details

property	value
status	complete
benchmark	cime5.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n144.star.cs.uiowa.edu
space	Secret_05_TRS

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	5.1798 seconds
cpu usage	15.5952
user time	14.8444
system time	0.750792
max virtual memory	1.858256E7
max residence set size	1767440.0

stage attributes

key	value
certification-result	CERTIFIED
starexec-result	CERTIFIED YES
certification-time	0.87
bare-result	YES

output

<?xml version="1.0" encoding="UTF-8" standalone="no"?><?xml-stylesheet type="text/xsl" href="cpfHTML.xsl"?><certificationProblem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="cpf.xsd"><input><trsInput><trs><rules><rule><lhs><funapp><name>intersect'ii'in</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>X0</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>X1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>intersect'ii'out</name></funapp></rhs></rule><rule><lhs><funapp><name>intersect'ii'in</name><arg><var>Xs</var></arg><arg><funapp><name>cons</name><arg><var>X0</var></arg><arg><var>Ys</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>u'1'1</name><arg><funapp><name>intersect'ii'in</name><arg><var>Xs</var></arg><arg><var>Ys</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u'1'1</name><arg><funapp><name>intersect'ii'out</name></funapp></arg></funapp></lhs><rhs><funapp><name>intersect'ii'out</name></funapp></rhs></rule><rule><lhs><funapp><name>intersect'ii'in</name><arg><funapp><name>cons</name><arg><var>X0</var></arg><arg><var>Xs</var></arg></funapp></arg><arg><var>Ys</var></arg></funapp></lhs><rhs><funapp><name>u'2'1</name><arg><funapp><name>intersect'ii'in</name><arg><var>Xs</var></arg><arg><var>Ys</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u'2'1</name><arg><funapp><name>intersect'ii'out</name></funapp></arg></funapp></lhs><rhs><funapp><name>intersect'ii'out</name></funapp></rhs></rule><rule><lhs><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>if</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><name>u'3'1</name><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><funapp><name>x'2d</name><arg><var>B</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u'3'1</name><arg><funapp><name>reduce'ii'out</name></funapp></arg></funapp></lhs><rhs><funapp><name>reduce'ii'out</name></funapp></rhs></rule><rule><lhs><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>iff</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><name>u'4'1</name><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2a</name><arg><funapp><name>if</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><funapp><name>if</name><arg><var>B</var></arg><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u'4'1</name><arg><funapp><name>reduce'ii'out</name></funapp></arg></funapp></lhs><rhs><funapp><name>reduce'ii'out</name></funapp></rhs></rule><rule><lhs><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2a</name><arg><var>F1</var></arg><arg><var>F2</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><name>u'5'1</name><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>F1</var></arg><arg><funapp><name>cons</name><arg><var>F2</var></arg><arg><var>Fs</var></arg></funapp></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u'5'1</name><arg><funapp><name>reduce'ii'out</name></funapp></arg></funapp></lhs><rhs><funapp><name>reduce'ii'out</name></funapp></rhs></rule><rule><lhs><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><var>F1</var></arg><arg><var>F2</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><name>u'6'1</name><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>F1</var></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg><arg><var>F2</var></arg><arg><var>Fs</var></arg><arg><var>Gs</var></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>u'6'1</name><arg><funapp><name>reduce'ii'out</name></funapp></arg><arg><var>F2</var></arg><arg><var>Fs</var></arg><arg><var>Gs</var></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><name>u'6'2</name><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>F2</var></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u'6'2</name><arg><funapp><name>reduce'ii'out</name></funapp></arg></funapp></lhs><rhs><funapp><name>reduce'ii'out</name></funapp></rhs></rule><rule><lhs><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2d</name><arg><var>F1</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><name>u'7'1</name><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>F1</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u'7'1</name><arg><funapp><name>reduce'ii'out</name></funapp></arg></funapp></lhs><rhs><funapp><name>reduce'ii'out</name></funapp></rhs></rule><rule><lhs><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>if</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><name>u'8'1</name><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><funapp><name>x'2d</name><arg><var>B</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u'8'1</name><arg><funapp><name>reduce'ii'out</name></funapp></arg></funapp></lhs><rhs><funapp><name>reduce'ii'out</name></funapp></rhs></rule><rule><lhs><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>iff</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><name>u'9'1</name><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2a</name><arg><funapp><name>if</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><funapp><name>if</name><arg><var>B</var></arg><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u'9'1</name><arg><funapp><name>reduce'ii'out</name></funapp></arg></funapp></lhs><rhs><funapp><name>reduce'ii'out</name></funapp></rhs></rule><rule><lhs><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><var>V</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><funapp><name>sequent</name><arg><var>Left</var></arg><arg><var>Right</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>u'10'1</name><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><var>Gs</var></arg></funapp></arg><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><var>V</var></arg></funapp></arg><arg><var>Left</var></arg></funapp></arg><arg><var>Right</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u'10'1</name><arg><funapp><name>reduce'ii'out</name></funapp></arg></funapp></lhs><rhs><funapp><name>reduce'ii'out</name></funapp></rhs></rule><rule><lhs><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><var>G1</var></arg><arg><var>G2</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><name>u'11'1</name><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>G1</var></arg><arg><funapp><name>cons</name><arg><var>G2</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u'11'1</name><arg><funapp><name>reduce'ii'out</name></funapp></arg></funapp></lhs><rhs><funapp><name>reduce'ii'out</name></funapp></rhs></rule><rule><lhs><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2a</name><arg><var>G1</var></arg><arg><var>G2</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><name>u'12'1</name><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>G1</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg><arg><var>Fs</var></arg><arg><var>G2</var></arg><arg><var>Gs</var></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>u'12'1</name><arg><funapp><name>reduce'ii'out</name></funapp></arg><arg><var>Fs</var></arg><arg><var>G2</var></arg><arg><var>Gs</var></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><name>u'12'2</name><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>G2</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u'12'2</name><arg><funapp><name>reduce'ii'out</name></funapp></arg></funapp></lhs><rhs><funapp><name>reduce'ii'out</name></funapp></rhs></rule><rule><lhs><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2d</name><arg><var>G1</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><name>u'13'1</name><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>G1</var></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u'13'1</name><arg><funapp><name>reduce'ii'out</name></funapp></arg></funapp></lhs><rhs><funapp><name>reduce'ii'out</name></funapp></rhs></rule><rule><lhs><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>nil</name></funapp></arg><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><var>V</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><funapp><name>sequent</name><arg><var>Left</var></arg><arg><var>Right</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>u'14'1</name><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>nil</name></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><funapp><name>sequent</name><arg><var>Left</var></arg><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><var>V</var></arg></funapp></arg><arg><var>Right</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u'14'1</name><arg><funapp><name>reduce'ii'out</name></funapp></arg></funapp></lhs><rhs><funapp><name>reduce'ii'out</name></funapp></rhs></rule><rule><lhs><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>nil</name></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg><arg><funapp><name>sequent</name><arg><var>F1</var></arg><arg><var>F2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>u'15'1</name><arg><funapp><name>intersect'ii'in</name><arg><var>F1</var></arg><arg><var>F2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u'15'1</name><arg><funapp><name>intersect'ii'out</name></funapp></arg></funapp></lhs><rhs><funapp><name>reduce'ii'out</name></funapp></rhs></rule><rule><lhs><funapp><name>tautology'i'in</name><arg><var>F</var></arg></funapp></lhs><rhs><funapp><name>u'16'1</name><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>nil</name></funapp></arg><arg><funapp><name>cons</name><arg><var>F</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>sequent</name><arg><funapp><name>nil</name></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u'16'1</name><arg><funapp><name>reduce'ii'out</name></funapp></arg></funapp></lhs><rhs><funapp><name>tautology'i'out</name></funapp></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><name>intersect'ii'in</name></sharp><arg><var>Xs</var></arg><arg><funapp><name>cons</name><arg><var>X0</var></arg><arg><var>Ys</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>u'1'1</name></sharp><arg><funapp><name>intersect'ii'in</name><arg><var>Xs</var></arg><arg><var>Ys</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>intersect'ii'in</name></sharp><arg><var>Xs</var></arg><arg><funapp><name>cons</name><arg><var>X0</var></arg><arg><var>Ys</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>intersect'ii'in</name></sharp><arg><var>Xs</var></arg><arg><var>Ys</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>intersect'ii'in</name></sharp><arg><funapp><name>cons</name><arg><var>X0</var></arg><arg><var>Xs</var></arg></funapp></arg><arg><var>Ys</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'2'1</name></sharp><arg><funapp><name>intersect'ii'in</name><arg><var>Xs</var></arg><arg><var>Ys</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>intersect'ii'in</name></sharp><arg><funapp><name>cons</name><arg><var>X0</var></arg><arg><var>Xs</var></arg></funapp></arg><arg><var>Ys</var></arg></funapp></lhs><rhs><funapp><sharp><name>intersect'ii'in</name></sharp><arg><var>Xs</var></arg><arg><var>Ys</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>if</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'3'1</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><funapp><name>x'2d</name><arg><var>B</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>if</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><funapp><name>x'2d</name><arg><var>B</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>iff</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'4'1</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2a</name><arg><funapp><name>if</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><funapp><name>if</name><arg><var>B</var></arg><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>iff</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2a</name><arg><funapp><name>if</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><funapp><name>if</name><arg><var>B</var></arg><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2a</name><arg><var>F1</var></arg><arg><var>F2</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'5'1</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>F1</var></arg><arg><funapp><name>cons</name><arg><var>F2</var></arg><arg><var>Fs</var></arg></funapp></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2a</name><arg><var>F1</var></arg><arg><var>F2</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>F1</var></arg><arg><funapp><name>cons</name><arg><var>F2</var></arg><arg><var>Fs</var></arg></funapp></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><var>F1</var></arg><arg><var>F2</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'6'1</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>F1</var></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg><arg><var>F2</var></arg><arg><var>Fs</var></arg><arg><var>Gs</var></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><var>F1</var></arg><arg><var>F2</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>F1</var></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>u'6'1</name></sharp><arg><funapp><name>reduce'ii'out</name></funapp></arg><arg><var>F2</var></arg><arg><var>Fs</var></arg><arg><var>Gs</var></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'6'2</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>F2</var></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>u'6'1</name></sharp><arg><funapp><name>reduce'ii'out</name></funapp></arg><arg><var>F2</var></arg><arg><var>Fs</var></arg><arg><var>Gs</var></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>F2</var></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2d</name><arg><var>F1</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'7'1</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>F1</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2d</name><arg><var>F1</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>F1</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>if</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'8'1</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><funapp><name>x'2d</name><arg><var>B</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>if</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><funapp><name>x'2d</name><arg><var>B</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>iff</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'9'1</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2a</name><arg><funapp><name>if</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><funapp><name>if</name><arg><var>B</var></arg><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>iff</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2a</name><arg><funapp><name>if</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><funapp><name>if</name><arg><var>B</var></arg><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><var>V</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><funapp><name>sequent</name><arg><var>Left</var></arg><arg><var>Right</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>u'10'1</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><var>Gs</var></arg></funapp></arg><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><var>V</var></arg></funapp></arg><arg><var>Left</var></arg></funapp></arg><arg><var>Right</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><var>V</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><funapp><name>sequent</name><arg><var>Left</var></arg><arg><var>Right</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><var>Gs</var></arg></funapp></arg><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><var>V</var></arg></funapp></arg><arg><var>Left</var></arg></funapp></arg><arg><var>Right</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><var>G1</var></arg><arg><var>G2</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'11'1</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>G1</var></arg><arg><funapp><name>cons</name><arg><var>G2</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><var>G1</var></arg><arg><var>G2</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>G1</var></arg><arg><funapp><name>cons</name><arg><var>G2</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2a</name><arg><var>G1</var></arg><arg><var>G2</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'12'1</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>G1</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg><arg><var>Fs</var></arg><arg><var>G2</var></arg><arg><var>Gs</var></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2a</name><arg><var>G1</var></arg><arg><var>G2</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>G1</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>u'12'1</name></sharp><arg><funapp><name>reduce'ii'out</name></funapp></arg><arg><var>Fs</var></arg><arg><var>G2</var></arg><arg><var>Gs</var></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'12'2</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>G2</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>u'12'1</name></sharp><arg><funapp><name>reduce'ii'out</name></funapp></arg><arg><var>Fs</var></arg><arg><var>G2</var></arg><arg><var>Gs</var></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>G2</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2d</name><arg><var>G1</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'13'1</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>G1</var></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2d</name><arg><var>G1</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>G1</var></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>nil</name></funapp></arg><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><var>V</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><funapp><name>sequent</name><arg><var>Left</var></arg><arg><var>Right</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>u'14'1</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>nil</name></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><funapp><name>sequent</name><arg><var>Left</var></arg><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><var>V</var></arg></funapp></arg><arg><var>Right</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>nil</name></funapp></arg><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><var>V</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><funapp><name>sequent</name><arg><var>Left</var></arg><arg><var>Right</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>nil</name></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><funapp><name>sequent</name><arg><var>Left</var></arg><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><var>V</var></arg></funapp></arg><arg><var>Right</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>nil</name></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg><arg><funapp><name>sequent</name><arg><var>F1</var></arg><arg><var>F2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>u'15'1</name></sharp><arg><funapp><name>intersect'ii'in</name><arg><var>F1</var></arg><arg><var>F2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>nil</name></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg><arg><funapp><name>sequent</name><arg><var>F1</var></arg><arg><var>F2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>intersect'ii'in</name></sharp><arg><var>F1</var></arg><arg><var>F2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>tautology'i'in</name></sharp><arg><var>F</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'16'1</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>nil</name></funapp></arg><arg><funapp><name>cons</name><arg><var>F</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>sequent</name><arg><funapp><name>nil</name></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>tautology'i'in</name></sharp><arg><var>F</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>nil</name></funapp></arg><arg><funapp><name>cons</name><arg><var>F</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>sequent</name><arg><funapp><name>nil</name></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>tautology'i'in</name></sharp><arg><var>F</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>nil</name></funapp></arg><arg><funapp><name>cons</name><arg><var>F</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>sequent</name><arg><funapp><name>nil</name></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><var>F1</var></arg><arg><var>F2</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'6'1</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>F1</var></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg><arg><var>F2</var></arg><arg><var>Fs</var></arg><arg><var>Gs</var></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>u'6'1</name></sharp><arg><funapp><name>reduce'ii'out</name></funapp></arg><arg><var>F2</var></arg><arg><var>Fs</var></arg><arg><var>Gs</var></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>F2</var></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>if</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><funapp><name>x'2d</name><arg><var>B</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><var>F1</var></arg><arg><var>F2</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>F1</var></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>iff</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2a</name><arg><funapp><name>if</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><funapp><name>if</name><arg><var>B</var></arg><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2a</name><arg><var>F1</var></arg><arg><var>F2</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>F1</var></arg><arg><funapp><name>cons</name><arg><var>F2</var></arg><arg><var>Fs</var></arg></funapp></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2d</name><arg><var>F1</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>F1</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>if</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><funapp><name>x'2d</name><arg><var>B</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><var>V</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><funapp><name>sequent</name><arg><var>Left</var></arg><arg><var>Right</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><var>Gs</var></arg></funapp></arg><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><var>V</var></arg></funapp></arg><arg><var>Left</var></arg></funapp></arg><arg><var>Right</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>iff</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2a</name><arg><funapp><name>if</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><funapp><name>if</name><arg><var>B</var></arg><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2a</name><arg><var>G1</var></arg><arg><var>G2</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'12'1</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>G1</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg><arg><var>Fs</var></arg><arg><var>G2</var></arg><arg><var>Gs</var></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>u'12'1</name></sharp><arg><funapp><name>reduce'ii'out</name></funapp></arg><arg><var>Fs</var></arg><arg><var>G2</var></arg><arg><var>Gs</var></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>G2</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><var>G1</var></arg><arg><var>G2</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>G1</var></arg><arg><funapp><name>cons</name><arg><var>G2</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2a</name><arg><var>G1</var></arg><arg><var>G2</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>G1</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2d</name><arg><var>G1</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>G1</var></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>nil</name></funapp></arg><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><var>V</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><funapp><name>sequent</name><arg><var>Left</var></arg><arg><var>Right</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>nil</name></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><funapp><name>sequent</name><arg><var>Left</var></arg><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><var>V</var></arg></funapp></arg><arg><var>Right</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><redPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>u'12'1</name></sharp><arity>5</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>5</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>u'6'1</name></sharp><arity>5</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>5</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>reduce'ii'in</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>-2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>sequent</name><arity>2</arity><polynomial><sum><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></sum></polynomial></interpret><interpret><name>cons</name><arity>2</arity><polynomial><sum><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></sum></polynomial></interpret><interpret><name>if</name><arity>2</arity><polynomial><sum><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></sum></polynomial></interpret><interpret><name>u'3'1</name><arity>1</arity><polynomial><coefficient><integer>2</integer></coefficient></polynomial></interpret><interpret><name>x'2b</name><arity>2</arity><polynomial><sum><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></sum></polynomial></interpret><interpret><name>x'2d</name><arity>1</arity><polynomial><variable>1</variable></polynomial></interpret><interpret><name>iff</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>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>u'4'1</name><arity>1</arity><polynomial><coefficient><integer>-2</integer></coefficient></polynomial></interpret><interpret><name>x'2a</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></sum></polynomial></interpret><interpret><name>u'5'1</name><arity>1</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></sum></polynomial></interpret><interpret><name>u'6'1</name><arity>5</arity><polynomial><sum><polynomial><coefficient><integer>-2</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></sum></polynomial></interpret><interpret><name>u'7'1</name><arity>1</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></sum></polynomial></interpret><interpret><name>u'8'1</name><arity>1</arity><polynomial><coefficient><integer>-2</integer></coefficient></polynomial></interpret><interpret><name>u'9'1</name><arity>1</arity><polynomial><coefficient><integer>1</integer></coefficient></polynomial></interpret><interpret><name>p</name><arity>1</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>u'10'1</name><arity>1</arity><polynomial><coefficient><integer>2</integer></coefficient></polynomial></interpret><interpret><name>u'11'1</name><arity>1</arity><polynomial><coefficient><integer>2</integer></coefficient></polynomial></interpret><interpret><name>u'12'1</name><arity>5</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></sum></polynomial></interpret><interpret><name>u'13'1</name><arity>1</arity><polynomial><coefficient><integer>-2</integer></coefficient></polynomial></interpret><interpret><name>nil</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>u'14'1</name><arity>1</arity><polynomial><coefficient><integer>-2</integer></coefficient></polynomial></interpret><interpret><name>reduce'ii'out</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>u'15'1</name><arity>1</arity><polynomial><coefficient><integer>-2</integer></coefficient></polynomial></interpret><interpret><name>intersect'ii'in</name><arity>2</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>u'12'2</name><arity>1</arity><polynomial><coefficient><integer>-2</integer></coefficient></polynomial></interpret><interpret><name>u'6'2</name><arity>1</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></sum></polynomial></interpret><interpret><name>intersect'ii'out</name><arity>0</arity><polynomial><coefficient><integer>2</integer></coefficient></polynomial></interpret><interpret><name>u'1'1</name><arity>1</arity><polynomial><coefficient><integer>-2</integer></coefficient></polynomial></interpret><interpret><name>u'2'1</name><arity>1</arity><polynomial><coefficient><integer>-2</integer></coefficient></polynomial></interpret><interpret><sharp><name>reduce'ii'in</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>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><var>F1</var></arg><arg><var>F2</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'6'1</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>F1</var></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg><arg><var>F2</var></arg><arg><var>Fs</var></arg><arg><var>Gs</var></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>u'6'1</name></sharp><arg><funapp><name>reduce'ii'out</name></funapp></arg><arg><var>F2</var></arg><arg><var>Fs</var></arg><arg><var>Gs</var></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>F2</var></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>if</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><funapp><name>x'2d</name><arg><var>B</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><var>F1</var></arg><arg><var>F2</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>F1</var></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2d</name><arg><var>F1</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>F1</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>if</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><funapp><name>x'2d</name><arg><var>B</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><var>V</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><funapp><name>sequent</name><arg><var>Left</var></arg><arg><var>Right</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><var>Gs</var></arg></funapp></arg><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><var>V</var></arg></funapp></arg><arg><var>Left</var></arg></funapp></arg><arg><var>Right</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>u'12'1</name></sharp><arg><funapp><name>reduce'ii'out</name></funapp></arg><arg><var>Fs</var></arg><arg><var>G2</var></arg><arg><var>Gs</var></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>G2</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><var>G1</var></arg><arg><var>G2</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>G1</var></arg><arg><funapp><name>cons</name><arg><var>G2</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2d</name><arg><var>G1</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>G1</var></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>nil</name></funapp></arg><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><var>V</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><funapp><name>sequent</name><arg><var>Left</var></arg><arg><var>Right</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>nil</name></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><funapp><name>sequent</name><arg><var>Left</var></arg><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><var>V</var></arg></funapp></arg><arg><var>Right</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><usableRules><rules/></usableRules><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>u'12'1</name></sharp><arg><funapp><name>reduce'ii'out</name></funapp></arg><arg><var>Fs</var></arg><arg><var>G2</var></arg><arg><var>Gs</var></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>G2</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>u'6'1</name></sharp><arg><funapp><name>reduce'ii'out</name></funapp></arg><arg><var>F2</var></arg><arg><var>Fs</var></arg><arg><var>Gs</var></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>F2</var></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>if</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><funapp><name>x'2d</name><arg><var>B</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><var>F1</var></arg><arg><var>F2</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'6'1</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>F1</var></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg><arg><var>F2</var></arg><arg><var>Fs</var></arg><arg><var>Gs</var></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><var>F1</var></arg><arg><var>F2</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>F1</var></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2d</name><arg><var>F1</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>F1</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>if</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><funapp><name>x'2d</name><arg><var>B</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><var>V</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><funapp><name>sequent</name><arg><var>Left</var></arg><arg><var>Right</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><var>Gs</var></arg></funapp></arg><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><var>V</var></arg></funapp></arg><arg><var>Left</var></arg></funapp></arg><arg><var>Right</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><var>G1</var></arg><arg><var>G2</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>G1</var></arg><arg><funapp><name>cons</name><arg><var>G2</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2d</name><arg><var>G1</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>G1</var></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>nil</name></funapp></arg><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><var>V</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><funapp><name>sequent</name><arg><var>Left</var></arg><arg><var>Right</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>nil</name></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><funapp><name>sequent</name><arg><var>Left</var></arg><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><var>V</var></arg></funapp></arg><arg><var>Right</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><redPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>u'6'1</name></sharp><arity>5</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>reduce'ii'in</name><arity>2</arity><polynomial><coefficient><integer>-2</integer></coefficient></polynomial></interpret><interpret><name>sequent</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>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>cons</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></sum></polynomial></interpret><interpret><name>if</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>u'3'1</name><arity>1</arity><polynomial><coefficient><integer>-2</integer></coefficient></polynomial></interpret><interpret><name>x'2b</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><variable>2</variable></polynomial></sum></polynomial></interpret><interpret><name>x'2d</name><arity>1</arity><polynomial><variable>1</variable></polynomial></interpret><interpret><name>iff</name><arity>2</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>u'4'1</name><arity>1</arity><polynomial><coefficient><integer>-2</integer></coefficient></polynomial></interpret><interpret><name>x'2a</name><arity>2</arity><polynomial><coefficient><integer>-2</integer></coefficient></polynomial></interpret><interpret><name>u'5'1</name><arity>1</arity><polynomial><coefficient><integer>2</integer></coefficient></polynomial></interpret><interpret><name>u'6'1</name><arity>5</arity><polynomial><sum><polynomial><coefficient><integer>-2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><variable>4</variable></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>5</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>u'7'1</name><arity>1</arity><polynomial><coefficient><integer>-2</integer></coefficient></polynomial></interpret><interpret><name>u'8'1</name><arity>1</arity><polynomial><coefficient><integer>-2</integer></coefficient></polynomial></interpret><interpret><name>u'9'1</name><arity>1</arity><polynomial><coefficient><integer>-2</integer></coefficient></polynomial></interpret><interpret><name>p</name><arity>1</arity><polynomial><coefficient><integer>2</integer></coefficient></polynomial></interpret><interpret><name>u'10'1</name><arity>1</arity><polynomial><coefficient><integer>-2</integer></coefficient></polynomial></interpret><interpret><name>u'11'1</name><arity>1</arity><polynomial><coefficient><integer>2</integer></coefficient></polynomial></interpret><interpret><name>u'12'1</name><arity>5</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></sum></polynomial></interpret><interpret><name>u'13'1</name><arity>1</arity><polynomial><coefficient><integer>-2</integer></coefficient></polynomial></interpret><interpret><name>reduce'ii'out</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>u'14'1</name><arity>1</arity><polynomial><coefficient><integer>1</integer></coefficient></polynomial></interpret><interpret><name>nil</name><arity>0</arity><polynomial><coefficient><integer>1</integer></coefficient></polynomial></interpret><interpret><name>u'15'1</name><arity>1</arity><polynomial><coefficient><integer>-2</integer></coefficient></polynomial></interpret><interpret><name>intersect'ii'in</name><arity>2</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>u'12'2</name><arity>1</arity><polynomial><coefficient><integer>2</integer></coefficient></polynomial></interpret><interpret><name>u'6'2</name><arity>1</arity><polynomial><coefficient><integer>2</integer></coefficient></polynomial></interpret><interpret><name>intersect'ii'out</name><arity>0</arity><polynomial><coefficient><integer>2</integer></coefficient></polynomial></interpret><interpret><name>u'1'1</name><arity>1</arity><polynomial><coefficient><integer>-2</integer></coefficient></polynomial></interpret><interpret><name>u'2'1</name><arity>1</arity><polynomial><coefficient><integer>-2</integer></coefficient></polynomial></interpret><interpret><sharp><name>reduce'ii'in</name></sharp><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>-2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>if</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><funapp><name>x'2d</name><arg><var>B</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2d</name><arg><var>F1</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>F1</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>if</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><funapp><name>x'2d</name><arg><var>B</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><var>G1</var></arg><arg><var>G2</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>G1</var></arg><arg><funapp><name>cons</name><arg><var>G2</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2d</name><arg><var>G1</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>G1</var></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules/></usableRules><dpProof><monoRedPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>sequent</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>cons</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>if</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>x'2b</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>x'2d</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><sharp><name>reduce'ii'in</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>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>if</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><funapp><name>x'2d</name><arg><var>B</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2d</name><arg><var>F1</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>F1</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>if</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><funapp><name>x'2d</name><arg><var>B</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><var>G1</var></arg><arg><var>G2</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>G1</var></arg><arg><funapp><name>cons</name><arg><var>G2</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2d</name><arg><var>G1</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>G1</var></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule></rules></dps><trs><rules/></trs><usableRules><rules/></usableRules><dpProof><monoRedPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>reduce'ii'in</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>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>sequent</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>cons</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>if</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>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>x'2b</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><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><interpret><name>x'2d</name><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></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><var>G1</var></arg><arg><var>G2</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>G1</var></arg><arg><funapp><name>cons</name><arg><var>G2</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></rhs></rule></rules></dps><trs><rules/></trs><usableRules><rules/></usableRules><dpProof><monoRedPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>reduce'ii'in</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>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>sequent</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>cons</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>x'2b</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></interpretation></redPair></orderingConstraintProof><dps><rules/></dps><trs><rules/></trs><usableRules><rules/></usableRules><dpProof><pIsEmpty/></dpProof></monoRedPairUrProc></dpProof></monoRedPairUrProc></dpProof></monoRedPairUrProc></dpProof></redPairUrProc></dpProof></component></depGraphProc></dpProof></redPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>nil</name></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg><arg><funapp><name>sequent</name><arg><var>F1</var></arg><arg><var>F2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>intersect'ii'in</name></sharp><arg><var>F1</var></arg><arg><var>F2</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>intersect'ii'in</name></sharp><arg><funapp><name>cons</name><arg><var>X0</var></arg><arg><var>Xs</var></arg></funapp></arg><arg><var>Ys</var></arg></funapp></lhs><rhs><funapp><sharp><name>intersect'ii'in</name></sharp><arg><var>Xs</var></arg><arg><var>Ys</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>intersect'ii'in</name></sharp><arg><var>Xs</var></arg><arg><funapp><name>cons</name><arg><var>X0</var></arg><arg><var>Ys</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>intersect'ii'in</name></sharp><arg><var>Xs</var></arg><arg><var>Ys</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><monoRedPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>cons</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>intersect'ii'in</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>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>intersect'ii'in</name></sharp><arg><funapp><name>cons</name><arg><var>X0</var></arg><arg><var>Xs</var></arg></funapp></arg><arg><var>Ys</var></arg></funapp></lhs><rhs><funapp><sharp><name>intersect'ii'in</name></sharp><arg><var>Xs</var></arg><arg><var>Ys</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>intersect'ii'in</name></sharp><arg><var>Xs</var></arg><arg><funapp><name>cons</name><arg><var>X0</var></arg><arg><var>Ys</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>intersect'ii'in</name></sharp><arg><var>Xs</var></arg><arg><var>Ys</var></arg></funapp></rhs></rule></rules></dps><trs><rules/></trs><usableRules><rules/></usableRules><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>intersect'ii'in</name></sharp><arg><funapp><name>cons</name><arg><var>X0</var></arg><arg><var>Xs</var></arg></funapp></arg><arg><var>Ys</var></arg></funapp></lhs><rhs><funapp><sharp><name>intersect'ii'in</name></sharp><arg><var>Xs</var></arg><arg><var>Ys</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge><edge><position>2</position><strict>false</strict><position>2</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>intersect'ii'in</name></sharp><arg><var>Xs</var></arg><arg><funapp><name>cons</name><arg><var>X0</var></arg><arg><var>Ys</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>intersect'ii'in</name></sharp><arg><var>Xs</var></arg><arg><var>Ys</var></arg></funapp></rhs></rule><edge><position>1</position><strict>false</strict><position>1</position></edge><edge><position>2</position><strict>true</strict><position>2</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></monoRedPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>intersect'ii'in</name></sharp><arg><var>Xs</var></arg><arg><funapp><name>cons</name><arg><var>X0</var></arg><arg><var>Ys</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>u'1'1</name></sharp><arg><funapp><name>intersect'ii'in</name><arg><var>Xs</var></arg><arg><var>Ys</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>intersect'ii'in</name></sharp><arg><funapp><name>cons</name><arg><var>X0</var></arg><arg><var>Xs</var></arg></funapp></arg><arg><var>Ys</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'2'1</name></sharp><arg><funapp><name>intersect'ii'in</name><arg><var>Xs</var></arg><arg><var>Ys</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>if</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'3'1</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><funapp><name>x'2d</name><arg><var>B</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>iff</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'4'1</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2a</name><arg><funapp><name>if</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><funapp><name>if</name><arg><var>B</var></arg><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2a</name><arg><var>F1</var></arg><arg><var>F2</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'5'1</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>F1</var></arg><arg><funapp><name>cons</name><arg><var>F2</var></arg><arg><var>Fs</var></arg></funapp></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>u'6'1</name></sharp><arg><funapp><name>reduce'ii'out</name></funapp></arg><arg><var>F2</var></arg><arg><var>Fs</var></arg><arg><var>Gs</var></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'6'2</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>F2</var></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>x'2d</name><arg><var>F1</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'7'1</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>F1</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>if</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'8'1</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><funapp><name>x'2d</name><arg><var>B</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>iff</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'9'1</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2a</name><arg><funapp><name>if</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><funapp><name>if</name><arg><var>B</var></arg><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><var>V</var></arg></funapp></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><funapp><name>sequent</name><arg><var>Left</var></arg><arg><var>Right</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>u'10'1</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><var>Gs</var></arg></funapp></arg><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><var>V</var></arg></funapp></arg><arg><var>Left</var></arg></funapp></arg><arg><var>Right</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2b</name><arg><var>G1</var></arg><arg><var>G2</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'11'1</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>G1</var></arg><arg><funapp><name>cons</name><arg><var>G2</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>u'12'1</name></sharp><arg><funapp><name>reduce'ii'out</name></funapp></arg><arg><var>Fs</var></arg><arg><var>G2</var></arg><arg><var>Gs</var></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'12'2</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><var>G2</var></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><var>Fs</var></arg><arg><funapp><name>cons</name><arg><funapp><name>x'2d</name><arg><var>G1</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><var>NF</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'13'1</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>cons</name><arg><var>G1</var></arg><arg><var>Fs</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><var>NF</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>nil</name></funapp></arg><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><var>V</var></arg></funapp></arg><arg><var>Gs</var></arg></funapp></arg></funapp></arg><arg><funapp><name>sequent</name><arg><var>Left</var></arg><arg><var>Right</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>u'14'1</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>nil</name></funapp></arg><arg><var>Gs</var></arg></funapp></arg><arg><funapp><name>sequent</name><arg><var>Left</var></arg><arg><funapp><name>cons</name><arg><funapp><name>p</name><arg><var>V</var></arg></funapp></arg><arg><var>Right</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>reduce'ii'in</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>nil</name></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg><arg><funapp><name>sequent</name><arg><var>F1</var></arg><arg><var>F2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>u'15'1</name></sharp><arg><funapp><name>intersect'ii'in</name><arg><var>F1</var></arg><arg><var>F2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>tautology'i'in</name></sharp><arg><var>F</var></arg></funapp></lhs><rhs><funapp><sharp><name>u'16'1</name></sharp><arg><funapp><name>reduce'ii'in</name><arg><funapp><name>sequent</name><arg><funapp><name>nil</name></funapp></arg><arg><funapp><name>cons</name><arg><var>F</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>sequent</name><arg><funapp><name>nil</name></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></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: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (11 real / 0 unknown / 0 assumptions / 11 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

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to TRS Standard Certified