details

property	value
status	complete
benchmark	Ex16_Luc06_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n012.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	27.4688060284 seconds
cpu usage	73.80006319
max memory	4.24321024E9

stage attributes

key	value
certification-result	CERTIFIED
output-size	335845
starexec-result	YES
certification-time	0.6

output

/export/starexec/sandbox2/solver/bin/starexec_run_certified /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES <?xml version="1.0" encoding="UTF-8" standalone="no"?><?xml-stylesheet type="text/xsl" href="cpfHTML.xsl"?><certificationProblem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" 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ame><arg><funapp><name>a</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>b</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>b</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>f</name><arg><var>X</var></arg><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>f</name><arg><funapp><name>a</name></funapp></arg><arg><funapp><name>b</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>b</name></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>a</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>proper</name><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>a</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>a</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>b</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>b</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>f</name><arg><var>X</var></arg><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>f</name><arg><funapp><name>a</name></funapp></arg><arg><funapp><name>b</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>b</name></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>a</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule></rules></usableRules><dpProof><narrowingProc><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><positionInTerm><position>1</position></positionInTerm><narrowings><rules><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><funapp><name>f</name><arg><funapp><name>a</name></funapp></arg><arg><funapp><name>b</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>b</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>f</name><arg><funapp><name>active</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></narrowings><dpProof><narrowingProc><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><positionInTerm><position>1</position></positionInTerm><narrowings><rules><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>f</name><arg><funapp><name>proper</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><funapp><name>b</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>b</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></narrowings><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>f</name><arg><funapp><name>proper</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><funapp><name>f</name><arg><funapp><name>a</name></funapp></arg><arg><funapp><name>b</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>f</name><arg><funapp><name>active</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><splitProc><dps><rules><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><funapp><name>f</name><arg><funapp><name>a</name></funapp></arg><arg><funapp><name>b</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules/></trs><dpProof><semlabProc><model><finiteModel><carrierSize>2</carrierSize><interpret><name>active</name><arity>1</arity><arithFunction><natural>0</natural></arithFunction></interpret><interpret><name>a</name><arity>0</arity><arithFunction><natural>1</natural></arithFunction></interpret><interpret><name>b</name><arity>0</arity><arithFunction><natural>0</natural></arithFunction></interpret><interpret><name>proper</name><arity>1</arity><arithFunction><natural>0</natural></arithFunction></interpret><interpret><name>f</name><arity>2</arity><arithFunction><natural>0</natural></arithFunction></interpret><interpret><sharp><name>top</name></sharp><arity>1</arity><arithFunction><natural>0</natural></arithFunction></interpret><interpret><name>ok</name><arity>1</arity><arithFunction><natural>0</natural></arithFunction></interpret><interpret><name>mark</name><arity>1</arity><arithFunction><natural>0</natural></arithFunction></interpret></finiteModel></model><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel>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rg><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule></rules></trs><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><redPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><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><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><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><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><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><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><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><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><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><labeledSymbol><name>a</name><numberLabel/></labeledSymbol><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>b</name><numberLabel/></labeledSymbol><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><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><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arity>1<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ol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><redPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><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><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>a</name><numberLabel/></labeledSymbol><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>b</name><numberLabel/></labeledSymbol><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><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><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><dpProof><pIsEmpty/></dpProof></redPairProc></dpProof></redPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></semlabProc></dpProof><dpProof><splitProc><dps><rules/></dps><trs><rules><rule><lhs><funapp><name>active</name><arg><funapp><name>b</name></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>a</name></funapp></arg></funapp></rhs></rule></rules></trs><dpProof><semlabProc><model><finiteModel><carrierSize>2</carrierSize><interpret><name>active</name><arity>1</arity><arithFunction><natural>0</natural></arithFunction></interpret><interpret><name>a</name><arity>0</arity><arithFunction><natural>0</natural></arithFunction></interpret><interpret><name>b</name><arity>0</arity><arithFunction><natural>1</natural></arithFunction></interpret><interpret><name>proper</name><arity>1</arity><arithFunction><natural>0</natural></arithFunction></interpret><interpret><name>f</name><arity>2</arity><arithFunction><product><arithFunction><natural>1</natural></arithFunction><arithFunction><variable>1</variable></arithFunction></product></arithFunction></interpret><interpret><sharp><name>top</name></sharp><arity>1</arity><arithFunction><natural>0</natural></arithFunction></interpret><interpret><name>ok</name><arity>1</arity><arithFunction><natural>0</natural></arithFunction></interpret><interpret><name>mark</name><arity>1</arity><arithFunction><natural>0</natural></arithFunction></interpret></finiteModel></model><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X</var></arg><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X</var></arg><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule></rules></trs><dpProof><monoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><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><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><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><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>a</name><numberLabel/></labeledSymbol><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><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><labeledSymbol><name>b</name><numberLabel/></labeledSymbol><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><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><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><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><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><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><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><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><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X</var></arg><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X</var></arg><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule></rules></trs><dpProof><redPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><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><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><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><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><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><labeledSymbol><name>a</name><numberLabel/></labeledSymbol><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>b</name><numberLabel/></labeledSymbol><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><dpProof><monoRedPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><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><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><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><labeledSymbol><name>a</name><numberLabel/></labeledSymbol><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><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><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>b</name><numberLabel/></labeledSymbol><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><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><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><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><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><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><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><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><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg>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l><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X</var></arg><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule></rules></usableRules><dpProof><pIsEmpty/></dpProof></monoRedPairUrProc></dpProof></redPairProc></dpProof></monoRedPairProc></dpProof></semlabProc></dpProof><dpProof><semlabProc><model><finiteModel><carrierSize>2</carrierSize><interpret><name>active</name><arity>1</arity><arithFunction><natural>0</natural></arithFunction></interpret><interpret><name>a</name><arity>0</arity><arithFunction><natural>1</natural></arithFunction></interpret><interpret><name>b</name><arity>0</arity><arithFunction><natural>0</natural></arithFunction></interpret><interpret><name>proper</name><arity>1</arity><arithFunction><natural>0</natural></arithFunction></interpret><interpret><name>f</name><arity>2</arity><arithFunction><product><arithFunction><natural>1</natural></arithFunction><arithFunction><variable>1</variable></arithFunction></product></arithFunction></interpret><interpret><sharp><name>top</name></sharp><arity>1</arity><arithFunction><natural>0</natural></arithFunction></interpret><interpret><name>ok</name><arity>1</arity><arithFunction><natural>0</natural></arithFunction></interpret><interpret><name>mark</name><arity>1</arity><arithFunction><natural>0</natural></arithFunction></interpret></finiteModel></model><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X</var></arg><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X</var></arg><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule></rules></trs><dpProof><monoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><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><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><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><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>a</name><numberLabel/></labeledSymbol><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><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><labeledSymbol><name>b</name><numberLabel/></labeledSymbol><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><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><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><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>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ar></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X</var></arg><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X</var></arg><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule></rules></trs><dpProof><redPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><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><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><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><labeledSymbol><name>active</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>a</name><numberLabel/></labeledSymbol><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>b</name><numberLabel/></labeledSymbol><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><dpProof><monoRedPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coeffici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p><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol>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Symbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X</var></arg><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSym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numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel/></labeledSymbol></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule></rules></trs><dpProof><monoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><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><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>a</name><numberLabel/></labeledSymbol><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>ok</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><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><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><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><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>b</name><numberLabel/></labeledSymbol><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><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><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>top</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x0</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numb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l></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>active</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule></rules></trs><dpProof><monoRedPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><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><labeledSymbol><name>f</name><numberLabel><number>1</number><number>0</number></numberLabel></labeledSymbol><arity>2</arity><polynomial><sum><polynomial><coeffi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bol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>mark</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>1</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>1</number></numberLabel></labeledSymbol><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><numberLabel><number>0</number><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>X1</var></arg></funapp></arg><arg><funapp><labeledSymbol><name>proper</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>proper</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>ok</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel/></labeledSymbol></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><pIsEmpty/></dpProof></monoRedPairUrProc></dpProof></monoRedPairProc></dpProof></monoRedPairProc></dpProof></monoRedPairUrProc></dpProof></redPairProc></dpProof></monoRedPairProc></dpProof></semlabProc></dpProof></splitProc></dpProof></splitProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><funapp><name>b</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>b</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>b</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><funapp><name>a</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></narrowingProc></dpProof></narrowingProc></dpProof></monoRedPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>active</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>top</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>proper</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>active</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><monoRedPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>f</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>active</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>active</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule></rules></dps><trs><rules/></trs><usableRules><rules/></usableRules><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>active</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></monoRedPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>proper</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>proper</name></sharp><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>proper</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>proper</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><monoRedPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>f</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>proper</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>proper</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>proper</name></sharp><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>proper</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>proper</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule></rules></dps><trs><rules/></trs><usableRules><rules/></usableRules><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>proper</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>proper</name></sharp><arg><var>X2</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>proper</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>proper</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></monoRedPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>f</name><arg><var>X</var></arg><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>a</name></funapp></arg><arg><funapp><name>b</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>proper</name></sharp><arg><funapp><name>f</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><monoRedPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>ok</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>mark</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>f</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule></rules></dps><trs><rules/></trs><usableRules><rules/></usableRules><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge><edge><position>2</position><strict>true</strict><position>2</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge><edge><position>2</position><strict>false</strict><position>2</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></monoRedPairUrProc></dpProof></component></depGraphProc></dpProof></dpTrans></trsTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (32 real / 0 unknown / 0 assumptions / 32 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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