details

property	value
status	complete
benchmark	RENAMED-BOOL_nokinds.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n152.star.cs.uiowa.edu
space	Mixed_AC

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	19.9636 seconds
cpu usage	34.5373
user time	33.0207
system time	1.51655
max virtual memory	1.8457028E7
max residence set size	3642804.0

stage attributes

key	value
certification-result	CERTIFIED
output-size	251906
starexec-result	YES
certification-time	0.7

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" 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lse</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U31</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>true</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U41</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_implies_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><name>U51</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_isEqualTo_</name><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><name>U61</name><arg><funapp><name>and</name><arg><funapp><name>isS</name><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></arg><arg><var>U'</var></arg><arg><var>U</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_isEqualTo_</name><arg><var>U</var></arg><arg><var>U</var></arg></funapp></lhs><rhs><funapp><name>U71</name><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_isNotEqualTo_</name><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><name>U81</name><arg><funapp><name>and</name><arg><funapp><name>isS</name><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></arg><arg><var>U'</var></arg><arg><var>U</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_isNotEqualTo_</name><arg><var>U</var></arg><arg><var>U</var></arg></funapp></lhs><rhs><funapp><name>U91</name><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_or_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><name>U101</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U111</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U121</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></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>equal</name><arg><var>X</var></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>if_then_else_fi</name><arg><var>B</var></arg><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><name>U131</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isS</name><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>B</var></arg><arg><var>U'</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>if_then_else_fi</name><arg><funapp><name>true</name></funapp></arg><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><name>U141</name><arg><funapp><name>and</name><arg><funapp><name>isS</name><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></arg><arg><var>U</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_and_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_implies_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_isEqualTo_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isUniversal</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isUniversal</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_isNotEqualTo_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isUniversal</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isUniversal</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_or_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_xor_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>not_</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>not_</name><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U151</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>not_</name><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>not_</name><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule></rules></trs><Asymbols><name>_and_</name><name>_or_</name><name>_xor_</name></Asymbols><Csymbols><name>_and_</name><name>_or_</name><name>_xor_</name></Csymbols></acRewriteSystem></input><cpfVersion>2.1</cpfVersion><proof><acTerminationProof><acDependencyPairs><equations><rules><rule><lhs><funapp><name>_and_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_or_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>_or_</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><var>x</var></arg><arg><funapp><name>_and_</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_or_</name><arg><funapp><name>_or_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>_or_</name><arg><var>x</var></arg><arg><funapp><name>_or_</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>_xor_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><var>x</var></arg><arg><funapp><name>_xor_</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule></rules></equations><dpEquations><rules><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_or_</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>_or_</name></sharp><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_xor_</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>_xor_</name></sharp><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><var>x</var></arg><arg><funapp><name>_and_</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_or_</name></sharp><arg><funapp><name>_or_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>_or_</name></sharp><arg><var>x</var></arg><arg><funapp><name>_or_</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_xor_</name></sharp><arg><funapp><name>_xor_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>_xor_</name></sharp><arg><var>x</var></arg><arg><funapp><name>_xor_</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><var>y</var></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_or_</name></sharp><arg><funapp><name>_or_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>_or_</name></sharp><arg><var>y</var></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_xor_</name></sharp><arg><funapp><name>_xor_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>_xor_</name></sharp><arg><var>y</var></arg><arg><var>z</var></arg></funapp></rhs></rule></rules></dpEquations><dps><rules><rule><lhs><funapp><sharp><name>U101</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>_xor_</name></sharp><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U101</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>_and_</name></sharp><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U101</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>_xor_</name></sharp><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U131</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>B</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><sharp><name>U132</name></sharp><arg><funapp><name>equal</name><arg><funapp><name>_isNotEqualTo_</name><arg><var>B</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg><arg><var>U'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U131</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>B</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><sharp><name>equal</name></sharp><arg><funapp><name>_isNotEqualTo_</name><arg><var>B</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg><arg><funapp><name>true</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U131</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>B</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><sharp><name>_isNotEqualTo_</name></sharp><arg><var>B</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U151</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><sharp><name>_xor_</name></sharp><arg><var>A</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></lhs><rhs><funapp><sharp><name>_xor_</name></sharp><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>C</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><var>A</var></arg><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>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><var>A</var></arg><arg><var>C</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U51</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>not_</name></sharp><arg><funapp><name>_xor_</name><arg><var>A</var></arg><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U51</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>_xor_</name></sharp><arg><var>A</var></arg><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U51</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>_and_</name></sharp><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>U'</var></arg><arg><var>U</var></arg></funapp></lhs><rhs><funapp><sharp><name>U62</name></sharp><arg><funapp><name>equal</name><arg><funapp><name>_isNotEqualTo_</name><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>U'</var></arg><arg><var>U</var></arg></funapp></lhs><rhs><funapp><sharp><name>equal</name></sharp><arg><funapp><name>_isNotEqualTo_</name><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>true</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>U'</var></arg><arg><var>U</var></arg></funapp></lhs><rhs><funapp><sharp><name>_isNotEqualTo_</name></sharp><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U81</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>U'</var></arg><arg><var>U</var></arg></funapp></lhs><rhs><funapp><sharp><name>if_then_else_fi</name></sharp><arg><funapp><name>_isEqualTo_</name><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>true</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U81</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>U'</var></arg><arg><var>U</var></arg></funapp></lhs><rhs><funapp><sharp><name>_isEqualTo_</name></sharp><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><var>A</var></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><sharp><name>U11</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><var>A</var></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>C</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><sharp><name>U41</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_implies_</name></sharp><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_implies_</name></sharp><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_implies_</name></sharp><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_implies_</name></sharp><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_isEqualTo_</name></sharp><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isS</name><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></arg><arg><var>U'</var></arg><arg><var>U</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_isEqualTo_</name></sharp><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isS</name><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_isEqualTo_</name></sharp><arg><var>U</var></arg><arg><var>U</var></arg></funapp></lhs><rhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_isNotEqualTo_</name></sharp><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><sharp><name>U81</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isS</name><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></arg><arg><var>U'</var></arg><arg><var>U</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_isNotEqualTo_</name></sharp><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isS</name><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_isNotEqualTo_</name></sharp><arg><var>U</var></arg><arg><var>U</var></arg></funapp></lhs><rhs><funapp><sharp><name>U91</name></sharp><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_or_</name></sharp><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>U101</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_or_</name></sharp><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_or_</name></sharp><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_or_</name></sharp><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_xor_</name></sharp><arg><var>A</var></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><sharp><name>U111</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_xor_</name></sharp><arg><var>A</var></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_xor_</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><sharp><name>U121</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_xor_</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if_then_else_fi</name></sharp><arg><var>B</var></arg><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><sharp><name>U131</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isS</name><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>B</var></arg><arg><var>U'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if_then_else_fi</name></sharp><arg><var>B</var></arg><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isS</name><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if_then_else_fi</name></sharp><arg><var>B</var></arg><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if_then_else_fi</name></sharp><arg><var>B</var></arg><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isS</name><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if_then_else_fi</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><sharp><name>U141</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isS</name><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></arg><arg><var>U</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if_then_else_fi</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isS</name><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_and_</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>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_and_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_and_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_implies_</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>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_implies_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_implies_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_isEqualTo_</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>isUniversal</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isUniversal</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_isNotEqualTo_</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>isUniversal</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isUniversal</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_or_</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>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_or_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_or_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_xor_</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>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_xor_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_xor_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>not_</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>not_</name></sharp><arg><var>A</var></arg></funapp></lhs><rhs><funapp><sharp><name>U151</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>not_</name></sharp><arg><var>A</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>U11</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U11</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>C</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>U31</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><funapp><name>true</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>U41</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><funapp><name>true</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U41</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><funapp><name>true</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_or_</name></sharp><arg><funapp><name>_or_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>_or_</name></sharp><arg><funapp><name>U101</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_or_</name></sharp><arg><funapp><name>_or_</name><arg><var>A</var></arg><arg><var>B</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>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_or_</name></sharp><arg><funapp><name>_or_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_or_</name></sharp><arg><funapp><name>_or_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_or_</name></sharp><arg><funapp><name>_or_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_xor_</name></sharp><arg><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>_xor_</name></sharp><arg><funapp><name>U111</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_xor_</name></sharp><arg><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U111</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_xor_</name></sharp><arg><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_xor_</name></sharp><arg><funapp><name>_xor_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>_xor_</name></sharp><arg><funapp><name>U121</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_xor_</name></sharp><arg><funapp><name>_xor_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U121</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_xor_</name></sharp><arg><funapp><name>_xor_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><extensions><rules><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U11</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U31</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><funapp><name>true</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U41</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_or_</name><arg><funapp><name>_or_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_or_</name><arg><funapp><name>U101</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>U111</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>_xor_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>U121</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule></rules></extensions><acDPTerminationProof><acDepGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>_or_</name></sharp><arg><funapp><name>_or_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>_or_</name></sharp><arg><var>y</var></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_or_</name></sharp><arg><funapp><name>_or_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>_or_</name></sharp><arg><funapp><name>U101</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_or_</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>_or_</name></sharp><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_or_</name></sharp><arg><funapp><name>_or_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>_or_</name></sharp><arg><var>x</var></arg><arg><funapp><name>_or_</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><acDPTerminationProof><acRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>2</degree></polynomial></type><interpret><sharp><name>_or_</name></sharp><arity>2</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>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>_or_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</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>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</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>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></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>isBool</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><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>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U11</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>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>_xor_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></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><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>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>true</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>false</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>not_</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>_isEqualTo_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isUniversal</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>_implies_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>_isNotEqualTo_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U111</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>4</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U31</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>_or_</name></sharp><arg><funapp><name>_or_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>_or_</name></sharp><arg><var>y</var></arg><arg><var>z</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>U121</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><var>A</var></rhs></rule><rule><lhs><funapp><name>U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><var>A</var></rhs></rule><rule><lhs><funapp><name>U41</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><var>A</var></rhs></rule><rule><lhs><funapp><name>U101</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U111</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>U21</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>C</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U31</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U31</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><funapp><name>true</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U41</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U11</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>true</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U41</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U31</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_or_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><name>U101</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_or_</name><arg><funapp><name>_or_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_or_</name><arg><funapp><name>U101</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U121</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U111</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>_xor_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>U121</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>U111</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><var>x</var></arg><arg><funapp><name>_and_</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_or_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>_or_</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_or_</name><arg><funapp><name>_or_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>_or_</name><arg><var>x</var></arg><arg><funapp><name>_or_</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>_xor_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><var>x</var></arg><arg><funapp><name>_xor_</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>2</degree></polynomial></type><interpret><sharp><name>_or_</name></sharp><arity>2</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>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>_or_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</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>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</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>2</integer></coefficient></polynomial><polynomial><variable>3</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>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><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isBool</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>_xor_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>false</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</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>U111</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>4</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</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>4</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>_and_</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>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>U41</name><arity>2</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></sum></polynomial></interpret><interpret><name>U31</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>true</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>not_</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>_isEqualTo_</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>isUniversal</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>_implies_</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>_isNotEqualTo_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><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>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>_or_</name></sharp><arg><funapp><name>_or_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>_or_</name></sharp><arg><funapp><name>U101</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U121</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U111</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>_xor_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>U121</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>U111</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></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>U21</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>C</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U111</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>U121</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><var>A</var></rhs></rule><rule><lhs><funapp><name>U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><var>A</var></rhs></rule><rule><lhs><funapp><name>U41</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><var>A</var></rhs></rule><rule><lhs><funapp><name>U31</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_xor_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>not_</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_isEqualTo_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isUniversal</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isUniversal</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_implies_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_isNotEqualTo_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isUniversal</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isUniversal</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_or_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_and_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U31</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><funapp><name>true</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U41</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U11</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>true</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U41</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U31</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U101</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_or_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><name>U101</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_or_</name><arg><funapp><name>_or_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_or_</name><arg><funapp><name>U101</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>_xor_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><var>x</var></arg><arg><funapp><name>_xor_</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><var>x</var></arg><arg><funapp><name>_and_</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_or_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>_or_</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_or_</name><arg><funapp><name>_or_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>_or_</name><arg><var>x</var></arg><arg><funapp><name>_or_</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><component><dps><rules><rule><lhs><funapp><sharp><name>_or_</name></sharp><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>U101</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_or_</name></sharp><arg><funapp><name>_or_</name><arg><var>A</var></arg><arg><var>B</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>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U101</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>_xor_</name></sharp><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U101</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>_and_</name></sharp><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U101</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>_xor_</name></sharp><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U81</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>U'</var></arg><arg><var>U</var></arg></funapp></lhs><rhs><funapp><sharp><name>if_then_else_fi</name></sharp><arg><funapp><name>_isEqualTo_</name><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>true</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>if_then_else_fi</name></sharp><arg><var>B</var></arg><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><sharp><name>U131</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isS</name><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>B</var></arg><arg><var>U'</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U131</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>B</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><sharp><name>U132</name></sharp><arg><funapp><name>equal</name><arg><funapp><name>_isNotEqualTo_</name><arg><var>B</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg><arg><var>U'</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U131</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>B</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><sharp><name>equal</name></sharp><arg><funapp><name>_isNotEqualTo_</name><arg><var>B</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg><arg><funapp><name>true</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U131</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>B</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><sharp><name>_isNotEqualTo_</name></sharp><arg><var>B</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_implies_</name></sharp><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U51</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>not_</name></sharp><arg><funapp><name>_xor_</name><arg><var>A</var></arg><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>not_</name></sharp><arg><var>A</var></arg></funapp></lhs><rhs><funapp><sharp><name>U151</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U151</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><sharp><name>_xor_</name></sharp><arg><var>A</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><var>A</var></arg><arg><var>C</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>U11</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>U31</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><funapp><name>true</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>U41</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><var>y</var></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><var>x</var></arg><arg><funapp><name>_and_</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><acDPTerminationProof><acRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>2</degree></polynomial></type><interpret><sharp><name>_and_</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>_and_</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>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>isBool</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>_xor_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>4</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>2</variable></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>U21</name></sharp><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>4</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>false</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U31</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>true</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>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>U111</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>not_</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>_isEqualTo_</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>isUniversal</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>_implies_</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>_isNotEqualTo_</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>_or_</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></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><funapp><name>true</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>U41</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><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>U31</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>U111</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U121</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U111</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>_xor_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>U121</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>U111</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></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>A</var></arg></funapp></lhs><rhs><var>A</var></rhs></rule><rule><lhs><funapp><name>U41</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><var>A</var></rhs></rule><rule><lhs><funapp><name>U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><var>A</var></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U31</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><funapp><name>true</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U41</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U11</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>true</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U41</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U31</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_xor_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>not_</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_isEqualTo_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isUniversal</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isUniversal</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_implies_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_isNotEqualTo_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isUniversal</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isUniversal</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_or_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_and_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U21</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>C</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>_xor_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><var>x</var></arg><arg><funapp><name>_xor_</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><var>x</var></arg><arg><funapp><name>_and_</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></usableRules><acDPTerminationProof><acDepGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><var>A</var></arg><arg><var>C</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>U11</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>U31</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><var>y</var></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><var>x</var></arg><arg><funapp><name>_and_</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><acDPTerminationProof><acRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>2</degree></polynomial></type><interpret><sharp><name>_and_</name></sharp><arity>2</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>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>_and_</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>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>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>isBool</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>_xor_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>4</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</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>4</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>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>false</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U31</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>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></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>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>true</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>not_</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>_isEqualTo_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isUniversal</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>_implies_</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><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>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>_isNotEqualTo_</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>_or_</name><arity>2</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>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U111</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>_and_</name></sharp><arg><funapp><name>_and_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>U31</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>U31</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>U21</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>C</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U41</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><var>A</var></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>U121</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><var>A</var></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_xor_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>not_</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_isEqualTo_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isUniversal</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isUniversal</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_implies_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_isNotEqualTo_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isUniversal</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isUniversal</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_or_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_and_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U111</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><var>A</var></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U121</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U111</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>_xor_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>U121</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>U111</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U31</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><funapp><name>true</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U41</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U11</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>true</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U41</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U31</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>_xor_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><var>x</var></arg><arg><funapp><name>_xor_</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><var>x</var></arg><arg><funapp><name>_and_</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>_and_</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>3</degree></polynomial></type><interpret><sharp><name>_and_</name></sharp><arity>2</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>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>_and_</name><arity>2</arity><polynomial><sum><polynomial><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>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</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>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isBool</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>_xor_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>4</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</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>4</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>false</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>U111</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>true</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>not_</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>_isEqualTo_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isUniversal</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>_implies_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>_isNotEqualTo_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>_or_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U31</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><var>y</var></arg><arg><var>z</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U121</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U111</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>_xor_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>U121</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>U111</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><var>A</var></rhs></rule><rule><lhs><funapp><name>U21</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>C</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U121</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><var>A</var></rhs></rule><rule><lhs><funapp><name>U111</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_xor_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>not_</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_isEqualTo_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isUniversal</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isUniversal</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_implies_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_isNotEqualTo_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isUniversal</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isUniversal</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_or_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_and_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U31</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>U41</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><var>A</var></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>_and_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U31</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><funapp><name>true</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U41</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U11</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>true</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U41</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U31</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>_xor_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><var>x</var></arg><arg><funapp><name>_xor_</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><var>x</var></arg><arg><funapp><name>_and_</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>_and_</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>2</degree></polynomial></type><interpret><sharp><name>_and_</name></sharp><arity>2</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>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>_and_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</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>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isBool</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>_xor_</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><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>4</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>3</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>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>4</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>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>true</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>false</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>not_</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>_isEqualTo_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isUniversal</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>_implies_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>_isNotEqualTo_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>_or_</name><arity>2</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>U31</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U111</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>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>U11</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>isBool</name><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_xor_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>not_</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_isEqualTo_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isUniversal</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isUniversal</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_implies_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_isNotEqualTo_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isUniversal</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isUniversal</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_or_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_and_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U121</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><var>A</var></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>U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><var>A</var></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U31</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><funapp><name>true</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U41</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U11</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>true</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U41</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U31</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U121</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U111</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>_xor_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>U121</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>U111</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U111</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>U41</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><var>A</var></rhs></rule><rule><lhs><funapp><name>U21</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>C</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U31</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><var>x</var></arg><arg><funapp><name>_and_</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>_xor_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><var>x</var></arg><arg><funapp><name>_xor_</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>2</degree></polynomial></type><interpret><sharp><name>_and_</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>_and_</name><arity>2</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>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>_xor_</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><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>4</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>3</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>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isBool</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U111</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>false</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U31</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><product><polynomial><coefficient><integer>2</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>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>true</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>not_</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>_isEqualTo_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isUniversal</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>_implies_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>_isNotEqualTo_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>_or_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></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></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>U31</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><var>A</var></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U121</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U111</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>_xor_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>U121</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>U111</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U41</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><var>A</var></rhs></rule><rule><lhs><funapp><name>U21</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>C</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U121</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><var>A</var></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>isBool</name><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_xor_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>not_</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_isEqualTo_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isUniversal</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isUniversal</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_implies_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_isNotEqualTo_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isUniversal</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isUniversal</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_or_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_and_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U31</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><funapp><name>true</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U41</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U11</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>true</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U41</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U31</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>_xor_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><var>x</var></arg><arg><funapp><name>_xor_</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><var>x</var></arg><arg><funapp><name>_and_</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></usableRules><acDPTerminationProof><acTrivialProc/></acDPTerminationProof></acRedPairProc></acDPTerminationProof></acRedPairProc></acDPTerminationProof></acRedPairProc></acDPTerminationProof></acRedPairProc></acDPTerminationProof></component></acDepGraphProc></acDPTerminationProof></acRedPairProc></acDPTerminationProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></lhs><rhs><funapp><sharp><name>_xor_</name></sharp><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>C</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>_xor_</name></sharp><arg><var>A</var></arg><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U81</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>U'</var></arg><arg><var>U</var></arg></funapp></lhs><rhs><funapp><sharp><name>_isEqualTo_</name></sharp><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_isEqualTo_</name></sharp><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isS</name><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></arg><arg><var>U'</var></arg><arg><var>U</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>U'</var></arg><arg><var>U</var></arg></funapp></lhs><rhs><funapp><sharp><name>U62</name></sharp><arg><funapp><name>equal</name><arg><funapp><name>_isNotEqualTo_</name><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>U'</var></arg><arg><var>U</var></arg></funapp></lhs><rhs><funapp><sharp><name>equal</name></sharp><arg><funapp><name>_isNotEqualTo_</name><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>true</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>U'</var></arg><arg><var>U</var></arg></funapp></lhs><rhs><funapp><sharp><name>_isNotEqualTo_</name></sharp><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><var>A</var></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><sharp><name>U11</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><var>A</var></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>B</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>C</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><sharp><name>U41</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_implies_</name></sharp><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBool</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>_implies_</name></sharp><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_implies_</name></sharp><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>B</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_isEqualTo_</name></sharp><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isS</name><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_isEqualTo_</name></sharp><arg><var>U</var></arg><arg><var>U</var></arg></funapp></lhs><rhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_isNotEqualTo_</name></sharp><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><sharp><name>U81</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isS</name><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></arg><arg><var>U'</var></arg><arg><var>U</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_isNotEqualTo_</name></sharp><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isS</name><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_isNotEqualTo_</name></sharp><arg><var>U</var></arg><arg><var>U</var></arg></funapp></lhs><rhs><funapp><sharp><name>U91</name></sharp><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_or_</name></sharp><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBool</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>_or_</name></sharp><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_or_</name></sharp><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>B</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_xor_</name></sharp><arg><funapp><name>_xor_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>_xor_</name></sharp><arg><funapp><name>U121</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_xor_</name></sharp><arg><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>_xor_</name></sharp><arg><funapp><name>U111</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_xor_</name></sharp><arg><funapp><name>_xor_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>_xor_</name></sharp><arg><var>y</var></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_xor_</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>_xor_</name></sharp><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_xor_</name></sharp><arg><funapp><name>_xor_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>_xor_</name></sharp><arg><var>x</var></arg><arg><funapp><name>_xor_</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>_xor_</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>_xor_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U111</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isBool</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>false</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</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>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>_isEqualTo_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isUniversal</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>_implies_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>_isNotEqualTo_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>_or_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>true</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>_and_</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>not_</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>_xor_</name></sharp><arg><funapp><name>_xor_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>_xor_</name></sharp><arg><var>y</var></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_xor_</name></sharp><arg><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>_xor_</name></sharp><arg><funapp><name>U111</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>_xor_</name></sharp><arg><funapp><name>_xor_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>_xor_</name></sharp><arg><funapp><name>U121</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>U121</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><var>A</var></rhs></rule><rule><lhs><funapp><name>U111</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U121</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U111</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>_xor_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>U121</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>U111</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>_xor_</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><var>x</var></arg><arg><funapp><name>_xor_</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><acDPTerminationProof><acTrivialProc/></acDPTerminationProof></acRedPairProc></acDPTerminationProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>_xor_</name></sharp><arg><var>A</var></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><sharp><name>U111</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_xor_</name></sharp><arg><var>A</var></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_xor_</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><sharp><name>U121</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_xor_</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>if_then_else_fi</name></sharp><arg><var>B</var></arg><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isS</name><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>if_then_else_fi</name></sharp><arg><var>B</var></arg><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>B</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>if_then_else_fi</name></sharp><arg><var>B</var></arg><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isS</name><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>if_then_else_fi</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><sharp><name>U141</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isS</name><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></arg><arg><var>U</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>if_then_else_fi</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isS</name><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>not_</name></sharp><arg><var>A</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>B</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>C</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><funapp><name>true</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_or_</name></sharp><arg><funapp><name>_or_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_or_</name></sharp><arg><funapp><name>_or_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>B</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_xor_</name></sharp><arg><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_xor_</name></sharp><arg><funapp><name>_xor_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_and_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_and_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_implies_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_implies_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_or_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_or_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_xor_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_xor_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>not_</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</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><sharp><name>isBool</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>_and_</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>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>_implies_</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>not_</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>_or_</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>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>_xor_</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></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_and_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_implies_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_implies_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>not_</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_and_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_or_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_xor_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_or_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_xor_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBool</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>U101</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><var>A</var></rhs></rule><rule><lhs><funapp><name>U111</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>U121</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><var>A</var></rhs></rule><rule><lhs><funapp><name>U131</name><arg><funapp><name>tt</name></funapp></arg><arg><var>B</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><name>U132</name><arg><funapp><name>equal</name><arg><funapp><name>_isNotEqualTo_</name><arg><var>B</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg><arg><var>U'</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U132</name><arg><funapp><name>tt</name></funapp></arg><arg><var>U'</var></arg></funapp></lhs><rhs><var>U'</var></rhs></rule><rule><lhs><funapp><name>U141</name><arg><funapp><name>tt</name></funapp></arg><arg><var>U</var></arg></funapp></lhs><rhs><var>U</var></rhs></rule><rule><lhs><funapp><name>U151</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><var>A</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U21</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>C</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U31</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>U41</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><var>A</var></rhs></rule><rule><lhs><funapp><name>U51</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><name>not_</name><arg><funapp><name>_xor_</name><arg><var>A</var></arg><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U61</name><arg><funapp><name>tt</name></funapp></arg><arg><var>U'</var></arg><arg><var>U</var></arg></funapp></lhs><rhs><funapp><name>U62</name><arg><funapp><name>equal</name><arg><funapp><name>_isNotEqualTo_</name><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U62</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>U71</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>U81</name><arg><funapp><name>tt</name></funapp></arg><arg><var>U'</var></arg><arg><var>U</var></arg></funapp></lhs><rhs><funapp><name>if_then_else_fi</name><arg><funapp><name>_isEqualTo_</name><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>false</name></funapp></arg><arg><funapp><name>true</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U91</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U31</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>true</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U41</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_implies_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><name>U51</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_isEqualTo_</name><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><name>U61</name><arg><funapp><name>and</name><arg><funapp><name>isS</name><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></arg><arg><var>U'</var></arg><arg><var>U</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_isEqualTo_</name><arg><var>U</var></arg><arg><var>U</var></arg></funapp></lhs><rhs><funapp><name>U71</name><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_isNotEqualTo_</name><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><name>U81</name><arg><funapp><name>and</name><arg><funapp><name>isS</name><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></arg><arg><var>U'</var></arg><arg><var>U</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_isNotEqualTo_</name><arg><var>U</var></arg><arg><var>U</var></arg></funapp></lhs><rhs><funapp><name>U91</name><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_or_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><name>U101</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U111</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U121</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></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>equal</name><arg><var>X</var></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>if_then_else_fi</name><arg><var>B</var></arg><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><name>U131</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isS</name><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>B</var></arg><arg><var>U'</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>if_then_else_fi</name><arg><funapp><name>true</name></funapp></arg><arg><var>U</var></arg><arg><var>U'</var></arg></funapp></lhs><rhs><funapp><name>U141</name><arg><funapp><name>and</name><arg><funapp><name>isS</name><arg><var>U'</var></arg></funapp></arg><arg><funapp><name>isS</name><arg><var>U</var></arg></funapp></arg></funapp></arg><arg><var>U</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_and_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_implies_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_isEqualTo_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isUniversal</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isUniversal</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_isNotEqualTo_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isUniversal</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isUniversal</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_or_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>_xor_</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBool</name><arg><funapp><name>not_</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isBool</name><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>not_</name><arg><var>A</var></arg></funapp></lhs><rhs><funapp><name>U151</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>not_</name><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>not_</name><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U11</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U21</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U31</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_and_</name><arg><funapp><name>_and_</name><arg><funapp><name>true</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_and_</name><arg><funapp><name>U41</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_or_</name><arg><funapp><name>_or_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_or_</name><arg><funapp><name>U101</name><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>U111</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>_xor_</name><arg><funapp><name>_xor_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>_xor_</name><arg><funapp><name>U121</name><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule></rules></trs><usableRules><rules/></usableRules><acDPTerminationProof><acTrivialProc/></acDPTerminationProof></acMonoRedPairProc></acDPTerminationProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_and_</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>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_implies_</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>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_isEqualTo_</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>isUniversal</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isUniversal</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_isNotEqualTo_</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>isUniversal</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isUniversal</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_or_</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>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>isBool</name></sharp><arg><funapp><name>_xor_</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>isBool</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U11</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><var>A</var></arg><arg><funapp><name>_xor_</name><arg><var>B</var></arg><arg><var>C</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBool</name><arg><var>B</var></arg></funapp></arg><arg><funapp><name>isBool</name><arg><var>C</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_and_</name></sharp><arg><funapp><name>_and_</name><arg><funapp><name>true</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U41</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_or_</name></sharp><arg><funapp><name>_or_</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>isBool</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>_xor_</name></sharp><arg><funapp><name>_xor_</name><arg><var>A</var></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U111</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>_xor_</name></sharp><arg><funapp><name>_xor_</name><arg><funapp><name>false</name></funapp></arg><arg><var>A</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U121</name></sharp><arg><funapp><name>isBool</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></acDepGraphProc></acDPTerminationProof></acDependencyPairs></acTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (16 real / 0 unknown / 0 assumptions / 16 total proof steps)</strategy><url>http://aprove.informatik.rwth-aachen.de</url></tool><toolUser><firstName>John</firstName><lastName>Doe</lastName></toolUser></proofOrigin><inputOrigin/></origin></certificationProblem> popout

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all output return to TRS_Equational Certified 2019-03-22 08.29