details

property	value
status	complete
benchmark	BAG_nokinds.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n145.star.cs.uiowa.edu
space	Mixed_AC

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	6.33539 seconds
cpu usage	16.7581
user time	16.1181
system time	0.639998
max virtual memory	1.840206E7
max residence set size	1430372.0

stage attributes

key	value
certification-result	CERTIFIED
starexec-result	CERTIFIED YES
certification-time	2.23
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" 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harp><name>plus</name></sharp><arg><funapp><name>sum</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>sum</name><arg><var>B</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U111</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>sum</name></sharp><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U111</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>sum</name></sharp><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>0</name></sharp><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>0</name><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>0</name></sharp><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>0</name></sharp><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>0</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>z</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>z</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U91</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>prod</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>prod</name><arg><var>B</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U91</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>prod</name></sharp><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U91</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>prod</name></sharp><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBag</name></sharp><arg><funapp><name>singl</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBag</name></sharp><arg><funapp><name>union</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBag</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBag</name></sharp><arg><funapp><name>union</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBag</name></sharp><arg><funapp><name>union</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>0</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>1</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>mult</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>mult</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>mult</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>prod</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>sum</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>U11</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>U41</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prod</name></sharp><arg><funapp><name>singl</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U81</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prod</name></sharp><arg><funapp><name>singl</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prod</name></sharp><arg><funapp><name>union</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U91</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBag</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBag</name><arg><var>B</var></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prod</name></sharp><arg><funapp><name>union</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBag</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBag</name><arg><var>B</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prod</name></sharp><arg><funapp><name>union</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prod</name></sharp><arg><funapp><name>union</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>empty</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>0</name></sharp><arg><funapp><name>z</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>singl</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U101</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>singl</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>union</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U111</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBag</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBag</name><arg><var>B</var></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>union</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBag</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBag</name><arg><var>B</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>union</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>union</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>U11</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U11</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>U31</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U41</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U41</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U51</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U61</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U71</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>union</name></sharp><arg><funapp><name>union</name><arg><var>X</var></arg><arg><funapp><name>empty</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>union</name></sharp><arg><var>X</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>union</name></sharp><arg><funapp><name>union</name><arg><funapp><name>empty</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>union</name></sharp><arg><var>X</var></arg><arg><var>ext</var></arg></funapp></rhs></rule></rules></dps><extensions><rules><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U11</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U31</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U41</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U51</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U61</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U71</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>union</name><arg><funapp><name>union</name><arg><var>X</var></arg><arg><funapp><name>empty</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>union</name><arg><var>X</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>union</name><arg><funapp><name>union</name><arg><funapp><name>empty</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>union</name><arg><var>X</var></arg><arg><var>ext</var></arg></funapp></rhs></rule></rules></extensions><acDPTerminationProof><acDepGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>U111</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>sum</name></sharp><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>union</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U111</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBag</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBag</name><arg><var>B</var></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U111</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>sum</name></sharp><arg><var>B</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><acDPTerminationProof><acMonoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>isBin</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>plus</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</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>and</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>isBag</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>singl</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>prod</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>sum</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>empty</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>union</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mult</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</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>1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>sum</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>U111</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>union</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U111</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBag</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBag</name><arg><var>B</var></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>union</name><arg><var>X</var></arg><arg><funapp><name>empty</name></funapp></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>union</name><arg><funapp><name>empty</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>0</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>U101</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>U11</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>U111</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>sum</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>sum</name><arg><var>B</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U21</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U31</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U41</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>U51</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U61</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U71</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>z</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U81</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>U91</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>prod</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>prod</name><arg><var>B</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBag</name><arg><funapp><name>empty</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBag</name><arg><funapp><name>singl</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBag</name><arg><funapp><name>union</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBag</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>0</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>1</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>mult</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>prod</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>sum</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U31</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U41</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U51</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U61</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U71</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>prod</name><arg><funapp><name>empty</name></funapp></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>z</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>prod</name><arg><funapp><name>singl</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U81</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>prod</name><arg><funapp><name>union</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U91</name><arg><funapp><name>and</name><arg><funapp><name>isBag</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBag</name><arg><var>B</var></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>sum</name><arg><funapp><name>empty</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>z</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>sum</name><arg><funapp><name>singl</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U101</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>sum</name><arg><funapp><name>union</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U111</name><arg><funapp><name>and</name><arg><funapp><name>isBag</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBag</name><arg><var>B</var></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U11</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U31</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U41</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U51</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U61</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U71</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>union</name><arg><funapp><name>union</name><arg><var>X</var></arg><arg><funapp><name>empty</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>union</name><arg><var>X</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>union</name><arg><funapp><name>union</name><arg><funapp><name>empty</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>union</name><arg><var>X</var></arg><arg><var>ext</var></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>isBin</name><arg><funapp><name>plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBag</name><arg><funapp><name>singl</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>0</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>prod</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>sum</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBag</name><arg><funapp><name>empty</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBag</name><arg><funapp><name>union</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBag</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>mult</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>1</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule></rules></usableRules><acDPTerminationProof><acDepGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>U111</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>sum</name></sharp><arg><var>B</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U111</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>sum</name></sharp><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></acDepGraphProc></acDPTerminationProof></acMonoRedPairProc></acDPTerminationProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>U111</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>sum</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>sum</name><arg><var>B</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U91</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>prod</name></sharp><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prod</name></sharp><arg><funapp><name>union</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U91</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBag</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBag</name><arg><var>B</var></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U91</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>prod</name></sharp><arg><var>B</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><acDPTerminationProof><acMonoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>isBin</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>plus</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</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>and</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>isBag</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>singl</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>prod</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>sum</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>empty</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>union</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mult</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</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>1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>U91</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><p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ame><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>U11</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>U31</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>x</var></arg><arg><funapp><name>mult</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><acDPTerminationProof><acRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>2</degree></polynomial></type><interpret><sharp><name>mult</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><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>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mult</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><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>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>1</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></sum></polynomial></interpret><interpret><name>U31</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isBin</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>U21</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>U31</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U11</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U61</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>plus</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>sum</name><arity>1</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>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isBag</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>prod</name><arity>1</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>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U51</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U71</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>singl</name><arity>1</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>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>empty</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>union</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><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>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>U31</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U31</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U11</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U31</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U61</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U21</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>sum</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>0</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>1</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>prod</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>mult</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U41</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>U11</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U61</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U51</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U61</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U51</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U41</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U71</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U71</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U41</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U51</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBag</name><arg><funapp><name>singl</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBag</name><arg><funapp><name>empty</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBag</name><arg><funapp><name>union</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBag</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U71</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>z</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>0</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>U31</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><var>x</var></arg><arg><funapp><name>mult</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>x</var></arg><arg><funapp><name>plus</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></usableRules><acDPTerminationProof><acDepGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>U11</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>x</var></arg><arg><funapp><name>mult</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><acDPTerminationProof><acRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>2</degree></polynomial></type><interpret><sharp><name>mult</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><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>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mult</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><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>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>1</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></sum></polynomial></interpret><interpret><name>U21</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isBin</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>U21</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U11</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isBag</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>singl</name><arity>1</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>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>empty</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>union</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><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>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U31</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>plus</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U71</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>1</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></sum></polynomial></interpret><interpret><name>U61</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U51</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>sum</name><arity>1</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>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>prod</name><arity>1</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>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>U41</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>U21</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>0</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>isBag</name><arg><funapp><name>singl</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBag</name><arg><funapp><name>empty</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBag</name><arg><funapp><name>union</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBag</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U31</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U71</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>z</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U11</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>U61</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U51</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U31</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U11</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U31</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>sum</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>0</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>1</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>prod</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>mult</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U61</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U51</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U61</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U51</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U41</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U71</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U71</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U41</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><var>x</var></arg><arg><funapp><name>mult</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>x</var></arg><arg><funapp><name>plus</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></usableRules><acDPTerminationProof><acDepGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>U11</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>x</var></arg><arg><funapp><name>mult</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><acDPTerminationProof><acRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>mult</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mult</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><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>0</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isBin</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U11</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><interpret><name>U51</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>plus</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>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>sum</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isBag</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>prod</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>singl</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>empty</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>union</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U61</name><arity>3</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>U31</name><arity>3</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>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U71</name><arity>3</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></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>U11</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>U51</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U41</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>sum</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>0</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>1</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>prod</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>mult</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>0</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>isBag</name><arg><funapp><name>singl</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBag</name><arg><funapp><name>empty</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBag</name><arg><funapp><name>union</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBag</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>U61</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U31</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U31</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U11</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U31</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U21</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U11</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>U71</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>z</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U61</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U51</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U61</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U51</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U41</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U71</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U71</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U41</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><var>x</var></arg><arg><funapp><name>mult</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>x</var></arg><arg><funapp><name>plus</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></usableRules><acDPTerminationProof><acTrivialProc/></acDPTerminationProof></acRedPairProc></acDPTerminationProof></component></acDepGraphProc></acDPTerminationProof></acRedPairProc></acDPTerminationProof></component></acDepGraphProc></acDPTerminationProof></acRedPairProc></acDPTerminationProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>0</name></sharp><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>0</name><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>0</name></sharp><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>z</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U41</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U51</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U61</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U71</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><var>x</var></arg><arg><funapp><name>plus</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><acDPTerminationProof><acRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>plus</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>plus</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>1</name><arity>1</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></sum></polynomial></interpret><interpret><sharp><name>U71</name></sharp><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isBin</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U61</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>U61</name></sharp><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U71</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U51</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>U51</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isBag</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>singl</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>empty</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>union</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>sum</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>prod</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>mult</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U71</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>z</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U61</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U51</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U61</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U51</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U41</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U71</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U71</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U41</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U71</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>z</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>0</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>U61</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U51</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U41</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>x</var></arg><arg><funapp><name>plus</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></usableRules><acDPTerminationProof><acDepGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U41</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U51</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U61</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><var>x</var></arg><arg><funapp><name>plus</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><acDPTerminationProof><acRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>plus</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>plus</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>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>1</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></sum></polynomial></interpret><interpret><name>U61</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isBin</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U51</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>U51</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>sum</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isBag</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>prod</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mult</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U71</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>singl</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>empty</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>union</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U41</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>0</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>U71</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>z</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U61</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U41</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U61</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U51</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U61</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U51</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U41</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U71</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U71</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U41</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U51</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>x</var></arg><arg><funapp><name>plus</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></usableRules><acDPTerminationProof><acRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>plus</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>plus</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>0</name><arity>1</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></sum></polynomial></interpret><interpret><name>1</name><arity>1</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></sum></polynomial></interpret><interpret><name>U61</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isBin</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U51</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>U51</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U71</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isBag</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>singl</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>empty</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>union</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>sum</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>prod</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>mult</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U61</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U51</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>U71</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>z</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U51</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U61</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U51</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U61</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U51</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U41</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U71</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U71</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U41</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>0</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>U61</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U41</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>x</var></arg><arg><funapp><name>plus</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></usableRules><acDPTerminationProof><acDepGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp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p></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>B</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>0</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>1</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>mult</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>mult</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>prod</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBag</name></sharp><arg><funapp><name>singl</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>sum</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBag</name></sharp><arg><funapp><name>union</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBag</name></sharp><arg><funapp><name>union</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><acDPTerminationProof><acMonoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>isBin</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>plus</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>sum</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>isBag</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>union</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomia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</funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U71</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>union</name><arg><funapp><name>union</name><arg><var>X</var></arg><arg><funapp><name>empty</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>union</name><arg><var>X</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>union</name><arg><funapp><name>union</name><arg><funapp><name>empty</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>union</name><arg><var>X</var></arg><arg><var>ext</var></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>union</name><arg><var>X</var></arg><arg><funapp><name>empty</name></funapp></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>union</name><arg><funapp><name>empty</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>union</name><arg><funapp><name>union</name><arg><var>X</var></arg><arg><funapp><name>empty</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>union</name><arg><var>X</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>union</name><arg><funapp><name>union</name><arg><funapp><name>empty</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>union</name><arg><var>X</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>union</name><arg><funapp><name>union</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><name>union</name><arg><var>x</var></arg><arg><funapp><name>union</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>union</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>union</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></usableRules><acDPTerminationProof><acMonoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>union</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>union</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>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mult</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>plus</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></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>union</name></sharp><arg><funapp><name>union</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><sharp><name>union</name></sharp><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></rhs></rule></rules></dps><trs><rules/></trs><usableRules><rules><rule><lhs><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>union</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>union</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><var>x</var></arg><arg><funapp><name>mult</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>x</var></arg><arg><funapp><name>plus</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>union</name><arg><funapp><name>union</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><name>union</name><arg><var>x</var></arg><arg><funapp><name>union</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><acDPTerminationProof><acTrivialProc/></acDPTerminationProof></acMonoRedPairProc></acDPTerminationProof></acMonoRedPairProc></acDPTerminationProof></component></acDepGraphProc></acDPTerminationProof></acDependencyPairs></acTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (23 real / 0 unknown / 0 assumptions / 23 total proof steps)</strategy><url>http://aprove.informatik.rwth-aachen.de</url></tool><toolUser><firstName>John</firstName><lastName>Doe</lastName></toolUser></proofOrigin><inputOrigin/></origin></certificationProblem> popout

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all output return to TRS Equational Certified