details

property	value
status	complete
benchmark	queue.raml.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n036.star.cs.uiowa.edu
space	raML

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	4.85812187195 seconds
cpu usage	13.998703416
max memory	6.40282624E8

stage attributes

key	value
certification-result	CERTIFIED
output-size	92744
starexec-result	YES
certification-time	0.0

output

/export/starexec/sandbox/solver/bin/starexec_run_certified /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES <?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" 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xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>startBreadth#2</name><arg><funapp><name>enqueue</name><arg><funapp><name>tuple#4</name><arg><var>@x</var></arg><arg><var>@x</var></arg><arg><var>@xs</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><funapp><name>empty</name><arg><funapp><name>#unit</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>startBreadth#1</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>startBreadth#2</name><arg><funapp><name>tuple#2</name><arg><var>@breadth@1</var></arg><arg><var>@breadth@2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>breadth</name><arg><var>@breadth@1</var></arg><arg><var>@breadth@2</var></arg></funapp></rhs></rule></rules></trs><strategy><innermost/></strategy></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><name>breadth</name></sharp><arg><var>@breadth@1</var></arg><arg><var>@breadth@2</var></arg></funapp></lhs><rhs><funapp><sharp><name>breadth#1</name></sharp><arg><funapp><name>dequeue</name><arg><var>@breadth@1</var></arg><arg><var>@breadth@2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>breadth</name></sharp><arg><var>@breadth@1</var></arg><arg><var>@breadth@2</var></arg></funapp></lhs><rhs><funapp><sharp><name>dequeue</name></sharp><arg><var>@breadth@1</var></arg><arg><var>@breadth@2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>breadth#1</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@queue'</var></arg><arg><var>@elem</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>breadth#2</name></sharp><arg><var>@elem</var></arg><arg><var>@queue'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>breadth#2</name></sharp><arg><funapp><name>::</name><arg><var>@z</var></arg><arg><var>@_@9</var></arg></funapp></arg><arg><var>@queue'</var></arg></funapp></lhs><rhs><funapp><sharp><name>breadth#3</name></sharp><arg><funapp><name>breadth#4</name><arg><var>@z</var></arg></funapp></arg><arg><var>@queue'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>breadth#2</name></sharp><arg><funapp><name>::</name><arg><var>@z</var></arg><arg><var>@_@9</var></arg></funapp></arg><arg><var>@queue'</var></arg></funapp></lhs><rhs><funapp><sharp><name>breadth#4</name></sharp><arg><var>@z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>breadth#3</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@x</var></arg><arg><var>@ys</var></arg></funapp></arg><arg><var>@queue'</var></arg></funapp></lhs><rhs><funapp><sharp><name>breadth#5</name></sharp><arg><funapp><name>enqueues</name><arg><var>@ys</var></arg><arg><var>@queue'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>breadth#3</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@x</var></arg><arg><var>@ys</var></arg></funapp></arg><arg><var>@queue'</var></arg></funapp></lhs><rhs><funapp><sharp><name>enqueues</name></sharp><arg><var>@ys</var></arg><arg><var>@queue'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>breadth#4</name></sharp><arg><funapp><name>tuple#4</name><arg><var>@children@3</var></arg><arg><var>@children@4</var></arg><arg><var>@children@5</var></arg><arg><var>@children@6</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>children</name></sharp><arg><var>@children@3</var></arg><arg><var>@children@4</var></arg><arg><var>@children@5</var></arg><arg><var>@children@6</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>breadth#5</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@breadth@7</var></arg><arg><var>@breadth@8</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>breadth</name></sharp><arg><var>@breadth@7</var></arg><arg><var>@breadth@8</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>children</name></sharp><arg><var>@a</var></arg><arg><var>@b</var></arg><arg><var>@l1</var></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><sharp><name>children#1</name></sharp><arg><var>@l1</var></arg><arg><var>@b</var></arg><arg><var>@l2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>children#1</name></sharp><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><var>@b</var></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><sharp><name>children#3</name></sharp><arg><var>@l2</var></arg><arg><var>@b</var></arg><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>children#1</name></sharp><arg><funapp><name>nil</name></funapp></arg><arg><var>@b</var></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><sharp><name>children#2</name></sharp><arg><var>@l2</var></arg><arg><var>@b</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>copyover</name></sharp><arg><var>@copyover@1</var></arg><arg><var>@copyover@2</var></arg></funapp></lhs><rhs><funapp><sharp><name>copyover#1</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@copyover@1</var></arg><arg><var>@copyover@2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>copyover#1</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@inq</var></arg><arg><var>@outq</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>copyover#2</name></sharp><arg><var>@inq</var></arg><arg><var>@outq</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>copyover#2</name></sharp><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><var>@outq</var></arg></funapp></lhs><rhs><funapp><sharp><name>copyover</name></sharp><arg><var>@xs</var></arg><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@outq</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dequeue</name></sharp><arg><var>@dequeue@1</var></arg><arg><var>@dequeue@2</var></arg></funapp></lhs><rhs><funapp><sharp><name>dequeue#1</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@dequeue@1</var></arg><arg><var>@dequeue@2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dequeue#1</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@inq</var></arg><arg><var>@outq</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>dequeue#2</name></sharp><arg><var>@outq</var></arg><arg><var>@inq</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dequeue#2</name></sharp><arg><funapp><name>nil</name></funapp></arg><arg><var>@inq</var></arg></funapp></lhs><rhs><funapp><sharp><name>dequeue#3</name></sharp><arg><var>@inq</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dequeue#3</name></sharp><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>dequeue#4</name></sharp><arg><funapp><name>copyover</name><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dequeue#3</name></sharp><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>copyover</name></sharp><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dequeue#4</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@dequeue@3</var></arg><arg><var>@dequeue@4</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>dequeue</name></sharp><arg><var>@dequeue@3</var></arg><arg><var>@dequeue@4</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>enqueue</name></sharp><arg><var>@x</var></arg><arg><var>@queue</var></arg></funapp></lhs><rhs><funapp><sharp><name>enqueue#1</name></sharp><arg><var>@queue</var></arg><arg><var>@x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>enqueues</name></sharp><arg><var>@l</var></arg><arg><var>@queue</var></arg></funapp></lhs><rhs><funapp><sharp><name>enqueues#1</name></sharp><arg><var>@l</var></arg><arg><var>@queue</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>enqueues#1</name></sharp><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><var>@queue</var></arg></funapp></lhs><rhs><funapp><sharp><name>enqueues</name></sharp><arg><var>@xs</var></arg><arg><funapp><name>enqueue</name><arg><var>@x</var></arg><arg><var>@queue</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>enqueues#1</name></sharp><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><var>@queue</var></arg></funapp></lhs><rhs><funapp><sharp><name>enqueue</name></sharp><arg><var>@x</var></arg><arg><var>@queue</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>startBreadth</name></sharp><arg><var>@xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>startBreadth#1</name></sharp><arg><var>@xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>startBreadth#1</name></sharp><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>startBreadth#2</name></sharp><arg><funapp><name>enqueue</name><arg><funapp><name>tuple#4</name><arg><var>@x</var></arg><arg><var>@x</var></arg><arg><var>@xs</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><funapp><name>empty</name><arg><funapp><name>#unit</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>startBreadth#1</name></sharp><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>enqueue</name></sharp><arg><funapp><name>tuple#4</name><arg><var>@x</var></arg><arg><var>@x</var></arg><arg><var>@xs</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><funapp><name>empty</name><arg><funapp><name>#unit</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>startBreadth#1</name></sharp><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>empty</name></sharp><arg><funapp><name>#unit</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>startBreadth#2</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@breadth@1</var></arg><arg><var>@breadth@2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>breadth</name></sharp><arg><var>@breadth@1</var></arg><arg><var>@breadth@2</var></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>startBreadth</name></sharp><arg><var>@xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>startBreadth#1</name></sharp><arg><var>@xs</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>startBreadth#1</name></sharp><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>startBreadth#2</name></sharp><arg><funapp><name>enqueue</name><arg><funapp><name>tuple#4</name><arg><var>@x</var></arg><arg><var>@x</var></arg><arg><var>@xs</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><funapp><name>empty</name><arg><funapp><name>#unit</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>startBreadth#2</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@breadth@1</var></arg><arg><var>@breadth@2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>breadth</name></sharp><arg><var>@breadth@1</var></arg><arg><var>@breadth@2</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>breadth#1</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@queue'</var></arg><arg><var>@elem</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>breadth#2</name></sharp><arg><var>@elem</var></arg><arg><var>@queue'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>breadth#2</name></sharp><arg><funapp><name>::</name><arg><var>@z</var></arg><arg><var>@_@9</var></arg></funapp></arg><arg><var>@queue'</var></arg></funapp></lhs><rhs><funapp><sharp><name>breadth#3</name></sharp><arg><funapp><name>breadth#4</name><arg><var>@z</var></arg></funapp></arg><arg><var>@queue'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>breadth#3</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@x</var></arg><arg><var>@ys</var></arg></funapp></arg><arg><var>@queue'</var></arg></funapp></lhs><rhs><funapp><sharp><name>breadth#5</name></sharp><arg><funapp><name>enqueues</name><arg><var>@ys</var></arg><arg><var>@queue'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>breadth#5</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@breadth@7</var></arg><arg><var>@breadth@8</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>breadth</name></sharp><arg><var>@breadth@7</var></arg><arg><var>@breadth@8</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>breadth</name></sharp><arg><var>@breadth@1</var></arg><arg><var>@breadth@2</var></arg></funapp></lhs><rhs><funapp><sharp><name>breadth#1</name></sharp><arg><funapp><name>dequeue</name><arg><var>@breadth@1</var></arg><arg><var>@breadth@2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>dequeue#1</name><arg><funapp><name>tuple#2</name><arg><var>@inq</var></arg><arg><var>@outq</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>dequeue#2</name><arg><var>@outq</var></arg><arg><var>@inq</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>dequeue#2</name><arg><funapp><name>nil</name></funapp></arg><arg><var>@inq</var></arg></funapp></lhs><rhs><funapp><name>dequeue#3</name><arg><var>@inq</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>dequeue#3</name><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>dequeue#4</name><arg><funapp><name>copyover</name><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>dequeue#4</name><arg><funapp><name>tuple#2</name><arg><var>@dequeue@3</var></arg><arg><var>@dequeue@4</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>dequeue</name><arg><var>@dequeue@3</var></arg><arg><var>@dequeue@4</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>dequeue</name><arg><var>@dequeue@1</var></arg><arg><var>@dequeue@2</var></arg></funapp></lhs><rhs><funapp><name>dequeue#1</name><arg><funapp><name>tuple#2</name><arg><var>@dequeue@1</var></arg><arg><var>@dequeue@2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>dequeue#2</name><arg><funapp><name>::</name><arg><var>@y</var></arg><arg><var>@ys</var></arg></funapp></arg><arg><var>@inq</var></arg></funapp></lhs><rhs><funapp><name>tuple#2</name><arg><funapp><name>tuple#2</name><arg><var>@inq</var></arg><arg><var>@ys</var></arg></funapp></arg><arg><funapp><name>::</name><arg><var>@y</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>dequeue#3</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>tuple#2</name><arg><funapp><name>tuple#2</name><arg><funapp><name>nil</name></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>copyover#1</name><arg><funapp><name>tuple#2</name><arg><var>@inq</var></arg><arg><var>@outq</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>copyover#2</name><arg><var>@inq</var></arg><arg><var>@outq</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>copyover#2</name><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><var>@outq</var></arg></funapp></lhs><rhs><funapp><name>copyover</name><arg><var>@xs</var></arg><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@outq</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>copyover</name><arg><var>@copyover@1</var></arg><arg><var>@copyover@2</var></arg></funapp></lhs><rhs><funapp><name>copyover#1</name><arg><funapp><name>tuple#2</name><arg><var>@copyover@1</var></arg><arg><var>@copyover@2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>copyover#2</name><arg><funapp><name>nil</name></funapp></arg><arg><var>@outq</var></arg></funapp></lhs><rhs><funapp><name>tuple#2</name><arg><funapp><name>nil</name></funapp></arg><arg><var>@outq</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>enqueues#1</name><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><var>@queue</var></arg></funapp></lhs><rhs><funapp><name>enqueues</name><arg><var>@xs</var></arg><arg><funapp><name>enqueue</name><arg><var>@x</var></arg><arg><var>@queue</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>enqueues</name><arg><var>@l</var></arg><arg><var>@queue</var></arg></funapp></lhs><rhs><funapp><name>enqueues#1</name><arg><var>@l</var></arg><arg><var>@queue</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>enqueue</name><arg><var>@x</var></arg><arg><var>@queue</var></arg></funapp></lhs><rhs><funapp><name>enqueue#1</name><arg><var>@queue</var></arg><arg><var>@x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>enqueues#1</name><arg><funapp><name>nil</name></funapp></arg><arg><var>@queue</var></arg></funapp></lhs><rhs><var>@queue</var></rhs></rule><rule><lhs><funapp><name>enqueue#1</name><arg><funapp><name>tuple#2</name><arg><var>@inq</var></arg><arg><var>@outq</var></arg></funapp></arg><arg><var>@x</var></arg></funapp></lhs><rhs><funapp><name>tuple#2</name><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@inq</var></arg></funapp></arg><arg><var>@outq</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>breadth#4</name><arg><funapp><name>tuple#4</name><arg><var>@children@3</var></arg><arg><var>@children@4</var></arg><arg><var>@children@5</var></arg><arg><var>@children@6</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>children</name><arg><var>@children@3</var></arg><arg><var>@children@4</var></arg><arg><var>@children@5</var></arg><arg><var>@children@6</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>children</name><arg><var>@a</var></arg><arg><var>@b</var></arg><arg><var>@l1</var></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><name>tuple#2</name><arg><funapp><name>tuple#2</name><arg><var>@a</var></arg><arg><var>@b</var></arg></funapp></arg><arg><funapp><name>children#1</name><arg><var>@l1</var></arg><arg><var>@b</var></arg><arg><var>@l2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>children#1</name><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><var>@b</var></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><name>children#3</name><arg><var>@l2</var></arg><arg><var>@b</var></arg><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>children#1</name><arg><funapp><name>nil</name></funapp></arg><arg><var>@b</var></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><name>children#2</name><arg><var>@l2</var></arg><arg><var>@b</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>children#2</name><arg><funapp><name>::</name><arg><var>@y</var></arg><arg><var>@ys</var></arg></funapp></arg><arg><var>@b</var></arg></funapp></lhs><rhs><funapp><name>::</name><arg><funapp><name>tuple#4</name><arg><var>@y</var></arg><arg><var>@b</var></arg><arg><funapp><name>nil</name></funapp></arg><arg><var>@ys</var></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>children#2</name><arg><funapp><name>nil</name></funapp></arg><arg><var>@b</var></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>children#3</name><arg><funapp><name>::</name><arg><var>@y</var></arg><arg><var>@ys</var></arg></funapp></arg><arg><var>@b</var></arg><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></lhs><rhs><funapp><name>::</name><arg><funapp><name>tuple#4</name><arg><var>@x</var></arg><arg><var>@b</var></arg><arg><funapp><name>nil</name></funapp></arg><arg><var>@xs</var></arg></funapp></arg><arg><funapp><name>::</name><arg><funapp><name>tuple#4</name><arg><var>@x</var></arg><arg><var>@y</var></arg><arg><var>@xs</var></arg><arg><var>@ys</var></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>children#3</name><arg><funapp><name>nil</name></funapp></arg><arg><var>@b</var></arg><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule></rules></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>breadth#4</name><arg><funapp><name>tuple#4</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp></arg></funapp><funapp><name>children</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp><funapp><name>children#1</name><arg><funapp><name>::</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp><funapp><name>children#1</name><arg><funapp><name>nil</name></funapp></arg><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp><funapp><name>children#2</name><arg><funapp><name>::</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp><funapp><name>children#2</name><arg><funapp><name>nil</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>children#3</name><arg><funapp><name>::</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg><arg><var>x3</var></arg><arg><var>x4</var></arg></funapp><funapp><name>children#3</name><arg><funapp><name>nil</name></funapp></arg><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp><funapp><name>copyover</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp><funapp><name>copyover#1</name><arg><funapp><name>tuple#2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>copyover#2</name><arg><funapp><name>::</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp><funapp><name>copyover#2</name><arg><funapp><name>nil</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>dequeue</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp><funapp><name>dequeue#1</name><arg><funapp><name>tuple#2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>dequeue#2</name><arg><funapp><name>::</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp><funapp><name>dequeue#2</name><arg><funapp><name>nil</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>dequeue#3</name><arg><funapp><name>::</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>dequeue#3</name><arg><funapp><name>nil</name></funapp></arg></funapp><funapp><name>dequeue#4</name><arg><funapp><name>tuple#2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>enqueue</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp><funapp><name>enqueue#1</name><arg><funapp><name>tuple#2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp><funapp><name>enqueues</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp><funapp><name>enqueues#1</name><arg><funapp><name>::</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp><funapp><name>enqueues#1</name><arg><funapp><name>nil</name></funapp></arg><arg><var>x0</var></arg></funapp></innermostLhss><dpProof><redPairProc><orderingConstraintProof><redPair><interpretation><type><matrixInterpretation><domain><integers/></domain><dimension>2</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><sharp><name>breadth#1</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tuple#2</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>breadth#2</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>::</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>breadth#3</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>breadth#4</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>breadth#5</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>enqueues</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>breadth</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>dequeue</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tuple#4</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>children</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>enqueues#1</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>enqueue</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>dequeue#2</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>nil</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>dequeue#3</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>dequeue#4</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>copyover</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>dequeue#1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>copyover#2</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>copyover#1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>enqueue#1</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>children#1</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>children#3</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>children#2</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>breadth#1</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@queue'</var></arg><arg><var>@elem</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>breadth#2</name></sharp><arg><var>@elem</var></arg><arg><var>@queue'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>breadth#3</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@x</var></arg><arg><var>@ys</var></arg></funapp></arg><arg><var>@queue'</var></arg></funapp></lhs><rhs><funapp><sharp><name>breadth#5</name></sharp><arg><funapp><name>enqueues</name><arg><var>@ys</var></arg><arg><var>@queue'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>breadth#5</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@breadth@7</var></arg><arg><var>@breadth@8</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>breadth</name></sharp><arg><var>@breadth@7</var></arg><arg><var>@breadth@8</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>breadth</name></sharp><arg><var>@breadth@1</var></arg><arg><var>@breadth@2</var></arg></funapp></lhs><rhs><funapp><sharp><name>breadth#1</name></sharp><arg><funapp><name>dequeue</name><arg><var>@breadth@1</var></arg><arg><var>@breadth@2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>breadth#3</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@x</var></arg><arg><var>@ys</var></arg></funapp></arg><arg><var>@queue'</var></arg></funapp></lhs><rhs><funapp><sharp><name>breadth#5</name></sharp><arg><funapp><name>enqueues</name><arg><var>@ys</var></arg><arg><var>@queue'</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>breadth#5</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@breadth@7</var></arg><arg><var>@breadth@8</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>breadth</name></sharp><arg><var>@breadth@7</var></arg><arg><var>@breadth@8</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>breadth</name></sharp><arg><var>@breadth@1</var></arg><arg><var>@breadth@2</var></arg></funapp></lhs><rhs><funapp><sharp><name>breadth#1</name></sharp><arg><funapp><name>dequeue</name><arg><var>@breadth@1</var></arg><arg><var>@breadth@2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>breadth#1</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@queue'</var></arg><arg><var>@elem</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>breadth#2</name></sharp><arg><var>@elem</var></arg><arg><var>@queue'</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></redPairProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>breadth#2</name></sharp><arg><funapp><name>::</name><arg><var>@z</var></arg><arg><var>@_@9</var></arg></funapp></arg><arg><var>@queue'</var></arg></funapp></lhs><rhs><funapp><sharp><name>breadth#4</name></sharp><arg><var>@z</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>breadth</name></sharp><arg><var>@breadth@1</var></arg><arg><var>@breadth@2</var></arg></funapp></lhs><rhs><funapp><sharp><name>dequeue</name></sharp><arg><var>@breadth@1</var></arg><arg><var>@breadth@2</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>breadth#3</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@x</var></arg><arg><var>@ys</var></arg></funapp></arg><arg><var>@queue'</var></arg></funapp></lhs><rhs><funapp><sharp><name>enqueues</name></sharp><arg><var>@ys</var></arg><arg><var>@queue'</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>breadth#4</name></sharp><arg><funapp><name>tuple#4</name><arg><var>@children@3</var></arg><arg><var>@children@4</var></arg><arg><var>@children@5</var></arg><arg><var>@children@6</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>children</name></sharp><arg><var>@children@3</var></arg><arg><var>@children@4</var></arg><arg><var>@children@5</var></arg><arg><var>@children@6</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>dequeue#3</name></sharp><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>dequeue#4</name></sharp><arg><funapp><name>copyover</name><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dequeue#4</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@dequeue@3</var></arg><arg><var>@dequeue@4</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>dequeue</name></sharp><arg><var>@dequeue@3</var></arg><arg><var>@dequeue@4</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dequeue</name></sharp><arg><var>@dequeue@1</var></arg><arg><var>@dequeue@2</var></arg></funapp></lhs><rhs><funapp><sharp><name>dequeue#1</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@dequeue@1</var></arg><arg><var>@dequeue@2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dequeue#1</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@inq</var></arg><arg><var>@outq</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>dequeue#2</name></sharp><arg><var>@outq</var></arg><arg><var>@inq</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dequeue#2</name></sharp><arg><funapp><name>nil</name></funapp></arg><arg><var>@inq</var></arg></funapp></lhs><rhs><funapp><sharp><name>dequeue#3</name></sharp><arg><var>@inq</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>copyover#1</name><arg><funapp><name>tuple#2</name><arg><var>@inq</var></arg><arg><var>@outq</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>copyover#2</name><arg><var>@inq</var></arg><arg><var>@outq</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>copyover#2</name><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><var>@outq</var></arg></funapp></lhs><rhs><funapp><name>copyover</name><arg><var>@xs</var></arg><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@outq</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>copyover</name><arg><var>@copyover@1</var></arg><arg><var>@copyover@2</var></arg></funapp></lhs><rhs><funapp><name>copyover#1</name><arg><funapp><name>tuple#2</name><arg><var>@copyover@1</var></arg><arg><var>@copyover@2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>copyover#2</name><arg><funapp><name>nil</name></funapp></arg><arg><var>@outq</var></arg></funapp></lhs><rhs><funapp><name>tuple#2</name><arg><funapp><name>nil</name></funapp></arg><arg><var>@outq</var></arg></funapp></rhs></rule></rules></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>copyover</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp><funapp><name>copyover#1</name><arg><funapp><name>tuple#2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>copyover#2</name><arg><funapp><name>::</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp><funapp><name>copyover#2</name><arg><funapp><name>nil</name></funapp></arg><arg><var>x0</var></arg></funapp></innermostLhss><dpProof><monoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>copyover#1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tuple#2</name><arity>2</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></sum></polynomial></interpret><interpret><name>copyover#2</name><arity>2</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></sum></polynomial></interpret><interpret><name>::</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><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></sum></polynomial></interpret><interpret><name>copyover</name><arity>2</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></sum></polynomial></interpret><interpret><name>nil</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>dequeue#3</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>dequeue#4</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>dequeue</name></sharp><arity>2</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></sum></polynomial></interpret><interpret><sharp><name>dequeue#1</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>dequeue#2</name></sharp><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></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>dequeue#3</name></sharp><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>dequeue#4</name></sharp><arg><funapp><name>copyover</name><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dequeue#4</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@dequeue@3</var></arg><arg><var>@dequeue@4</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>dequeue</name></sharp><arg><var>@dequeue@3</var></arg><arg><var>@dequeue@4</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dequeue</name></sharp><arg><var>@dequeue@1</var></arg><arg><var>@dequeue@2</var></arg></funapp></lhs><rhs><funapp><sharp><name>dequeue#1</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@dequeue@1</var></arg><arg><var>@dequeue@2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dequeue#1</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@inq</var></arg><arg><var>@outq</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>dequeue#2</name></sharp><arg><var>@outq</var></arg><arg><var>@inq</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dequeue#2</name></sharp><arg><funapp><name>nil</name></funapp></arg><arg><var>@inq</var></arg></funapp></lhs><rhs><funapp><sharp><name>dequeue#3</name></sharp><arg><var>@inq</var></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>copyover#1</name><arg><funapp><name>tuple#2</name><arg><var>@inq</var></arg><arg><var>@outq</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>copyover#2</name><arg><var>@inq</var></arg><arg><var>@outq</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>copyover</name><arg><var>@copyover@1</var></arg><arg><var>@copyover@2</var></arg></funapp></lhs><rhs><funapp><name>copyover#1</name><arg><funapp><name>tuple#2</name><arg><var>@copyover@1</var></arg><arg><var>@copyover@2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>copyover#2</name><arg><funapp><name>nil</name></funapp></arg><arg><var>@outq</var></arg></funapp></lhs><rhs><funapp><name>tuple#2</name><arg><funapp><name>nil</name></funapp></arg><arg><var>@outq</var></arg></funapp></rhs></rule></rules></trs><dpProof><redPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>dequeue#4</name></sharp><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>copyover</name><arity>2</arity><polynomial><coefficient><integer>1</integer></coefficient></polynomial></interpret><interpret><name>copyover#1</name><arity>1</arity><polynomial><coefficient><integer>1</integer></coefficient></polynomial></interpret><interpret><name>tuple#2</name><arity>2</arity><polynomial><variable>1</variable></polynomial></interpret><interpret><name>copyover#2</name><arity>2</arity><polynomial><coefficient><integer>1</integer></coefficient></polynomial></interpret><interpret><name>nil</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><sharp><name>dequeue#3</name></sharp><arity>1</arity><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></interpret><interpret><name>::</name><arity>2</arity><polynomial><coefficient><integer>2</integer></coefficient></polynomial></interpret><interpret><sharp><name>dequeue</name></sharp><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>dequeue#1</name></sharp><arity>1</arity><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></interpret><interpret><sharp><name>dequeue#2</name></sharp><arity>2</arity><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>dequeue#4</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@dequeue@3</var></arg><arg><var>@dequeue@4</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>dequeue</name></sharp><arg><var>@dequeue@3</var></arg><arg><var>@dequeue@4</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dequeue#1</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@inq</var></arg><arg><var>@outq</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>dequeue#2</name></sharp><arg><var>@outq</var></arg><arg><var>@inq</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dequeue#2</name></sharp><arg><funapp><name>nil</name></funapp></arg><arg><var>@inq</var></arg></funapp></lhs><rhs><funapp><sharp><name>dequeue#3</name></sharp><arg><var>@inq</var></arg></funapp></rhs></rule></rules></dps><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>dequeue#1</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@inq</var></arg><arg><var>@outq</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>dequeue#2</name></sharp><arg><var>@outq</var></arg><arg><var>@inq</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>dequeue#4</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@dequeue@3</var></arg><arg><var>@dequeue@4</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>dequeue</name></sharp><arg><var>@dequeue@3</var></arg><arg><var>@dequeue@4</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>dequeue#2</name></sharp><arg><funapp><name>nil</name></funapp></arg><arg><var>@inq</var></arg></funapp></lhs><rhs><funapp><sharp><name>dequeue#3</name></sharp><arg><var>@inq</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></redPairProc></dpProof></monoRedPairProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>enqueues#1</name></sharp><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><var>@queue</var></arg></funapp></lhs><rhs><funapp><sharp><name>enqueues</name></sharp><arg><var>@xs</var></arg><arg><funapp><name>enqueue</name><arg><var>@x</var></arg><arg><var>@queue</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>enqueues</name></sharp><arg><var>@l</var></arg><arg><var>@queue</var></arg></funapp></lhs><rhs><funapp><sharp><name>enqueues#1</name></sharp><arg><var>@l</var></arg><arg><var>@queue</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>enqueue</name><arg><var>@x</var></arg><arg><var>@queue</var></arg></funapp></lhs><rhs><funapp><name>enqueue#1</name><arg><var>@queue</var></arg><arg><var>@x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>enqueue#1</name><arg><funapp><name>tuple#2</name><arg><var>@inq</var></arg><arg><var>@outq</var></arg></funapp></arg><arg><var>@x</var></arg></funapp></lhs><rhs><funapp><name>tuple#2</name><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@inq</var></arg></funapp></arg><arg><var>@outq</var></arg></funapp></rhs></rule></rules></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>enqueue</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp><funapp><name>enqueue#1</name><arg><funapp><name>tuple#2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></innermostLhss><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>enqueues</name></sharp><arg><var>@l</var></arg><arg><var>@queue</var></arg></funapp></lhs><rhs><funapp><sharp><name>enqueues#1</name></sharp><arg><var>@l</var></arg><arg><var>@queue</var></arg></funapp></rhs></rule><edge><position>1</position><strict>false</strict><position>1</position></edge><edge><position>2</position><strict>false</strict><position>2</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>enqueues#1</name></sharp><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><var>@queue</var></arg></funapp></lhs><rhs><funapp><sharp><name>enqueues</name></sharp><arg><var>@xs</var></arg><arg><funapp><name>enqueue</name><arg><var>@x</var></arg><arg><var>@queue</var></arg></funapp></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>children</name></sharp><arg><var>@a</var></arg><arg><var>@b</var></arg><arg><var>@l1</var></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><sharp><name>children#1</name></sharp><arg><var>@l1</var></arg><arg><var>@b</var></arg><arg><var>@l2</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>dequeue#3</name></sharp><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>copyover</name></sharp><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>enqueues#1</name></sharp><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><var>@queue</var></arg></funapp></lhs><rhs><funapp><sharp><name>enqueue</name></sharp><arg><var>@x</var></arg><arg><var>@queue</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>startBreadth#1</name></sharp><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>enqueue</name></sharp><arg><funapp><name>tuple#4</name><arg><var>@x</var></arg><arg><var>@x</var></arg><arg><var>@xs</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><funapp><name>empty</name><arg><funapp><name>#unit</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>children#1</name></sharp><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><var>@b</var></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><sharp><name>children#3</name></sharp><arg><var>@l2</var></arg><arg><var>@b</var></arg><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>children#1</name></sharp><arg><funapp><name>nil</name></funapp></arg><arg><var>@b</var></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><sharp><name>children#2</name></sharp><arg><var>@l2</var></arg><arg><var>@b</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>copyover#1</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@inq</var></arg><arg><var>@outq</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>copyover#2</name></sharp><arg><var>@inq</var></arg><arg><var>@outq</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>copyover#2</name></sharp><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><var>@outq</var></arg></funapp></lhs><rhs><funapp><sharp><name>copyover</name></sharp><arg><var>@xs</var></arg><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@outq</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>copyover</name></sharp><arg><var>@copyover@1</var></arg><arg><var>@copyover@2</var></arg></funapp></lhs><rhs><funapp><sharp><name>copyover#1</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@copyover@1</var></arg><arg><var>@copyover@2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss/><dpProof><monoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>copyover#1</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tuple#2</name><arity>2</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></sum></polynomial></interpret><interpret><sharp><name>copyover#2</name></sharp><arity>2</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></sum></polynomial></interpret><interpret><name>::</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><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></sum></polynomial></interpret><interpret><sharp><name>copyover</name></sharp><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><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></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>copyover#1</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@inq</var></arg><arg><var>@outq</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>copyover#2</name></sharp><arg><var>@inq</var></arg><arg><var>@outq</var></arg></funapp></rhs></rule></rules></dps><trs><rules/></trs><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>copyover#1</name></sharp><arg><funapp><name>tuple#2</name><arg><var>@inq</var></arg><arg><var>@outq</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>copyover#2</name></sharp><arg><var>@inq</var></arg><arg><var>@outq</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge><edge><position>1</position><strict>true</strict><position>2</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></monoRedPairProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>enqueue</name></sharp><arg><var>@x</var></arg><arg><var>@queue</var></arg></funapp></lhs><rhs><funapp><sharp><name>enqueue#1</name></sharp><arg><var>@queue</var></arg><arg><var>@x</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>startBreadth#1</name></sharp><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>empty</name></sharp><arg><funapp><name>#unit</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></dpTrans></trsTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (18 real / 0 unknown / 0 assumptions / 18 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> popout

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all output return to TRS Inner certi 67861