details

property	value
status	complete
benchmark	MYNAT_nokinds_noand_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	4.25814 seconds
cpu usage	12.9718
user time	12.5761
system time	0.39569
max virtual memory	1.8642304E7
max residence set size	650692.0

stage attributes

key	value
certification-result	CERTIFIED
starexec-result	CERTIFIED YES
certification-time	0.72
bare-result	YES

output

<?xml version="1.0" encoding="UTF-8" standalone="no"?><?xml-stylesheet type="text/xsl" href="cpfHTML.xsl"?><certificationProblem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="cpf.xsd"><input><trsInput><trs><rules><rule><lhs><funapp><name>a__U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>a__U12</name><arg><funapp><name>a__isNat</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U12</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>a__U21</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>a__U31</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>a__U32</name><arg><funapp><name>a__isNat</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U32</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>a__U41</name><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U51</name><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><name>a__U52</name><arg><funapp><name>a__isNat</name><arg><var>N</var></arg></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U52</name><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>a__plus</name><arg><funapp><name>mark</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>mark</name><arg><var>M</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U61</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>a__U71</name><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><name>a__U72</name><arg><funapp><name>a__isNat</name><arg><var>N</var></arg></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U72</name><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><name>a__plus</name><arg><funapp><name>a__x</name><arg><funapp><name>mark</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>mark</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>mark</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__U11</name><arg><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__U21</name><arg><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>x</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__U31</name><arg><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__plus</name><arg><var>N</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__U41</name><arg><funapp><name>a__isNat</name><arg><var>N</var></arg></funapp></arg><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__plus</name><arg><var>N</var></arg><arg><funapp><name>s</name><arg><var>M</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__U51</name><arg><funapp><name>a__isNat</name><arg><var>M</var></arg></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__x</name><arg><var>N</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__U61</name><arg><funapp><name>a__isNat</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__x</name><arg><var>N</var></arg><arg><funapp><name>s</name><arg><var>M</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__U71</name><arg><funapp><name>a__isNat</name><arg><var>M</var></arg></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>U11</name><arg><var>X1</var></a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napp><name>a__U21</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U31</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>U31</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U32</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U32</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U41</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>U41</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U51</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></lhs><rhs><funapp><name>U51</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U52</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></lhs><rhs><funapp><name>U52</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U61</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U61</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U71</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></lhs><rhs><funapp><name>U71</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U72</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></lhs><rhs><funapp><name>U72</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__x</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>x</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><name>a__U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>a__U12</name></sharp><arg><funapp><name>a__isNat</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>a__isNat</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__U31</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>a__U32</name></sharp><arg><funapp><name>a__isNat</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__U31</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>a__isNat</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__U41</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>a__U52</name></sharp><arg><funapp><name>a__isNat</name><arg><var>N</var></arg></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>a__isNat</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__U52</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>a__plus</name></sharp><arg><funapp><name>mark</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>mark</name><arg><var>M</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__U52</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__U52</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>M</var></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><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U61</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U71</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__U71</name></sharp><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>a__U72</name></sharp><arg><funapp><name>a__isNat</name><arg><var>N</var></arg></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__U72</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>a__plus</name></sharp><arg><funapp><name>a__x</name><arg><funapp><name>mark</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>mark</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>mark</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__U72</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>a__x</name></sharp><arg><funapp><name>mark</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>mark</name><arg><var>M</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__x</name></sharp><arg><var>N</var></arg><arg><funapp><name>s</name><arg><var>M</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__U71</name></sharp><arg><funapp><name>a__isNat</name><arg><var>M</var></arg></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__U72</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U71</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U72</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__U72</name></sharp><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__U72</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>M</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U72</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>x</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__x</name></sharp><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>x</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>x</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><redPairProc><orderingConstraintProof><redPair><pathOrder><st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entFilterEntry><sharp><name>a__plus</name></sharp><arity>2</arity><nonCollapsing><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>0</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>s</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>U52</name><arity>3</arity><nonCollapsing><position>1</position><position>2</position><position>3</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>plus</name><arity>2</arity><nonCollapsing><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>U61</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>U71</name><arity>3</arity><nonCollapsing><position>2</position><position>3</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><sharp><name>a__U71</name></sharp><arity>3</arity><nonCollapsing><position>2</position><position>3</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><sharp><name>a__U72</name></sharp><arity>3</arity><nonCollapsing><position>2</position><position>3</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>a__x</name><arity>2</arity><nonCollapsing><position>2</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><sharp><name>a__x</name></sharp><arity>2</arity><nonCollapsing><position>2</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>U72</name><arity>3</arity><nonCollapsing><position>2</position><position>3</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>x</name><arity>2</arity><nonCollapsing><position>2</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>a__U11</name><arity>2</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>a__U12</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>isNat</name><arity>1</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>a__U21</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>a__U31</name><arity>2</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>a__U32</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>a__U41</name><arity>2</arity><nonCollapsing><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>a__plus</name><arity>2</arity><nonCollapsing><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>a__U71</name><arity>3</arity><nonCollapsing><position>2</position><position>3</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>a__U72</name><arity>3</arity><nonCollapsing><position>2</position><position>3</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>a__U51</name><arity>3</arity><nonCollapsing><position>1</position><position>2</position><position>3</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>a__U52</name><arity>3</arity><nonCollapsing><position>1</position><position>2</position><position>3</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>a__U61</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry></argumentFilter></pathOrder></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U12</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U21</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U31</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U32</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__U41</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>a__U52</name></sharp><arg><funapp><name>a__isNat</name><arg><var>N</var></arg></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U61</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>a__U72</name></sharp><arg><funapp><name>a__isNat</name><arg><var>N</var></arg></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></rhs></rule></rules></dps><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>a__U41</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>N</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U12</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U21</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U31</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U32</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U61</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><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>U12</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U11</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U31</name><arity>2</arity><polynomial><sum><polynomial><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>U32</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U61</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>mark</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U12</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U21</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U31</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U32</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U61</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><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>mark</name></sharp><arg><funapp><name>U12</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U21</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U31</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U32</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U61</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></monoRedPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>a__U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>a__U52</name></sharp><arg><funapp><name>a__isNat</name><arg><var>N</var></arg></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>a__U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>a__U72</name></sharp><arg><funapp><name>a__isNat</name><arg><var>N</var></arg></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></redPairProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__U11</name></sharp><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>a__U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>a__isNat</name></sharp><arg><var>N</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>a__U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>a__isNat</name></sharp><arg><var>N</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>a__plus</name></sharp><arg><var>N</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__isNat</name></sharp><arg><var>N</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>a__plus</name></sharp><arg><var>N</var></arg><arg><funapp><name>s</name><arg><var>M</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__isNat</name></sharp><arg><var>M</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>a__x</name></sharp><arg><var>N</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__isNat</name></sharp><arg><var>N</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>a__x</name></sharp><arg><var>N</var></arg><arg><funapp><name>s</name><arg><var>M</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__isNat</name></sharp><arg><var>M</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>isNat</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__isNat</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U31</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__U31</name></sharp><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>a__U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>a__isNat</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__isNat</name></sharp><arg><funapp><name>plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__U11</name></sharp><arg><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__isNat</name></sharp><arg><funapp><name>plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__isNat</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__isNat</name></sharp><arg><funapp><name>s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__isNat</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__isNat</name></sharp><arg><funapp><name>x</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__U31</name></sharp><arg><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__U31</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>a__isNat</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__isNat</name></sharp><arg><funapp><name>x</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__isNat</name></sharp><arg><var>V1</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>a__isNat</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>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>plus</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>a__U11</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>s</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>a__U21</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>x</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>a__U31</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isNat</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>a__U32</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U31</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U32</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U21</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>a__U12</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U11</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U12</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>a__isNat</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>a__U11</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>a__U31</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>a__U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>a__isNat</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__isNat</name></sharp><arg><funapp><name>plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__U11</name></sharp><arg><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__isNat</name></sharp><arg><funapp><name>plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__isNat</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__isNat</name></sharp><arg><funapp><name>s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__isNat</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__isNat</name></sharp><arg><funapp><name>x</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__U31</name></sharp><arg><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__U31</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>a__isNat</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__isNat</name></sharp><arg><funapp><name>x</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__isNat</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__U11</name><arg><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__U21</name><arg><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>x</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__U31</name><arg><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>isNat</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U31</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>a__U32</name><arg><funapp><name>a__isNat</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U31</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>U31</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U32</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>a__U32</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U32</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U21</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>a__U21</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>a__U12</name><arg><funapp><name>a__isNat</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U12</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>a__U12</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U12</name><arg><var>X</var></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__U11</name><arg><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__U21</name><arg><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><funapp><name>x</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__U31</name><arg><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__isNat</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>isNat</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U31</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>a__U32</name><arg><funapp><name>a__isNat</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U31</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>U31</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U32</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>a__U32</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U32</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U21</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>a__U21</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>a__U12</name><arg><funapp><name>a__isNat</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__U12</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>a__U12</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U12</name><arg><var>X</var></arg></funapp></rhs></rule></rules></usableRules><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>a__isNat</name></sharp><arg><funapp><name>plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__U11</name></sharp><arg><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>2</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>a__isNat</name></sharp><arg><funapp><name>x</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__U31</name></sharp><arg><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>2</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>a__U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>a__isNat</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><edge><position>2</position><strict>false</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>a__U31</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>a__isNat</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><edge><position>2</position><strict>false</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>a__isNat</name></sharp><arg><funapp><name>plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__isNat</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>a__isNat</name></sharp><arg><funapp><name>s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__isNat</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>a__isNat</name></sharp><arg><funapp><name>x</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__isNat</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></monoRedPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>a__U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>a__U12</name></sharp><arg><funapp><name>a__isNat</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>a__U31</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>a__U32</name></sharp><arg><funapp><name>a__isNat</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>a__isNat</name></sharp><arg><funapp><name>s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__U21</name></sharp><arg><funapp><name>a__isNat</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>a__x</name></sharp><arg><var>N</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__U61</name></sharp><arg><funapp><name>a__isNat</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U12</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__U12</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U21</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__U21</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U32</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__U32</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>U61</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__U61</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></dpTrans></trsTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (8 real / 0 unknown / 0 assumptions / 8 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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