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	n097.star.cs.uiowa.edu
space	Mixed_relative_SRS

run statistics

property	value
solver	ttt2-1.19
configuration	ttt2_cert
runtime (wallclock)	5.35252 seconds
cpu usage	19.9853
user time	16.0387
system time	3.94661
max virtual memory	3432460.0
max residence set size	80812.0

stage attributes

key	value
certification-result	CERTIFIED
output-size	60839
starexec-result	YES
certification-time	0.2

output

YES <?xml version="1.0"?> <?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><stringReversal><trs><rules><rule><lhs><funapp><name>n</name><arg><funapp><name>d</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>d</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>u</name><arg><funapp><name>o</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><trs><rules><rule><lhs><funapp><name>u</name><arg><funapp><name>t</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>d</name><arg><funapp><name>c</name><arg><funapp><name>t</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>d</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>d</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>g</name><arg><funapp><name>d</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>g</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u</name><arg><funapp><name>n</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>n</name><arg><funapp><name>f</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>n</name><arg><funapp><name>c</name><arg><funapp><name>t</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>n</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>o</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>o</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>o</name><arg><funapp><name>c</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>f</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>d</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>d</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><relativeTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><arctic><domain><integers/></domain></arctic></domain><degree>1</degree></polynomial></type><interpret><name>g</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>11</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>f</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>c</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>t</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>12</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>u</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>o</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>d</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>n</name><arg><funapp><name>d</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>u</name><arg><funapp><name>t</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>d</name><arg><funapp><name>c</name><arg><funapp><name>t</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>d</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>d</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>g</name><arg><funapp><name>d</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>g</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u</name><arg><funapp><name>n</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>n</name><arg><funapp><name>f</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>n</name><arg><funapp><name>c</name><arg><funapp><name>t</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>n</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>o</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>o</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>o</name><arg><funapp><name>c</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>f</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>d</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>d</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><relativeTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><matrices><dimension>3</dimension><strictDimension>1</strictDimension><domain><naturals/></domain></matrices></domain><degree>1</degree></polynomial></type><interpret><name>g</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>f</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>c</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>t</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>u</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>o</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>d</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>n</name><arg><funapp><name>d</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>u</name><arg><funapp><name>t</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>d</name><arg><funapp><name>c</name><arg><funapp><name>t</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>d</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>d</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u</name><arg><funapp><name>n</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>n</name><arg><funapp><name>f</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>n</name><arg><funapp><name>c</name><arg><funapp><name>t</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>n</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>o</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>o</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>o</name><arg><funapp><name>c</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>f</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>d</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>d</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><relativeTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><arctic><domain><integers/></domain></arctic></domain><degree>1</degree></polynomial></type><interpret><name>f</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>5</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>c</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></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><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>u</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>5</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>o</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>d</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>n</name><arg><funapp><name>d</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>f</name><arg><funapp><name>d</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>d</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u</name><arg><funapp><name>n</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>n</name><arg><funapp><name>f</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>n</name><arg><funapp><name>c</name><arg><funapp><name>t</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>n</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>o</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>o</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>o</name><arg><funapp><name>c</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>f</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>d</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>d</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><relativeTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><matrices><dimension>3</dimension><strictDimension>1</strictDimension><domain><naturals/></domain></matrices></domain><degree>1</degree></polynomial></type><interpret><name>f</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>c</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>t</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>u</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>o</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>d</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>n</name><arg><funapp><name>d</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>u</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u</name><arg><funapp><name>n</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>n</name><arg><funapp><name>f</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>n</name><arg><funapp><name>c</name><arg><funapp><name>t</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>n</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>o</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>o</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>o</name><arg><funapp><name>c</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>f</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>d</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>d</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><relativeTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><matrices><dimension>3</dimension><strictDimension>1</strictDimension><domain><naturals/></domain></matrices></domain><degree>1</degree></polynomial></type><interpret><name>f</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>c</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>t</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>u</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>o</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>d</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules/></trs><trs><rules><rule><lhs><funapp><name>u</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u</name><arg><funapp><name>n</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>n</name><arg><funapp><name>f</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>n</name><arg><funapp><name>c</name><arg><funapp><name>t</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>n</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>n</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>o</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>o</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>o</name><arg><funapp><name>c</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>f</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>u</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>u</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>d</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>d</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></stringReversal></relativeTerminationProof></proof><origin><proofOrigin><tool><name>ttt2</name><version>ttt2 1.18 [hg: 65024290f751]</version><strategy>((if standard then var else fail) | con | (if srs then ((sleep -t 25?;rlab;(((( (if srs then arctic -dim 1 -ib 4 -ob 5 else fail) || (if srs then arctic -dim 2 -ib 2 -ob 3 else fail) || (if srs then arctic -dim 3 -ib 1 -ob 2 else fail) || (if srs then arctic -dim 3 -ib 2 -ob 2 else fail) || matrix -dim 1 -ib 5 -ob 8 || matrix -dim 2 -ib 3 -ob 4 || matrix -dim 3 -ib 2 -ob 3 || matrix -dim 3 -ib 1 -ob 2 || matrix -dim 4 -ib 1 -ob 2 || matrix -dim 5 -ib 1 -ob 1 || kbo -ib 3 -ob 4 || fail)[5]*);((dp;(edg -gtcap -nl[1.0]?;(sccs | ((sc || sc -rec -defs || sc -mulex -defs) || sct || {ur?;( matrix -dp -ur -dim 1 -ib 3 -ob 5 || matrix -dp -ur -dim 1 -ib 3 -ob 8 -rat 2 -db 1 || matrix -dp -ur -dim 1 -ib 4 -ob 10 -rat 4 -db 1 || matrix -dp -ur -dim 2 -ib 2 -ob 3 || matrix -dp -ur -dim 2 -ib 3 -ob 4 -rat 2 -db 0 || matrix -dp -ur -dim 3 -ib 1 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 -rat 2 -db 0 || matrix -dp -ur -dim 4 -ib 1 -ob 2 || lpo -ur -af || (arctic -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || (arctic -bz -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -bz -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -bz -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -bz -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || fail) } restore) )*[29])) || (bounds -cert || fail;(bounds -rfc -qc))))! || (( unfold || fail)*[7])!)[299])! || ((((( (if srs then arctic -dim 1 -ib 4 -ob 5 else fail) || (if srs then arctic -dim 2 -ib 2 -ob 3 else fail) || (if srs then arctic -dim 3 -ib 1 -ob 2 else fail) || (if srs then arctic -dim 3 -ib 2 -ob 2 else fail) || matrix -dim 1 -ib 5 -ob 8 || matrix -dim 2 -ib 3 -ob 4 || matrix -dim 3 -ib 2 -ob 3 || matrix -dim 3 -ib 1 -ob 2 || matrix -dim 4 -ib 1 -ob 2 || matrix -dim 5 -ib 1 -ob 1 || kbo -ib 3 -ob 4 || fail)[5]*);((dp;(edg -gtcap -nl[1.0]?;(sccs | ((sc || sc -rec -defs || sc -mulex -defs) || sct || {ur?;( matrix -dp -ur -dim 1 -ib 3 -ob 5 || matrix -dp -ur -dim 1 -ib 3 -ob 8 -rat 2 -db 1 || matrix -dp -ur -dim 1 -ib 4 -ob 10 -rat 4 -db 1 || matrix -dp -ur -dim 2 -ib 2 -ob 3 || matrix -dp -ur -dim 2 -ib 3 -ob 4 -rat 2 -db 0 || matrix -dp -ur -dim 3 -ib 1 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 -rat 2 -db 0 || matrix -dp -ur -dim 4 -ib 1 -ob 2 || lpo -ur -af || (arctic -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || (arctic -bz -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -bz -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -bz -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -bz -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || fail) } restore) )*[29])) || (bounds -cert || fail;(bounds -rfc -qc))))! || (( unfold || fail)*[7])!)[299])! || (rev?;((( (if srs then arctic -dim 1 -ib 4 -ob 5 else fail) || (if srs then arctic -dim 2 -ib 2 -ob 3 else fail) || (if srs then arctic -dim 3 -ib 1 -ob 2 else fail) || (if srs then arctic -dim 3 -ib 2 -ob 2 else fail) || matrix -dim 1 -ib 5 -ob 8 || matrix -dim 2 -ib 3 -ob 4 || matrix -dim 3 -ib 2 -ob 3 || matrix -dim 3 -ib 1 -ob 2 || matrix -dim 4 -ib 1 -ob 2 || matrix -dim 5 -ib 1 -ob 1 || kbo -ib 3 -ob 4 || fail)[5]*);((dp;(edg -gtcap -nl[1.0]?;(sccs | ((sc || sc -rec -defs || sc -mulex -defs) || sct || {ur?;( matrix -dp -ur -dim 1 -ib 3 -ob 5 || matrix -dp -ur -dim 1 -ib 3 -ob 8 -rat 2 -db 1 || matrix -dp -ur -dim 1 -ib 4 -ob 10 -rat 4 -db 1 || matrix -dp -ur -dim 2 -ib 2 -ob 3 || matrix -dp -ur -dim 2 -ib 3 -ob 4 -rat 2 -db 0 || matrix -dp -ur -dim 3 -ib 1 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 -rat 2 -db 0 || matrix -dp -ur -dim 4 -ib 1 -ob 2 || lpo -ur -af || (arctic -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || (arctic -bz -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -bz -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -bz -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -bz -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || fail) } restore) )*[29])) || (bounds -cert || fail;(bounds -rfc -qc))))![299])! ) else ((((( (if srs then arctic -dim 1 -ib 4 -ob 5 else fail) || (if srs then arctic -dim 2 -ib 2 -ob 3 else fail) || (if srs then arctic -dim 3 -ib 1 -ob 2 else fail) || (if srs then arctic -dim 3 -ib 2 -ob 2 else fail) || matrix -dim 1 -ib 5 -ob 8 || matrix -dim 2 -ib 3 -ob 4 || matrix -dim 3 -ib 2 -ob 3 || matrix -dim 3 -ib 1 -ob 2 || matrix -dim 4 -ib 1 -ob 2 || matrix -dim 5 -ib 1 -ob 1 || kbo -ib 3 -ob 4 || fail)[5]*);((dp;(edg -gtcap -nl[1.0]?;(sccs | ((sc || sc -rec -defs || sc -mulex -defs) || sct || {ur?;( matrix -dp -ur -dim 1 -ib 3 -ob 5 || matrix -dp -ur -dim 1 -ib 3 -ob 8 -rat 2 -db 1 || matrix -dp -ur -dim 1 -ib 4 -ob 10 -rat 4 -db 1 || matrix -dp -ur -dim 2 -ib 2 -ob 3 || matrix -dp -ur -dim 2 -ib 3 -ob 4 -rat 2 -db 0 || matrix -dp -ur -dim 3 -ib 1 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 -rat 2 -db 0 || matrix -dp -ur -dim 4 -ib 1 -ob 2 || lpo -ur -af || (arctic -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || (arctic -bz -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -bz -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -bz -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -bz -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || fail) } restore) )*[29])) || (bounds -cert || fail;(bounds -rfc -qc))))! || (( unfold || fail)*[7])!)[299])))</strategy></tool></proofOrigin></origin></certificationProblem> popout

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all output return to SRS_Relative 2019-03-22 08.27