details

property	value
status	complete
benchmark	zr04.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n140.star.cs.uiowa.edu
space	Mixed_relative_SRS

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	4.81063 seconds
cpu usage	15.7744
user time	14.8999
system time	0.874563
max virtual memory	1.961236E7
max residence set size	1959552.0

stage attributes

key	value
certification-result	CERTIFIED
starexec-result	CERTIFIED YES
certification-time	0.33
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>d</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>d</name><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>d</name><arg><funapp><name>o</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>d</name><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>o</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>u</name><arg><var>x1</var></arg></funapp></rhs></rule></rules></trs><relativeRules><rules><rule><lhs><funapp><name>t</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>t</name><arg><funapp><name>c</name><arg><funapp><name>d</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>d</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>d</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>d</name><arg><funapp><name>g</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>u</name><arg><funapp><name>g</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>u</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>n</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>u</name><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>t</name><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><name>t</name><arg><funapp><name>c</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>n</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>o</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>o</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>o</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>o</name><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>u</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>d</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>d</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></relativeRules></trsInput></input><cpfVersion>2.1</cpfVersion><proof><relativeTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>d</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>n</name><arity>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>o</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>u</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>t</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>c</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>f</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>g</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>d</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>d</name><arg><var>x1</var></arg></funapp></rhs></rule></rules></trs><trs><rules><rule><lhs><funapp><name>t</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>t</name><arg><funapp><name>c</name><arg><funapp><name>d</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>d</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>d</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>d</name><arg><funapp><name>g</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>u</name><arg><funapp><name>g</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>u</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>n</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>u</name><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>t</name><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><name>t</name><arg><funapp><name>c</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>n</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>o</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>o</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>o</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>o</name><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>u</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>d</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>d</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><relativeTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><matrixInterpretation><domain><integers/></domain><dimension>2</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><name>d</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>2</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>n</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>t</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>u</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>2</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>f</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>g</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>2</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>o</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>d</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>d</name><arg><var>x1</var></arg></funapp></rhs></rule></rules></trs><trs><rules><rule><lhs><funapp><name>t</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>t</name><arg><funapp><name>c</name><arg><funapp><name>d</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>d</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>d</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>u</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>n</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>u</name><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>t</name><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><name>t</name><arg><funapp><name>c</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>n</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>o</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>o</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>o</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>o</name><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>u</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>d</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>d</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><relativeTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>d</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>n</name><arity>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>t</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>u</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>c</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>f</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>o</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>d</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>d</name><arg><var>x1</var></arg></funapp></rhs></rule></rules></trs><trs><rules><rule><lhs><funapp><name>d</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>d</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>u</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>n</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>u</name><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>t</name><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><name>t</name><arg><funapp><name>c</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>n</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>o</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>o</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>o</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>o</name><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>u</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>d</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>d</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><relativeTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><matrixInterpretation><domain><integers/></domain><dimension>2</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><name>d</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>n</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>f</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>u</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>2</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>t</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>2</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>o</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>d</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>d</name><arg><var>x1</var></arg></funapp></rhs></rule></rules></trs><trs><rules><rule><lhs><funapp><name>d</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>d</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>n</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>u</name><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>t</name><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><name>t</name><arg><funapp><name>c</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>n</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>o</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>o</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>o</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>o</name><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>u</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>d</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>d</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><relativeTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><matrixInterpretation><domain><integers/></domain><dimension>2</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><name>d</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>2</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>n</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>f</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>2</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>u</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>t</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>2</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>o</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>d</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>d</name><arg><var>x1</var></arg></funapp></rhs></rule></rules></trs><trs><rules><rule><lhs><funapp><name>n</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>u</name><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>t</name><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><name>t</name><arg><funapp><name>c</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>n</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>o</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>o</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>o</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>o</name><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>u</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>d</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>d</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><relativeTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><matrixInterpretation><domain><integers/></domain><dimension>2</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><name>d</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>n</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>u</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>f</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>t</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>2</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>o</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules/></trs><trs><rules><rule><lhs><funapp><name>n</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>u</name><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>t</name><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><name>t</name><arg><funapp><name>c</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>n</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>o</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>o</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>o</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>o</name><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>u</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>d</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>d</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><relativeTerminationProof><rIsEmpty/></relativeTerminationProof></ruleRemoval></relativeTerminationProof></ruleRemoval></relativeTerminationProof></ruleRemoval></relativeTerminationProof></ruleRemoval></relativeTerminationProof></ruleRemoval></relativeTerminationProof></ruleRemoval></relativeTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (7 real / 0 unknown / 0 assumptions / 7 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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