details

property	value
status	complete
benchmark	14.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n111.star.cs.uiowa.edu
space	Various_04

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	3.28379321098 seconds
cpu usage	9.132655788
max memory	6.54053376E8

stage attributes

key	value
certification-result	CERTIFIED
output-size	166057
starexec-result	YES
certification-time	0.3

output

/export/starexec/sandbox/solver/bin/starexec_run_certified /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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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app></arg></funapp></arg><arg><funapp><name>BS</name><arg><funapp><name>r</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>Size</name><arg><funapp><name>L</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>Size</name><arg><funapp><name>N</name><arg><var>x</var></arg><arg><funapp><name>l</name></funapp></arg><arg><funapp><name>r</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>+</name><arg><funapp><name>+</name><arg><funapp><name>Size</name><arg><funapp><name>l</name></funapp></arg></funapp></arg><arg><funapp><name>Size</name><arg><funapp><name>r</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>1</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>WB</name><arg><funapp><name>L</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>WB</name><arg><funapp><name>N</name><arg><var>x</var></arg><arg><funapp><name>l</name></funapp></arg><arg><funapp><name>r</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>if</name><arg><funapp><name>ge</name><arg><funapp><name>Size</name><arg><funapp><name>l</name></funapp></arg></funapp></arg><arg><funapp><name>Size</name><arg><funapp><name>r</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>ge</name><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>-</name><arg><funapp><name>Size</name><arg><funapp><name>l</name></funapp></arg></funapp></arg><arg><funapp><name>Size</name><arg><funapp><name>r</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>ge</name><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>-</name><arg><funapp><name>Size</name><arg><funapp><name>r</name></funapp></arg></funapp></arg><arg><funapp><name>Size</name><arg><funapp><name>l</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>WB</name><arg><funapp><name>l</name></funapp></arg></funapp></arg><arg><funapp><name>WB</name><arg><funapp><name>r</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>O</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>+</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>I</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>-</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>not</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>true</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>false</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>if</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>ge</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>Log'</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>Log</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>Val</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>L</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>N</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>l</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>r</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>Min</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>Max</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>BS</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>Size</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>WB</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></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>O</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>+</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>O</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>O</name><arg><funapp><name>+</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><var>x</var></arg><arg><funapp><name>+</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>+</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>O</name><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>-</name><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>1</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>O</name><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>not</name><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>not</name><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>if</name><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>if</name><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>y</var></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ge</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>not</name><arg><funapp><name>ge</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ge</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ge</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ge</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>Log'</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>Log'</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>+</name><arg><funapp><name>Log'</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>Log'</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>if</name><arg><funapp><name>ge</name><arg><var>x</var></arg><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>+</name><arg><funapp><name>Log'</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>Val</name><arg><funapp><name>L</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>Val</name><arg><funapp><name>N</name><arg><var>x</var></arg><arg><funapp><name>l</name></funapp></arg><arg><funapp><name>r</name></funapp></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>Min</name><arg><funapp><name>L</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>Min</name><arg><funapp><name>N</name><arg><var>x</var></arg><arg><funapp><name>l</name></funapp></arg><arg><funapp><name>r</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>Min</name><arg><funapp><name>l</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>Max</name><arg><funapp><name>L</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>Max</name><arg><funapp><name>N</name><arg><var>x</var></arg><arg><funapp><name>l</name></funapp></arg><arg><funapp><name>r</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>Max</name><arg><funapp><name>r</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>BS</name><arg><funapp><name>L</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>BS</name><arg><funapp><name>N</name><arg><var>x</var></arg><arg><funapp><name>l</name></funapp></arg><arg><funapp><name>r</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>ge</name><arg><var>x</var></arg><arg><funapp><name>Max</name><arg><funapp><name>l</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>ge</name><arg><funapp><name>Min</name><arg><funapp><name>r</name></funapp></arg></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>BS</name><arg><funapp><name>l</name></funapp></arg></funapp></arg><arg><funapp><name>BS</name><arg><funapp><name>r</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>Size</name><arg><funapp><name>L</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>Size</name><arg><funapp><name>N</name><arg><var>x</var></arg><arg><funapp><name>l</name></funapp></arg><arg><funapp><name>r</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>+</name><arg><funapp><name>+</name><arg><funapp><name>Size</name><arg><funapp><name>l</name></funapp></arg></funapp></arg><arg><funapp><name>Size</name><arg><funapp><name>r</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>1</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>WB</name><arg><funapp><name>L</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>WB</name><arg><funapp><name>N</name><arg><var>x</var></arg><arg><funapp><name>l</name></funapp></arg><arg><funapp><name>r</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>if</name><arg><funapp><name>ge</name><arg><funapp><name>Size</name><arg><funapp><name>l</name></funapp></arg></funapp></arg><arg><funapp><name>Size</name><arg><funapp><name>r</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>ge</name><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>-</name><arg><funapp><name>Size</name><arg><funapp><name>l</name></funapp></arg></funapp></arg><arg><funapp><name>Size</name><arg><funapp><name>r</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>ge</name><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>-</name><arg><funapp><name>Size</name><arg><funapp><name>r</name></funapp></arg></funapp></arg><arg><funapp><name>Size</name><arg><funapp><name>l</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>WB</name><arg><funapp><name>l</name></funapp></arg></funapp></arg><arg><funapp><name>WB</name><arg><funapp><name>r</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>O</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>+</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>I</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>-</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>not</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>true</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>false</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>if</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>ge</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>Log'</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>Val</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>L</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>N</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>l</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>r</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>Min</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>Max</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>BS</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>Size</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>WB</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></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>O</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>+</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>O</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>O</name><arg><funapp><name>+</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><var>x</var></arg><arg><funapp><name>+</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>+</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>O</name><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>-</name><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>1</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>O</name><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>not</name><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>not</name><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>if</name><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>if</name><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>y</var></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ge</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>not</name><arg><funapp><name>ge</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ge</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ge</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ge</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>Log'</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>Log'</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>+</name><arg><funapp><name>Log'</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>Log'</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>if</name><arg><funapp><name>ge</name><arg><var>x</var></arg><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>+</name><arg><funapp><name>Log'</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>Min</name><arg><funapp><name>L</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>Min</name><arg><funapp><name>N</name><arg><var>x</var></arg><arg><funapp><name>l</name></funapp></arg><arg><funapp><name>r</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>Min</name><arg><funapp><name>l</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>Max</name><arg><funapp><name>L</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>Max</name><arg><funapp><name>N</name><arg><var>x</var></arg><arg><funapp><name>l</name></funapp></arg><arg><funapp><name>r</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>Max</name><arg><funapp><name>r</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>BS</name><arg><funapp><name>L</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>BS</name><arg><funapp><name>N</name><arg><var>x</var></arg><arg><funapp><name>l</name></funapp></arg><arg><funapp><name>r</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>ge</name><arg><var>x</var></arg><arg><funapp><name>Max</name><arg><funapp><name>l</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>ge</name><arg><funapp><name>Min</name><arg><funapp><name>r</name></funapp></arg></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>BS</name><arg><funapp><name>l</name></funapp></arg></funapp></arg><arg><funapp><name>BS</name><arg><funapp><name>r</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>Size</name><arg><funapp><name>L</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>Size</name><arg><funapp><name>N</name><arg><var>x</var></arg><arg><funapp><name>l</name></funapp></arg><arg><funapp><name>r</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>+</name><arg><funapp><name>+</name><arg><funapp><name>Size</name><arg><funapp><name>l</name></funapp></arg></funapp></arg><arg><funapp><name>Size</name><arg><funapp><name>r</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>1</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>WB</name><arg><funapp><name>L</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>WB</name><arg><funapp><name>N</name><arg><var>x</var></arg><arg><funapp><name>l</name></funapp></arg><arg><funapp><name>r</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>if</name><arg><funapp><name>ge</name><arg><funapp><name>Size</name><arg><funapp><name>l</name></funapp></arg></funapp></arg><arg><funapp><name>Size</name><arg><funapp><name>r</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>ge</name><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>-</name><arg><funapp><name>Size</name><arg><funapp><name>l</name></funapp></arg></funapp></arg><arg><funapp><name>Size</name><arg><funapp><name>r</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>ge</name><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>-</name><arg><funapp><name>Size</name><arg><funapp><name>r</name></funapp></arg></funapp></arg><arg><funapp><name>Size</name><arg><funapp><name>l</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>and</name><arg><funapp><name>WB</name><arg><funapp><name>l</name></funapp></arg></funapp></arg><arg><funapp><name>WB</name><arg><funapp><name>r</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>O</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>+</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>I</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>-</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>not</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>true</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>false</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>if</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>ge</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>Log'</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>Min</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>L</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>N</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>l</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>r</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>Max</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>BS</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>Size</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>WB</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></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>O</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>+</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>O</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>O</name><arg><funapp><name>+</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><var>x</var></arg><arg><funapp><name>+</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>+</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>O</name><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>-</name><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>1</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>O</name><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>not</name><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>not</name><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>if</name><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>if</name><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>y</var></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ge</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>not</name><arg><funapp><name>ge</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ge</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ge</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ge</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>Log'</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>Log'</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>+</name><arg><funapp><name>Log'</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>Log'</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>if</name><arg><funapp><name>ge</name><arg><var>x</var></arg><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>+</name><arg><funapp><name>Log'</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>Min</name><arg><funapp><name>L</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>BS</name><arg><funapp><name>L</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>Size</name><arg><funapp><name>L</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>WB</name><arg><funapp><name>L</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>O</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>+</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>I</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>-</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>not</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>true</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>false</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>if</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>ge</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>Log'</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>Min</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>L</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>BS</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>Size</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>WB</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>O</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>+</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>O</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>O</name><arg><funapp><name>+</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><var>x</var></arg><arg><funapp><name>+</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>+</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>O</name><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>-</name><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>1</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>O</name><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>not</name><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>not</name><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>if</name><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>if</name><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>y</var></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ge</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>not</name><arg><funapp><name>ge</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ge</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ge</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ge</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>Log'</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>Log'</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>+</name><arg><funapp><name>Log'</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>Log'</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>if</name><arg><funapp><name>ge</name><arg><var>x</var></arg><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>+</name><arg><funapp><name>Log'</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>Min</name><arg><funapp><name>L</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>Size</name><arg><funapp><name>L</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>O</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>+</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>I</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>-</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>not</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>true</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>false</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>if</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>ge</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>Log'</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>Min</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>L</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>Size</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></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>O</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>+</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>O</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>O</name><arg><funapp><name>+</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><var>x</var></arg><arg><funapp><name>+</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>+</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>O</name><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>-</name><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>1</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>O</name><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>not</name><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>not</name><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>if</name><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>if</name><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>y</var></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ge</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>not</name><arg><funapp><name>ge</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ge</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ge</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ge</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>Log'</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>Log'</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>+</name><arg><funapp><name>Log'</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>Log'</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>if</name><arg><funapp><name>ge</name><arg><var>x</var></arg><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>+</name><arg><funapp><name>Log'</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>Size</name><arg><funapp><name>L</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>O</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>+</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>I</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>-</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>not</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>true</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>false</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>if</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>ge</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>Log'</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>Size</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>L</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>O</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>+</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>O</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>O</name><arg><funapp><name>+</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><var>x</var></arg><arg><funapp><name>+</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>+</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>O</name><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>-</name><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>1</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>O</name><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>not</name><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>not</name><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>if</name><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>if</name><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>y</var></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ge</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>not</name><arg><funapp><name>ge</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ge</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ge</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ge</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ge</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>Log'</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>Log'</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>+</name><arg><funapp><name>Log'</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>Log'</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>if</name><arg><funapp><name>ge</name><arg><var>x</var></arg><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>+</name><arg><funapp><name>Log'</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>O</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>+</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>I</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>-</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>not</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>true</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>false</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>if</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>ge</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>Log'</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>O</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>+</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>O</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>O</name><arg><funapp><name>+</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>+</name><arg><var>x</var></arg><arg><funapp><name>+</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>+</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><var>x</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>O</name><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>-</name><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>1</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>I</name><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>-</name><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>O</name><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></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><rhs><funapp><sharp><name>ge</name></sharp><arg><funapp><name>0</name></funapp></arg><arg><var>x</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>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>O</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>ge</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>ge</name></sharp><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>ge</name></sharp><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></dps><trs><rules/></trs><usableRules><rules/></usableRules><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>ge</name></sharp><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>ge</name></sharp><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></rhs></rule><edge><position>1</position><strict>false</strict><position>1</position></edge><edge><position>2</position><strict>true</strict><position>2</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></monoRedPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>+</name></sharp><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>O</name></sharp><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>+</name></sharp><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>O</name></sharp><arg><funapp><name>+</name><arg><funapp><name>+</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>-</name></sharp><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>O</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>O</name></sharp><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>-</name></sharp><arg><funapp><name>I</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>O</name></sharp><arg><funapp><name>-</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>ge</name></sharp><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>not</name></sharp><arg><funapp><name>ge</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>Log'</name></sharp><arg><funapp><name>O</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>ge</name><arg><var>x</var></arg><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>+</name><arg><funapp><name>Log'</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>I</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></dpTrans></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></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 % (21 real / 0 unknown / 0 assumptions / 21 total proof steps)</strategy><url>http://aprove.informatik.rwth-aachen.de</url></tool><toolUser><firstName>John</firstName><lastName>Doe</lastName></toolUser></proofOrigin><inputOrigin/></origin></certificationProblem> popout

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all output return to TRS Standard Certified