -rat 2 -db 1 || matrix -dp -ur -dim 1 -ib 4 -ob 10 -rat 4 -db 1 || matrix -dp -ur -dim 2 -ib 2 -ob 3 || matrix -dp -ur -dim 2 -ib 3 -ob 4 -rat 2 -db 0 || matrix -dp -ur -dim 3 -ib 1 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 -rat 2 -db 0 || matrix -dp -ur -dim 4 -ib 1 -ob 2 || lpo -ur -af || (arctic -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || (arctic -bz -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -bz -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -bz -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -bz -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || fail) } restore) )*[29])) || (bounds -cert || fail;(bounds -rfc -qc))))![299])! ) else ((((( (if srs then arctic -dim 1 -ib 4 -ob 5 else fail) || (if srs then arctic -dim 2 -ib 2 -ob 3 else fail) || (if srs then arctic -dim 3 -ib 1 -ob 2 else fail) || (if srs then arctic -dim 3 -ib 2 -ob 2 else fail) || matrix -dim 1 -ib 5 -ob 8 || matrix -dim 2 -ib 3 -ob 4 || matrix -dim 3 -ib 2 -ob 3 || matrix -dim 3 -ib 1 -ob 2 || matrix -dim 4 -ib 1 -ob 2 || matrix -dim 5 -ib 1 -ob 1 || kbo -ib 3 -ob 4 || wpo -msum -ib 3 -ob 4 -cpf || fail)[5]*);((dp;(edg -gtcap -nl[1.0]?;(sccs | ((sc || sc -rec -defs || sc -mulex -defs) || sct || {ur?;( (wpo -cpf -dp -ur -sum -ib 3 -ob 3 [3] | wpo -cpf -dp -ur -pol -ib 3 -ob 3 [3] | wpo -cpf -dp -ur -max -ib 3 -ob 3 [3] | wpo -cpf -dp -ur -msum -ib 3 -ob 3 [4] | wpo -cpf -dp -ur -mat -dim 2 -ib 3 -ob 3 [5] | wpo -cpf -dp -ur -mat -dim 3 -ib 3 -ob 3 [5] | wpo -cpf -dp -ur -ib 3 -ob 3 [9] | fail ) || matrix -dp -ur -dim 1 -ib 3 -ob 5 || matrix -dp -ur -dim 1 -ib 3 -ob 8 -rat 2 -db 1 || matrix -dp -ur -dim 1 -ib 4 -ob 10 -rat 4 -db 1 || matrix -dp -ur -dim 2 -ib 2 -ob 3 || matrix -dp -ur -dim 2 -ib 3 -ob 4 -rat 2 -db 0 || matrix -dp -ur -dim 3 -ib 1 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 -rat 2 -db 0 || matrix -dp -ur -dim 4 -ib 1 -ob 2 || lpo -ur -af || (arctic -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || (arctic -bz -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -bz -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -bz -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -bz -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || fail) } restore) )*[29])) || (bounds -cert || fail;(bounds -rfc -qc))))! || (( unfold || fail)*[7])!)[299])))</strategy></tool></proofOrigin></origin></certificationProblem> popout

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