details

property	value
status	complete
benchmark	PEANO_nokinds_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n146.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	2.42313 seconds
cpu usage	6.32832
user time	6.02211
system time	0.30621
max virtual memory	1.8528676E7
max residence set size	412740.0

stage attributes

key	value
certification-result	CERTIFIED
starexec-result	CERTIFIED YES
certification-time	0.38
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" 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ar></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><var>X1</var></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>tt</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>U21</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isNat</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNat</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U11</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U21</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>U21</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>s</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNat</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isNat</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><pathOrder><statusPrecedence><statusPrecedenceEntry><name>U11</name><arity>2</arity><precedence>0</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>tt</name><arity>0</arity><precedence>3</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>U21</name><arity>3</arity><precedence>3</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>s</name><arity>1</arity><precedence>2</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>plus</name><arity>2</arity><precedence>3</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>and</name><arity>2</arity><precedence>1</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>0</name><arity>0</arity><precedence>3</precedence><mul/></statusPrecedenceEntry></statusPrecedence><argumentFilter><argumentFilterEntry><name>active</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>U11</name><arity>2</arity><nonCollapsing><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>tt</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>mark</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>U21</name><arity>3</arity><nonCollapsing><position>3</position><position>2</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>s</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>plus</name><arity>2</arity><nonCollapsing><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>and</name><arity>2</arity><nonCollapsing><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>isNat</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>0</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>proper</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>ok</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>top</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry></argumentFilter></pathOrder></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>active</name><arg><funapp><name>isNat</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>tt</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>U21</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>X1</var></arg><arg><funapp><name>active</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U11</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U21</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>U21</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><var>X1</var></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>tt</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>U21</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isNat</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNat</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U11</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U21</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>U21</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>s</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNat</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isNat</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>active</name><arg><var>X</var></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>active</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>isNat</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>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>mark</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>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U11</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>s</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>plus</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>proper</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>ok</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>top</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></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>active</name><arg><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>U21</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>X1</var></arg><arg><funapp><name>active</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>tt</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>U21</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isNat</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNat</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U11</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U21</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>U21</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>s</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNat</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isNat</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>active</name><arg><var>X</var></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>active</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><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>s</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>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>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>proper</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>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>ok</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>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>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>top</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>active</name><arg><funapp><name>U11</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>U21</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>X1</var></arg><arg><funapp><name>active</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>U21</name><arg><var>X1</var></arg><arg><var>X2</var></arg><arg><var>X3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>isNat</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNat</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNat</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>isNat</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><knuthBendixOrder><w0>1</w0><precedenceWeight><precedenceWeightEntry><name>active</name><arity>1</arity><precedence>5</precedence><weight>3</weight></precedenceWeightEntry><precedenceWeightEntry><name>s</name><arity>1</arity><precedence>2</precedence><weight>1</weight></precedenceWeightEntry><precedenceWeightEntry><name>proper</name><arity>1</arity><precedence>8</precedence><weight>0</weight></precedenceWeightEntry><precedenceWeightEntry><name>isNat</name><arity>1</arity><precedence>7</precedence><weight>2</weight></precedenceWeightEntry><precedenceWeightEntry><name>ok</name><arity>1</arity><precedence>6</precedence><weight>1</weight></precedenceWeightEntry><precedenceWeightEntry><name>U11</name><arity>2</arity><precedence>0</precedence><weight>0</weight></precedenceWeightEntry><precedenceWeightEntry><name>U21</name><arity>3</arity><precedence>1</precedence><weight>0</weight></precedenceWeightEntry><precedenceWeightEntry><name>plus</name><arity>2</arity><precedence>3</precedence><weight>0</weight></precedenceWeightEntry><precedenceWeightEntry><name>and</name><arity>2</arity><precedence>4</precedence><weight>0</weight></precedenceWeightEntry></precedenceWeight></knuthBendixOrder></redPair></orderingConstraintProof><trs><rules/></trs><trsTerminationProof><rIsEmpty/></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 % (5 real / 0 unknown / 0 assumptions / 5 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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