details

property	value
status	complete
benchmark	addList.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n082.star.cs.uiowa.edu
space	Secret_06_TRS

run statistics

property	value
solver	ttt2-1.17+nonreach
configuration	ttt2-1.17+nonreach-cert
runtime (wallclock)	9.56481599808 seconds
cpu usage	35.516686869
max memory	1.01902336E9

stage attributes

key	value
certification-result	CERTIFIED
output-size	46311
starexec-result	YES
certification-time	0.0

output

/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach-cert /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES <?xml version="1.0"?> <?xml-stylesheet type="text/xsl" href="cpfHTML.xsl"?><certificationProblem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" 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rg><var>xs</var></arg></funapp></arg><arg><funapp><name>isEmpty</name><arg><var>ys</var></arg></funapp></arg><arg><funapp><name>isZero</name><arg><funapp><name>head</name><arg><var>xs</var></arg></funapp></arg></funapp></arg><arg><funapp><name>tail</name><arg><var>xs</var></arg></funapp></arg><arg><funapp><name>tail</name><arg><var>ys</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><funapp><name>head</name><arg><var>xs</var></arg></funapp></arg></funapp></arg><arg><funapp><name>tail</name><arg><var>xs</var></arg></funapp></arg></funapp></arg><arg><funapp><name>cons</name><arg><funapp><name>inc</name><arg><funapp><name>head</name><arg><var>ys</var></arg></funapp></arg></funapp></arg><arg><funapp><name>tail</name><arg><var>ys</var></arg></funapp></arg></funapp></arg><arg><var>zs</var></arg><arg><funapp><name>append</name><arg><var>zs</var></arg><arg><funapp><name>head</name><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>false</name></funapp></arg><arg><var>xs</var></arg><arg><var>ys</var></arg><arg><var>xs2</var></arg><arg><var>ys2</var></arg><arg><var>zs</var></arg><arg><var>zs2</var></arg></funapp></lhs><rhs><funapp><sharp><name>addLists</name></sharp><arg><var>xs2</var></arg><arg><var>ys2</var></arg><arg><var>zs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>true</name></funapp></arg><arg><var>xs</var></arg><arg><var>ys</var></arg><arg><var>xs2</var></arg><arg><var>ys2</var></arg><arg><var>zs</var></arg><arg><var>zs2</var></arg></funapp></lhs><rhs><funapp><sharp><name>addLists</name></sharp><arg><var>xs</var></arg><arg><var>ys</var></arg><arg><var>zs2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>addList</name></sharp><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><sharp><name>addLists</name></sharp><arg><var>xs</var></arg><arg><var>ys</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>addList</name></sharp><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></lhs><rhs><funapp><sharp><name>addLists</name></sharp><arg><var>xs</var></arg><arg><var>ys</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs><forwardArc>1</forwardArc><forwardArc>2</forwardArc><forwardArc>3</forwardArc><forwardArc>4</forwardArc><forwardArc>5</forwardArc><forwardArc>6</forwardArc><forwardArc>7</forwardArc><forwardArc>8</forwardArc><forwardArc>10</forwardArc><forwardArc>12</forwardArc><forwardArc>13</forwardArc></arcs></component><component><dps><rules><rule><lhs><funapp><sharp><name>addLists</name></sharp><arg><var>xs</var></arg><arg><var>ys</var></arg><arg><var>zs</var></arg></funapp></lhs><rhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>isEmpty</name><arg><var>xs</var></arg></funapp></arg><arg><funapp><name>isEmpty</name><arg><var>ys</var></arg></funapp></arg><arg><funapp><name>isZero</name><arg><funapp><name>head</name><arg><var>xs</var></arg></funapp></arg></funapp></arg><arg><funapp><name>tail</name><arg><var>xs</var></arg></funapp></arg><arg><funapp><name>tail</name><arg><var>ys</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><funapp><name>head</name><arg><var>xs</var></arg></funapp></arg></funapp></arg><arg><funapp><name>tail</name><arg><var>xs</var></arg></funapp></arg></funapp></arg><arg><funapp><name>cons</name><arg><funapp><name>inc</name><arg><funapp><name>head</name><arg><var>ys</var></arg></funapp></arg></funapp></arg><arg><funapp><name>tail</name><arg><var>ys</var></arg></funapp></arg></funapp></arg><arg><var>zs</var></arg><arg><funapp><name>append</name><arg><var>zs</var></arg><arg><funapp><name>head</name><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>false</name></funapp></arg><arg><var>xs</var></arg><arg><var>ys</var></arg><arg><var>xs2</var></arg><arg><var>ys2</var></arg><arg><var>zs</var></arg><arg><var>zs2</var></arg></funapp></lhs><rhs><funapp><sharp><name>addLists</name></sharp><arg><var>xs2</var></arg><arg><var>ys2</var></arg><arg><var>zs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>true</name></funapp></arg><arg><var>xs</var></arg><arg><var>ys</var></arg><arg><var>xs2</var></arg><arg><var>ys2</var></arg><arg><var>zs</var></arg><arg><var>zs2</var></arg></funapp></lhs><rhs><funapp><sharp><name>addLists</name></sharp><arg><var>xs</var></arg><arg><var>ys</var></arg><arg><var>zs2</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><arcs><forwardArc>1</forwardArc><forwardArc>2</forwardArc><forwardArc>3</forwardArc><forwardArc>4</forwardArc><forwardArc>5</forwardArc><forwardArc>6</forwardArc><forwardArc>7</forwardArc><forwardArc>9</forwardArc><forwardArc>11</forwardArc><forwardArc>12</forwardArc></arcs><dpProof><redPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><arctic><domain><integers/></domain></arctic></domain><degree>1</degree></polynomial></type><interpret><sharp><name>if</name></sharp><arity>9</arity><polynomial><sum><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>-1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>-1</integer></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>5</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>-2</integer></coefficient></polynomial><polynomial><variable>6</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>-1</integer></coefficient></polynomial><polynomial><variable>7</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>8</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>9</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>addLists</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>-2</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><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>inc</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>p</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>append</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><minusInfinity/></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>tail</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>-1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>head</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>-6</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>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isZero</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>-1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>7</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>true</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>5</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>false</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isEmpty</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>cons</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>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>addLists</name></sharp><arg><var>xs</var></arg><arg><var>ys</var></arg><arg><var>zs</var></arg></funapp></lhs><rhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>isEmpty</name><arg><var>xs</var></arg></funapp></arg><arg><funapp><name>isEmpty</name><arg><var>ys</var></arg></funapp></arg><arg><funapp><name>isZero</name><arg><funapp><name>head</name><arg><var>xs</var></arg></funapp></arg></funapp></arg><arg><funapp><name>tail</name><arg><var>xs</var></arg></funapp></arg><arg><funapp><name>tail</name><arg><var>ys</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><funapp><name>head</name><arg><var>xs</var></arg></funapp></arg></funapp></arg><arg><funapp><name>tail</name><arg><var>xs</var></arg></funapp></arg></funapp></arg><arg><funapp><name>cons</name><arg><funapp><name>inc</name><arg><funapp><name>head</name><arg><var>ys</var></arg></funapp></arg></funapp></arg><arg><funapp><name>tail</name><arg><var>ys</var></arg></funapp></arg></funapp></arg><arg><var>zs</var></arg><arg><funapp><name>append</name><arg><var>zs</var></arg><arg><funapp><name>head</name><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>false</name></funapp></arg><arg><var>xs</var></arg><arg><var>ys</var></arg><arg><var>xs2</var></arg><arg><var>ys2</var></arg><arg><var>zs</var></arg><arg><var>zs2</var></arg></funapp></lhs><rhs><funapp><sharp><name>addLists</name></sharp><arg><var>xs2</var></arg><arg><var>ys2</var></arg><arg><var>zs</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>head</name><arg><funapp><name>cons</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>inc</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>inc</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>inc</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>tail</name><arg><funapp><name>cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><var>xs</var></rhs></rule><rule><lhs><funapp><name>tail</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>p</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>p</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>p</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>p</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>isZero</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>isZero</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule></rules></usableRules><dpProof><redPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><arctic><domain><integers/></domain></arctic></domain><degree>1</degree></polynomial></type><interpret><sharp><name>if</name></sharp><arity>9</arity><polynomial><sum><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>5</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>6</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>7</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>8</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>9</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>addLists</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><coefficient><integer>4</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>inc</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>p</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>-1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>append</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>tail</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>-2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>head</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>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isZero</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>-2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</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><name>true</name><arity>0</arity><polynomial><sum><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>false</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isEmpty</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>cons</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><minusInfinity/></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>-8</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>false</name></funapp></arg><arg><var>xs</var></arg><arg><var>ys</var></arg><arg><var>xs2</var></arg><arg><var>ys2</var></arg><arg><var>zs</var></arg><arg><var>zs2</var></arg></funapp></lhs><rhs><funapp><sharp><name>addLists</name></sharp><arg><var>xs2</var></arg><arg><var>ys2</var></arg><arg><var>zs</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>head</name><arg><funapp><name>cons</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>p</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>p</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>p</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>p</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>isZero</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>isZero</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule></rules></usableRules><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>false</name></funapp></arg><arg><var>xs</var></arg><arg><var>ys</var></arg><arg><var>xs2</var></arg><arg><var>ys2</var></arg><arg><var>zs</var></arg><arg><var>zs2</var></arg></funapp></lhs><rhs><funapp><sharp><name>addLists</name></sharp><arg><var>xs2</var></arg><arg><var>ys2</var></arg><arg><var>zs</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs/></component></depGraphProc></dpProof></redPairUrProc></dpProof></redPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>addLists</name></sharp><arg><var>xs</var></arg><arg><var>ys</var></arg><arg><var>zs</var></arg></funapp></lhs><rhs><funapp><sharp><name>isEmpty</name></sharp><arg><var>xs</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs/></component><component><dps><rules><rule><lhs><funapp><sharp><name>addLists</name></sharp><arg><var>xs</var></arg><arg><var>ys</var></arg><arg><var>zs</var></arg></funapp></lhs><rhs><funapp><sharp><name>isEmpty</name></sharp><arg><var>ys</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs/></component><component><dps><rules><rule><lhs><funapp><sharp><name>addLists</name></sharp><arg><var>xs</var></arg><arg><var>ys</var></arg><arg><var>zs</var></arg></funapp></lhs><rhs><funapp><sharp><name>isZero</name></sharp><arg><funapp><name>head</name><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs/></component><component><dps><rules><rule><lhs><funapp><sharp><name>addLists</name></sharp><arg><var>xs</var></arg><arg><var>ys</var></arg><arg><var>zs</var></arg></funapp></lhs><rhs><funapp><sharp><name>head</name></sharp><arg><var>xs</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs/></component><component><dps><rules><rule><lhs><funapp><sharp><name>addLists</name></sharp><arg><var>xs</var></arg><arg><var>ys</var></arg><arg><var>zs</var></arg></funapp></lhs><rhs><funapp><sharp><name>tail</name></sharp><arg><var>xs</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs/></component><component><dps><rules><rule><lhs><funapp><sharp><name>addLists</name></sharp><arg><var>xs</var></arg><arg><var>ys</var></arg><arg><var>zs</var></arg></funapp></lhs><rhs><funapp><sharp><name>tail</name></sharp><arg><var>ys</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs/></component><component><dps><rules><rule><lhs><funapp><sharp><name>addLists</name></sharp><arg><var>xs</var></arg><arg><var>ys</var></arg><arg><var>zs</var></arg></funapp></lhs><rhs><funapp><sharp><name>p</name></sharp><arg><funapp><name>head</name><arg><var>xs</var></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>p</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>p</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><arcs/><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>p</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>p</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></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>addLists</name></sharp><arg><var>xs</var></arg><arg><var>ys</var></arg><arg><var>zs</var></arg></funapp></lhs><rhs><funapp><sharp><name>inc</name></sharp><arg><funapp><name>head</name><arg><var>ys</var></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>inc</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>inc</name></sharp><arg><var>x</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><arcs/><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>inc</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>inc</name></sharp><arg><var>x</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>addLists</name></sharp><arg><var>xs</var></arg><arg><var>ys</var></arg><arg><var>zs</var></arg></funapp></lhs><rhs><funapp><sharp><name>head</name></sharp><arg><var>ys</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs/></component><component><dps><rules><rule><lhs><funapp><sharp><name>addLists</name></sharp><arg><var>xs</var></arg><arg><var>ys</var></arg><arg><var>zs</var></arg></funapp></lhs><rhs><funapp><sharp><name>append</name></sharp><arg><var>zs</var></arg><arg><funapp><name>head</name><arg><var>ys</var></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>append</name></sharp><arg><funapp><name>cons</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><sharp><name>append</name></sharp><arg><var>ys</var></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><arcs/><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>append</name></sharp><arg><funapp><name>cons</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><sharp><name>append</name></sharp><arg><var>ys</var></arg><arg><var>x</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></depGraphProc></dpProof></dpTrans></trsTerminationProof></proof><origin><proofOrigin><tool><name>ttt2</name><version>ttt2 1.17 [hg: a28b6edf8379]</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 || fail)[5]*);((dp;(edg -gtcap -nl[1.0]?;(sccs | ((sc || sc -rec -defs || sc -mulex -defs) || sct || {ur?;( 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[5] | arctic -dp -ur -dim 2 -ib 2 -ob 2[8] | arctic -dp -ur -dim 3 -ib 1 -ob 1[8] | arctic -dp -ur -dim 4 -ib 1 -ob 1[8] | fail) || (arctic -bz -dp -ur -dim 1 -ib 4 -ob 3[5] | arctic -bz -dp -ur -dim 2 -ib 2 -ob 2[8] | arctic -bz -dp -ur -dim 3 -ib 1 -ob 1[8] | arctic -bz -dp -ur -dim 4 -ib 1 -ob 1[8] | fail) || fail) } restore) )*[29])) || (bounds -cert || fail;(bounds -rfc -qc))))! || (( unfold || fail)*[7])!)[42])! || ((((( (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 || fail)[5]*);((dp;(edg -gtcap -nl[1.0]?;(sccs | ((sc || sc -rec -defs || sc -mulex -defs) || sct || {ur?;( 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[5] | arctic -dp -ur -dim 2 -ib 2 -ob 2[8] | arctic -dp -ur -dim 3 -ib 1 -ob 1[8] | arctic -dp -ur -dim 4 -ib 1 -ob 1[8] | fail) || (arctic -bz -dp -ur -dim 1 -ib 4 -ob 3[5] | arctic -bz -dp -ur -dim 2 -ib 2 -ob 2[8] | arctic -bz -dp -ur -dim 3 -ib 1 -ob 1[8] | arctic -bz -dp -ur -dim 4 -ib 1 -ob 1[8] | fail) || fail) } restore) )*[29])) || (bounds -cert || fail;(bounds -rfc -qc))))! || (( unfold || fail)*[7])!)[42])! || (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 || fail)[5]*);((dp;(edg -gtcap -nl[1.0]?;(sccs | ((sc || sc -rec -defs || sc -mulex -defs) || sct || {ur?;( 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[5] | arctic -dp -ur -dim 2 -ib 2 -ob 2[8] | arctic -dp -ur -dim 3 -ib 1 -ob 1[8] | arctic -dp -ur -dim 4 -ib 1 -ob 1[8] | fail) || (arctic -bz -dp -ur -dim 1 -ib 4 -ob 3[5] | arctic -bz -dp -ur -dim 2 -ib 2 -ob 2[8] | arctic -bz -dp -ur -dim 3 -ib 1 -ob 1[8] | arctic -bz -dp -ur -dim 4 -ib 1 -ob 1[8] | fail) || fail) } restore) )*[29])) || (bounds -cert || fail;(bounds -rfc -qc))))![42])! ) 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 || fail)[5]*);((dp;(edg -gtcap -nl[1.0]?;(sccs | ((sc || sc -rec -defs || sc -mulex -defs) || sct || {ur?;( 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[5] | arctic -dp -ur -dim 2 -ib 2 -ob 2[8] | arctic -dp -ur -dim 3 -ib 1 -ob 1[8] | arctic -dp -ur -dim 4 -ib 1 -ob 1[8] | fail) || (arctic -bz -dp -ur -dim 1 -ib 4 -ob 3[5] | arctic -bz -dp -ur -dim 2 -ib 2 -ob 2[8] | arctic -bz -dp -ur -dim 3 -ib 1 -ob 1[8] | arctic -bz -dp -ur -dim 4 -ib 1 -ob 1[8] | fail) || fail) } restore) )*[29])) || (bounds -cert || fail;(bounds -rfc -qc))))! || (( unfold || fail)*[7])!)[42])))</strategy></tool></proofOrigin></origin></certificationProblem> popout

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