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TRS_Equational Certified 2019-03-22 08.29 pair #430114147
details
property
value
status
complete
benchmark
BAG_complete.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n118.star.cs.uiowa.edu
space
Mixed_AC
run statistics
property
value
solver
AProVE
configuration
certified
runtime (wallclock)
180.279 seconds
cpu usage
198.142
user time
195.824
system time
2.31747
max virtual memory
1.8459896E7
max residence set size
5202624.0
stage attributes
key
value
certification-result
CERTIFIED
output-size
649148
starexec-result
YES
certification-time
1.6
output
YES <?xml version="1.0" encoding="UTF-8" standalone="no"?><?xml-stylesheet type="text/xsl" href="cpfHTML.xsl"?><certificationProblem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="cpf.xsd"><input><acRewriteSystem><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><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><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><name>U12</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U111</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>U12</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U121</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>U131</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>U141</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>U151</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>U161</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>U171</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>U181</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>U191</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>V1</var></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U22</name><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U22</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U23</name><arg><funapp><name>isBag</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U23</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U31</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><name>U32</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U32</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U41</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><name>U42</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U42</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></f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</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>U111</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>U111</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>U131</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>U131</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>U141</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>U151</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>U151</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>U151</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>U171</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>U171</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>U171</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>U191</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><rule><lhs><funapp><sharp><name>U191</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>U191</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>V1</var></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>U22</name></sharp><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U22</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>U23</name></sharp><arg><funapp><name>isBag</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U22</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><sharp><name>U32</name></sharp><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U41</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><sharp><name>U42</name></sharp><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U41</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>U52</name></sharp><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U52</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>U53</name></sharp><arg><funapp><name>isBin</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U52</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>U62</name></sharp><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U62</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>U63</name></sharp><arg><funapp><name>isBin</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U62</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><sharp><name>U72</name></sharp><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U81</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><sharp><name>U82</name></sharp><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U81</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></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>U11</name></sharp><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><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>isBinKind</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>U21</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBagKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBagKind</name><arg><var>V2</var></arg></funapp></arg></funapp></arg><arg><var>V1</var></arg><arg><var>V2</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>isBagKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBagKind</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>isBagKind</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>isBagKind</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBagKind</name></sharp><arg><funapp><name>singl</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBinKind</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBagKind</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>isBagKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBagKind</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBagKind</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>isBagKind</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBagKind</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>isBagKind</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>U31</name></sharp><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><var>V1</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>isBinKind</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>U41</name></sharp><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><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>isBinKind</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>U51</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>V2</var></arg></funapp></arg></funapp></arg><arg><var>V1</var></arg><arg><var>V2</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>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBinKind</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>isBinKind</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>isBinKind</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>U61</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>V2</var></arg></funapp></arg></funapp></arg><arg><var>V1</var></arg><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>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBinKind</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>isBinKind</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>isBinKind</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>U71</name></sharp><arg><funapp><name>isBagKind</name><arg><var>V1</var></arg></funapp></arg><arg><var>V1</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>isBagKind</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>U81</name></sharp><arg><funapp><name>isBagKind</name><arg><var>V1</var></arg></funapp></arg><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>isBagKind</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBinKind</name></sharp><arg><funapp><name>0</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBinKind</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBinKind</name></sharp><arg><funapp><name>1</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBinKind</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBinKind</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>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBinKind</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>isBinKind</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBinKind</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>isBinKind</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBinKind</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>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBinKind</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>isBinKind</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBinKind</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>isBinKind</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBinKind</name></sharp><arg><funapp><name>prod</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBagKind</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBinKind</name></sharp><arg><funapp><name>sum</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBagKind</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>U91</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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>and</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</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>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBinKind</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>U101</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>and</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</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>isBinKind</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>and</name></sharp><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</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>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>isBinKind</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>U111</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>and</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</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>isBinKind</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>and</name></sharp><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</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>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>isBinKind</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>U121</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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>and</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBinKind</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>U131</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>and</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</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>isBinKind</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>and</name></sharp><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</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>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>isBinKind</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>U141</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>and</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</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>isBinKind</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>and</name></sharp><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</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>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>isBinKind</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>U151</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>and</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</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>isBinKind</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>and</name></sharp><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</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>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>isBinKind</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>U161</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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>and</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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>singl</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBinKind</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>U171</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBag</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBagKind</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBag</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBagKind</name><arg><var>B</var></arg></funapp></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>and</name><arg><funapp><name>isBag</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBagKind</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBag</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBagKind</name><arg><var>B</var></arg></funapp></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>and</name></sharp><arg><funapp><name>isBag</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBagKind</name><arg><var>A</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>isBagKind</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>and</name></sharp><arg><funapp><name>isBag</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBagKind</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>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>isBagKind</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>U181</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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>and</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></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>isBin</name></sharp><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>isBinKind</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>U191</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBag</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBagKind</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBag</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBagKind</name><arg><var>B</var></arg></funapp></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>and</name><arg><funapp><name>isBag</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBagKind</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBag</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBagKind</name><arg><var>B</var></arg></funapp></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>and</name></sharp><arg><funapp><name>isBag</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBagKind</name><arg><var>A</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>isBagKind</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>and</name></sharp><arg><funapp><name>isBag</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBagKind</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>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>isBagKind</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>U91</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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>U91</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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>and</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</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>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBinKind</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>U101</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U101</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>and</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</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>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>isBinKind</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>and</name></sharp><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</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>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>isBinKind</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>U111</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U111</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>and</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</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>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>isBinKind</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>and</name></sharp><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</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>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>isBinKind</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>U121</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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>U121</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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>and</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></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>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>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBinKind</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>U131</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U131</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>and</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</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>isBinKind</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>and</name></sharp><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</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>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>isBinKind</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>U141</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U141</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>and</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</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>isBinKind</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>and</name></sharp><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</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>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>isBinKind</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>U151</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U151</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>and</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</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>isBinKind</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>and</name></sharp><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</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>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>isBinKind</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>U91</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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>U101</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U111</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U121</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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>U131</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U141</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U151</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U171</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>U171</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBag</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBagKind</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBag</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBagKind</name><arg><var>B</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U171</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>U51</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><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>U52</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>isBin</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>U42</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>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>empty</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></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></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><product><polynomial><coefficient><integer>2</integer></coefficient></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>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>isBinKind</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>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U22</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>singl</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>U11</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U82</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>isBagKind</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>U12</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>U31</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U32</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>U72</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>plus</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>U61</name><arity>3</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><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>3</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>U53</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>U23</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>union</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>U71</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>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>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U81</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>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>U62</name><arity>2</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><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U63</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>mult</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><sharp><name>prod</name></sharp><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>U171</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>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></interpretation></redPair></orderingConstraintProof><dps><rules><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>U171</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBag</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBagKind</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBag</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBagKind</name><arg><var>B</var></arg></funapp></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><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>U111</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>U121</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>U131</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>U141</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>U151</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>U161</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>U171</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>U181</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>U191</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>U61</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U62</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U62</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U63</name><arg><funapp><name>isBin</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U91</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></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>U11</name><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><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>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBagKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBagKind</name><arg><var>V2</var></arg></funapp></arg></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBagKind</name><arg><funapp><name>empty</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBagKind</name><arg><funapp><name>singl</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBagKind</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>isBagKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBagKind</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>U31</name><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><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>U41</name><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><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>U51</name><arg><funapp><name>and</name><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>V2</var></arg></funapp></arg></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></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>U61</name><arg><funapp><name>and</name><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>V2</var></arg></funapp></arg></funapp></arg><arg><var>V1</var></arg><arg><var>V2</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>U71</name><arg><funapp><name>isBagKind</name><arg><var>V1</var></arg></funapp></arg><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>U81</name><arg><funapp><name>isBagKind</name><arg><var>V1</var></arg></funapp></arg><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBinKind</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBinKind</name><arg><funapp><name>0</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBinKind</name><arg><funapp><name>1</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBinKind</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>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBinKind</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>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBinKind</name><arg><funapp><name>prod</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBagKind</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBinKind</name><arg><funapp><name>sum</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBagKind</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>U91</name><arg><funapp><name>and</name><arg><funapp>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pp><name>isBinKind</name><arg><var>X</var></arg></funapp></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>U101</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U101</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U111</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U111</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>3</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>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U91</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></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>isBinKind</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><sharp><name>U101</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>U111</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>U101</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><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>U111</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>1</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><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U71</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U72</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></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><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U42</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U81</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U82</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></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>U141</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>U131</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>U121</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>U151</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>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U11</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U12</name><arity>1</arity><polynomial><sum><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>U63</name><arity>1</arity><polynomial><sum><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>U23</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</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>isBagKind</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>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U53</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>U31</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U61</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</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>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U52</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></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></sum></polynomial></interpret><interpret><name>singl</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U62</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U32</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U22</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></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>U111</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U111</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>V1</var></arg></funapp></lhs><rhs><funapp><name>U72</name><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U41</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><name>U42</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U81</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><name>U82</name><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></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>U141</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>i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g><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>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></rules></usableRules><acDPTerminationProof><acDepGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>U111</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>U101</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U101</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>U91</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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>U101</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U101</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U111</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>3</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>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U91</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></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>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isBinKind</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><sharp><name>U101</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><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>U101</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>1</variable></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</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>U111</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>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U23</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></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>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U52</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><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U53</name><arity>1</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>U42</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isBagKind</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></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>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>U21</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>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U22</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><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>U71</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>U72</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U11</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>U141</name><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>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>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>U81</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></sum></polynomial></interpret><interpret><name>U82</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U131</name><arity>3</arity><polynomial><sum><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>sum</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><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U121</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>U32</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>U62</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></sum></polynomial></interpret><interpret><name>U63</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>U12</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>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>U61</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>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U151</name><arity>3</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>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></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>U111</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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></rules></dps><usableRules><rules><rule><lhs><funapp><name>U91</name><arg><funapp><name>tt</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><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>isBagKind</name><arg><funapp><name>empty</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBagKind</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>isBagKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBagKind</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBagKind</name><arg><funapp><name>singl</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U141</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>0</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>U131</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>isBinKind</name><arg><funapp><name>sum</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBagKind</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBinKind</name><arg><funapp><name>prod</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBagKind</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBinKind</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>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBinKind</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>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBinKind</name><arg><funapp><name>0</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBinKind</name><arg><funapp><name>1</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBinKind</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U121</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>U151</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>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>U111</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>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>U141</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>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>U131</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U121</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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>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>U131</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>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>U151</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U121</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><var>X</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>U151</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>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>U141</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>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>U101</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U91</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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>U91</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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>U101</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U111</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>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>U111</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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><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><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></rules></usableRules><acDPTerminationProof><acRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>3</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>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U91</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></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>isBinKind</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><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>U101</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><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>U101</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></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isBagKind</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></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></sum></polynomial></interpret><interpret><name>singl</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U61</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U62</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></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><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>U11</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></sum></polynomial></interpret><interpret><name>U21</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U131</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>U72</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U82</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U151</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>U111</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>1</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><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U121</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>U23</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</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>prod</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U141</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>U22</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U32</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>U12</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>U53</name><arity>1</arity><polynomial><sum><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>U31</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U81</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U71</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U51</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U52</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U63</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U42</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></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>U101</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U101</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>isBagKind</name><arg><funapp><name>empty</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBagKind</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>isBagKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBagKind</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBagKind</name><arg><funapp><name>singl</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U61</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U62</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</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>singl</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><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>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBagKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBagKind</name><arg><var>V2</var></arg></funapp></arg></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U131</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>U72</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U82</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U151</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>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>U101</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U91</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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>U91</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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>U101</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U111</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>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>U111</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U121</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>U23</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBinKind</name><arg><funapp><name>sum</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBagKind</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBinKind</name><arg><funapp><name>prod</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBagKind</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBinKind</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>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBinKind</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>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBinKind</name><arg><funapp><name>0</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBinKind</name><arg><funapp><name>1</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBinKind</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U141</name><arg><funapp><name>tt</name></funapp></arg><arg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g><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>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>U141</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U32</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U12</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U53</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></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>U31</name><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><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>U41</name><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><var>V1</var></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>U61</name><arg><funapp><name>and</name><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>V2</var></arg></funapp></arg></funapp></arg><arg><var>V1</var></arg><arg><var>V2</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>U81</name><arg><funapp><name>isBagKind</name><arg><var>V1</var></arg></funapp></arg><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>U71</name><arg><funapp><name>isBagKind</name><arg><var>V1</var></arg></funapp></arg><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>U51</name><arg><funapp><name>and</name><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>V2</var></arg></funapp></arg></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U101</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>U52</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U53</name><arg><funapp><name>isBin</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>U111</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>U51</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U52</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U62</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U63</name><arg><funapp><name>isBin</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><name>U12</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U81</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><name>U82</name><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U91</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>U42</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U63</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U31</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><name>U32</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U41</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><name>U42</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U22</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U23</name><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>V1</var></arg></funapp></lhs><rhs><funapp><name>U72</name><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></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>U101</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>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>U101</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U91</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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><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>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><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>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U91</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></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>isBinKind</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><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U101</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U11</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</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>U12</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U81</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U82</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</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>1</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U111</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</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>singl</name><arity>1</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>U21</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><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>isBagKind</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U22</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U23</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></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>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>U141</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U131</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U121</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>U151</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U31</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</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>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U61</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><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>sum</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><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U71</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</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>3</integer></coefficient></polynomial><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>U53</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U52</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U63</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U32</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U42</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U62</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U72</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></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>U101</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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></rules></dps><usableRules><rules><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>U101</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U91</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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>U91</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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>U101</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U111</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>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>U111</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>0</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></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>U141</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>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>U131</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U121</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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>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>U131</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>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>U151</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U121</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><var>X</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>U151</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>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>U141</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U111</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>U91</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>U121</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>U101</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>U141</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>U131</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>U151</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>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><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>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><coefficient><integer>2</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>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U91</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></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>isBinKind</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U72</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</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>U111</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</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>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>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U141</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U131</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U121</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>U151</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U23</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</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>isBagKind</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><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U71</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</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>U32</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U82</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</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>singl</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U11</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><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>U81</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U12</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U31</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U53</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U22</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U42</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U61</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><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>U51</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><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>U52</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U63</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U101</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U62</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></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>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>U91</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>U111</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>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>U141</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>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>U131</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U121</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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>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>U131</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>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>U151</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U121</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><var>X</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>U151</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>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>U141</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U91</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>U151</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>U141</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>U121</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>0</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>U131</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>U101</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>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>U101</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U91</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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>U91</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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>U101</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U111</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>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>U111</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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><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><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></rules></usableRules><acDPTerminationProof><acTrivialProc/></acDPTerminationProof></acRedPairProc></acDPTerminationProof></acRedPairProc></acDPTerminationProof></component></acDepGraphProc></acDPTerminationProof></acRedPairProc></acDPTerminationProof></acRedPairProc></acDPTerminationProof></component></acDepGraphProc></acDPTerminationProof></acRedPairProc></acDPTerminationProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>U101</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>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></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>isBin</name></sharp><arg><var>X</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>isBin</name></sharp><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>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></rules></dps><realScc>false</realScc></component><component><dps><rules><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></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>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>U191</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>U191</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBag</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBagKind</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBag</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBagKind</name><arg><var>B</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U191</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>U51</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><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>U52</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>isBin</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>U42</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>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>empty</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></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></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><product><polynomial><coefficient><integer>2</integer></coefficient></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>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>isBinKind</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>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U22</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>singl</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>U11</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U82</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>isBagKind</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>U12</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>U31</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U32</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>U72</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>plus</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>U61</name><arity>3</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><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>3</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>U53</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>U23</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>union</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>U71</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>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>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U81</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>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>U62</name><arity>2</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><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U63</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>mult</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><sharp><name>sum</name></sharp><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>U191</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>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></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>U191</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBag</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBagKind</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBag</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBagKind</name><arg><var>B</var></arg></funapp></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><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>U111</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>U121</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>U131</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>U141</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>U151</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>U161</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>U171</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>U181</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>U191</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>U61</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U62</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U62</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U63</name><arg><funapp><name>isBin</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U91</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></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>U11</name><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><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>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBagKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBagKind</name><arg><var>V2</var></arg></funapp></arg></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBagKind</name><arg><funapp><name>empty</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBagKind</name><arg><funapp><name>singl</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBagKind</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>isBagKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBagKind</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>U31</name><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><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>U41</name><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><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>U51</name><arg><funapp><name>and</name><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>V2</var></arg></funapp></arg></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></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>U61</name><arg><funapp><name>and</name><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>V2</var></arg></funapp></arg></funapp></arg><arg><var>V1</var></arg><arg><var>V2</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>U71</name><arg><funapp><name>isBagKind</name><arg><var>V1</var></arg></funapp></arg><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>U81</name><arg><funapp><name>isBagKind</name><arg><var>V1</var></arg></funapp></arg><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBinKind</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBinKind</name><arg><funapp><name>0</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBinKind</name><arg><funapp><name>1</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBinKind</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>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBinKind</name><arg><funapp><name>plus</name><arg><var>V1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</arg></funapp></lhs><rhs><funapp><name>U62</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U53</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U62</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U63</name><arg><funapp><name>isBin</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U81</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><name>U82</name><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBinKind</name><arg><funapp><name>1</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U63</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></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>U71</name><arg><funapp><name>isBagKind</name><arg><var>V1</var></arg></funapp></arg><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>U51</name><arg><funapp><name>and</name><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>V2</var></arg></funapp></arg></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBinKind</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBinKind</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>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><acDPTerminationProof><acDepGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>U191</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><component><dps><rules><rule><lhs><funapp><sharp><name>U191</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></acDepGraphProc></acDPTerminationProof></acMonoRedPairProc></acDPTerminationProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>U191</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>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>U131</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U131</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>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U141</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U141</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>U151</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U151</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>U121</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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>U131</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U131</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U141</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U141</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U151</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U151</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U151</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>U151</name></sharp><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>plus</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><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><product><polynomial><coefficient><integer>2</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>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U141</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></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><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isBinKind</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>U141</name></sharp><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U131</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U151</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</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>U121</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>U131</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U23</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>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U52</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U53</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U71</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U72</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>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>U12</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U32</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U62</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U63</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U22</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U82</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>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>sum</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isBagKind</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><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>mult</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>empty</name><arity>0</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>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>U11</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>union</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>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U31</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U81</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U42</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>U151</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>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U141</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U141</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U141</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>U151</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U151</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U151</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>0</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></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>U141</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>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>U131</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U121</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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>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>U131</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>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>U151</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U121</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><var>X</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>U151</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>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>U141</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U121</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>U151</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>U131</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>U141</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>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><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>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>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>U141</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>isBinKind</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U131</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>U151</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>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U121</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>U131</name></sharp><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</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>U41</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U42</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isBagKind</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>singl</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U81</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U82</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</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>U11</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U12</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><coefficient><integer>3</integer></coefficient></polynomial><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>U52</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U53</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</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>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><interpret><name>U63</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U22</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U23</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U31</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U32</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U71</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U72</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U51</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><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>U61</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><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>U62</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></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>U141</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U131</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>plus</name></sharp><arg><funapp><name>U151</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U131</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U131</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U131</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>U151</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>U141</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>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>U141</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>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>U131</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U121</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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>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>U131</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>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>U151</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U121</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><var>X</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>U151</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>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>U141</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U121</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>U131</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></rules></dps><realScc>false</realScc></component><component><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>U121</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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><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><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>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U121</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></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>isBinKind</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U151</name><arity>3</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>0</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>1</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>empty</name><arity>0</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>U11</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></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>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><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>isBagKind</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U63</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U82</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U12</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U32</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U53</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U42</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U22</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U52</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U61</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><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>U62</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U141</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U131</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U72</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U51</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><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>U23</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U71</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</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>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><interpret><name>U31</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U81</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></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></rules></dps><usableRules><rules><rule><lhs><funapp><name>U151</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>U121</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>U141</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>U131</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>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>U141</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>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>U131</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>U121</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></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>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>U131</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>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>U151</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U121</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><var>X</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>U151</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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>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>U141</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>Y</var></arg></funapp></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><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><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>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U121</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>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>isBinKind</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U82</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</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>sum</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isBagKind</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><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><interpret><name>0</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U151</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U42</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U12</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U23</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U53</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U141</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U51</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><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>U52</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U31</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U61</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><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>U81</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U71</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</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>union</name><arity>2</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>U32</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U63</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U22</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</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>U62</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U11</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U72</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><coefficient><integer>3</integer></coefficient></polynomial><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>U131</name><arity>3</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>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>U121</name><arg><funapp><name>and</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>U151</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>U141</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>U121</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>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp>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t><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>isBin</name></sharp><arg><var>X</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>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></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>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></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>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></rules></dps><realScc>false</realScc></component><component><dps><rules><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></rules></dps><realScc>false</realScc></component><component><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>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></rules></dps><realScc>false</realScc></component><component><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>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></rules></dps><realScc>false</realScc></component><component><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>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><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>isBin</name></sharp><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><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></rules></dps><realScc>false</realScc></component><component><dps><rules><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></rules></dps><realScc>false</realScc></component><component><dps><rules><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></rules></dps><realScc>false</realScc></component><component><dps><rules><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></rules></dps><realScc>false</realScc></component><component><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>isBag</name></sharp><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><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>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>U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></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>0</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></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>U41</name></sharp><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U41</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></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>U51</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>V2</var></arg></funapp></arg></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>U52</name></sharp><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U52</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></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>U61</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>V2</var></arg></funapp></arg></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>U62</name></sharp><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U62</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></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>U71</name></sharp><arg><funapp><name>isBagKind</name><arg><var>V1</var></arg></funapp></arg><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></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>U11</name></sharp><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><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>U21</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBagKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBagKind</name><arg><var>V2</var></arg></funapp></arg></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>U22</name></sharp><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U22</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></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>U81</name></sharp><arg><funapp><name>isBagKind</name><arg><var>V1</var></arg></funapp></arg><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U81</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</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>U51</name><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><polynomial><coefficient><integer>2</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>U52</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>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>U42</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>isBag</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>empty</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></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></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><product><polynomial><coefficient><integer>2</integer></coefficient></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>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>isBinKind</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>U21</name><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><interpret><name>U22</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>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>U11</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U82</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>isBagKind</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>U12</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>U31</name><arity>2</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><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U32</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>U72</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>plus</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>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U61</name><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><interpret><name>sum</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>U53</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>U23</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>union</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>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U71</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>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>prod</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>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U81</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</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>U62</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U63</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>mult</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><sharp><name>U71</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><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><sharp><name>U61</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><interpret><sharp><name>U62</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>U51</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><interpret><sharp><name>U52</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>isBin</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>U41</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>U21</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><interpret><sharp><name>U22</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>U11</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>U31</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>U81</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>1</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U41</name></sharp><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><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>U61</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>V2</var></arg></funapp></arg></funapp></arg><arg><var>V1</var></arg><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>U31</name></sharp><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><var>V1</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>U71</name></sharp><arg><funapp><name>isBagKind</name><arg><var>V1</var></arg></funapp></arg><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>U11</name></sharp><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><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>U21</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBagKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBagKind</name><arg><var>V2</var></arg></funapp></arg></funapp></arg><arg><var>V1</var></arg><arg><var>V2</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>U51</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBinKind</name><arg><var>V2</var></arg></funapp></arg></funapp></arg><arg><var>V1</var></arg><arg><var>V2</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>U81</name></sharp><arg><funapp><name>isBagKind</name><arg><var>V1</var></arg></funapp></arg><arg><var>V1</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><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>U111</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>U121</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>U131</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>U141</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>U151</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><r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g><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>isBinKind</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><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>isBinKind</name></sharp><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><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>isBagKind</name></sharp><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><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>isBagKind</name></sharp><arg><var>B</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><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>isBagKind</name></sharp><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><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>isBagKind</name></sharp><arg><var>B</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>isBinKind</name></sharp><arg><funapp><name>0</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBinKind</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBinKind</name></sharp><arg><funapp><name>1</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBinKind</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBinKind</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>isBinKind</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBinKind</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>isBinKind</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBinKind</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>isBinKind</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBinKind</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>isBinKind</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBinKind</name></sharp><arg><funapp><name>prod</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBagKind</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBagKind</name></sharp><arg><funapp><name>singl</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBinKind</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBinKind</name></sharp><arg><funapp><name>sum</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBagKind</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBagKind</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>isBagKind</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBagKind</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>isBagKind</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>isBagKind</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>union</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><sharp><name>isBinKind</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>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>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>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>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>mult</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>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><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>isBagKind</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>isBagKind</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBinKind</name></sharp><arg><funapp><name>0</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBinKind</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBinKind</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>isBinKind</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBinKind</name></sharp><arg><funapp><name>1</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBinKind</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBinKind</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>isBinKind</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBinKind</name></sharp><arg><funapp><name>sum</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBagKind</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBinKind</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>isBinKind</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBinKind</name></sharp><arg><funapp><name>prod</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBagKind</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBagKind</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>isBagKind</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBinKind</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>isBinKind</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBagKind</name></sharp><arg><funapp><name>singl</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBinKind</name></sharp><arg><var>V1</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><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><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><name>U12</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U111</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>U12</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U121</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>U131</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>U141</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>U151</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>U161</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>U171</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>U181</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>U191</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>V1</var></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U22</name><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U22</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U23</name><arg><funapp><name>isBag</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U23</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U31</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><name>U32</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U32</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U41</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><name>U42</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U42</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U51</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U52</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U52</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U53</name><arg><funapp><name>isBin</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U53</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U61</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U62</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U62</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U63</name><arg><funapp><name>isBin</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U63</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U71</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><name>U72</name><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U72</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U81</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><name>U82</name><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U82</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U91</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>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>U11</name><arg><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></arg><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>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBagKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBagKind</name><arg><var>V2</var></arg></funapp></arg></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBagKind</name><arg><funapp><name>empty</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBagKind</name><arg><funapp><name>singl</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBinKind</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBagKind</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>isBagKind</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBagKind</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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Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (27 real / 0 unknown / 0 assumptions / 27 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>
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return to TRS_Equational Certified 2019-03-22 08.29