details

property	value
status	complete
benchmark	Ex1_Luc04b_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n050.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	ttt2-1.17+nonreach
configuration	ttt2-1.17+nonreach-cert
runtime (wallclock)	7.3462870121 seconds
cpu usage	26.998407351
max memory	6.34380288E8

stage attributes

key	value
certification-result	CERTIFIED
output-size	157493
starexec-result	YES
certification-time	0.1

output

/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach-cert /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES <?xml version="1.0"?> <?xml-stylesheet type="text/xsl" href="cpfHTML.xsl"?><certificationProblem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" 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efficient><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>proper</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>1</integer></coefficient><coefficient><integer>1</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>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>tail</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>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>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>head</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>1</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>s</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>1</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>odds</name><arity>0</arity><polynomial><sum><polynomial><coefficient><matrix><vector><coefficient><integer>0</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></sum></polynomial></interpret><interpret><name>pairs</name><arity>0</arity><polynomial><sum><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>mark</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>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>cons</name><arity>2</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><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>2</variable></polynomial></product></polynomial><polynomial><coefficient><matrix><vector><coefficient><integer>0</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></sum></polynomial></interpret><interpret><name>incr</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>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>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><matrix><vector><coefficient><integer>0</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></sum></polynomial></interpret><interpret><name>active</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>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>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></sum></polynomial></interpret><interpret><name>nats</name><arity>0</arity><polynomial><sum><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></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>active</name><arg><funapp><name>nats</name></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>incr</name><arg><funapp><name>nats</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>pairs</name></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>incr</name><arg><funapp><name>odds</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>odds</name></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>incr</name><arg><funapp><name>pairs</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>incr</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>cons</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>incr</name><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>head</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>incr</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>head</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>head</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>tail</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>tail</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>cons</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>incr</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>head</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>head</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>tail</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>tail</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>nats</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>nats</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>incr</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>pairs</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>pairs</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>odds</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>odds</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>head</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>head</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>tail</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>tail</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>cons</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>incr</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>s</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>head</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>head</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>tail</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>tail</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><matrices><dimension>3</dimension><strictDimension>1</strictDimension><domain><naturals/></domain></matrices></domain><degree>1</degree></polynomial></type><interpret><name>top</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>ok</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>proper</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>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>tail</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>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>head</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>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></sum></polynomial></interpret><interpret><name>s</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>1</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>odds</name><arity>0</arity><polynomial><sum><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>pairs</name><arity>0</arity><polynomial><sum><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>mark</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>cons</name><arity>2</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><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>2</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>incr</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>0</name><arity>0</arity><polynomial><sum><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>active</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>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</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>nats</name><arity>0</arity><polynomial><sum><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>active</name><arg><funapp><name>nats</name></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>incr</name><arg><funapp><name>nats</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>pairs</name></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>incr</name><arg><funapp><name>odds</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>odds</name></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>incr</name><arg><funapp><name>pairs</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>incr</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>cons</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>incr</name><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>incr</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>head</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>head</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>tail</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>tail</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>cons</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>incr</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>head</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>head</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>tail</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>tail</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>nats</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>nats</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>incr</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>pairs</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>pairs</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>odds</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>odds</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>head</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>head</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>tail</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>tail</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>cons</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>incr</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>s</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>head</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>head</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>tail</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>tail</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><matrices><dimension>3</dimension><strictDimension>1</strictDimension><domain><naturals/></domain></matrices></domain><degree>1</degree></polynomial></type><interpret><name>top</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>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>ok</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>proper</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>1</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>tail</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>head</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>s</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>1</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>odds</name><arity>0</arity><polynomial><sum><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>pairs</name><arity>0</arity><polynomial><sum><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>mark</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>cons</name><arity>2</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><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>2</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>incr</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>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>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>0</name><arity>0</arity><polynomial><sum><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>active</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>1</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>nats</name><arity>0</arity><polynomial><sum><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></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>active</name><arg><funapp><name>pairs</name></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>incr</name><arg><funapp><name>odds</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>odds</name></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>incr</name><arg><funapp><name>pairs</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>incr</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>cons</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>incr</name><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>incr</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>head</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>head</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>tail</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>tail</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>cons</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>incr</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>head</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>head</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>tail</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>tail</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>nats</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>nats</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>incr</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>pairs</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>pairs</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>odds</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>odds</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>head</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>head</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>tail</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>tail</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>cons</name><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>incr</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>s</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>head</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>head</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>tail</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>tail</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>proper</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><matrices><dimension>3</dimension><strictDimension>1</strictDimension><domain><naturals/></domain></matrices></domain><degree>1</degree></polynomial></type><interpret><name>top</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>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>ok</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>1</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>proper</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>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>tail</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>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>head</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>s</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>odds</name><arity>0</arity><polynomial><sum><polynomial><coefficient><matrix><vector><coefficient><integer>0</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></sum></polynomial></interpret><interpret><name>pairs</name><arity>0</arity><polynomial><sum><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></sum></polynomial></interpret><interpret><name>mark</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>cons</name><arity>2</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>1</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><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>2</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>incr</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>1</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>0</name><arity>0</arity><polynomial><sum><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>active</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>1</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>nats</name><arity>0</arity><polynomial><sum><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>active</name><arg><funapp><name>odds</name></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>incr</name><arg><funapp><name>pairs</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>incr</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>cons</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>incr</name><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>incr</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>head</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>head</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>active</name><arg><funapp><name>tail</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>tail</name><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>cons</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>incr</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>head</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>head</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>tail</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><funapp><name>tail</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>nats</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>nats</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>proper</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>proper</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>ok</name><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>proper</name><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>incr</name><arg><funapp><name>proper</name><arg><var>X</var>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sharp><name>active</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>active</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>active</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>active</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>odds</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>incr</name></sharp><arg><funapp><name>pairs</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs/></component><component><dps><rules><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>incr</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>incr</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs><forwardArc>6</forwardArc></arcs></component><component><dps><rules><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>incr</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs><forwardArc>7</forwardArc></arcs></component><component><dps><rules><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>incr</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cons</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>incr</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs><forwardArc>2</forwardArc></arcs></component><component><dps><rules><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cons</name></sharp><arg><funapp><name>active</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs><forwardArc>1</forwardArc></arcs></component><component><dps><rules><rule><lhs><funapp><sharp><name>cons</name></sharp><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cons</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>cons</name></sharp><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><sharp><name>cons</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><arcs/><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>cons</name></sharp><arg><funapp><name>ok</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>ok</name><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>cons</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><edge><position>2</position><strict>true</strict><position>2</position></edge><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>cons</name></sharp><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><sharp><name>cons</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><edge><position>2</position><strict>false</strict><position>2</position></edge><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>incr</name></sharp><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs><forwardArc>1</forwardArc></arcs></component><component><dps><rules><rule><lhs><funapp><sharp><name>incr</name></sharp><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>incr</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>incr</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>incr</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><arcs/><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>incr</name></sharp><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>incr</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>incr</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>incr</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs><forwardArc>1</forwardArc></arcs></component><component><dps><rules><rule><lhs><funapp><sharp><name>s</name></sharp><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>s</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><arcs/><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>s</name></sharp><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>s</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>head</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>head</name></sharp><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs><forwardArc>1</forwardArc></arcs></component><component><dps><rules><rule><lhs><funapp><sharp><name>head</name></sharp><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>head</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>head</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>head</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><arcs/><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>head</name></sharp><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>head</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>head</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>head</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>active</name></sharp><arg><funapp><name>tail</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>tail</name></sharp><arg><funapp><name>active</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs><forwardArc>1</forwardArc></arcs></component><component><dps><rules><rule><lhs><funapp><sharp><name>tail</name></sharp><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>tail</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>tail</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>tail</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><arcs/><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>tail</name></sharp><arg><funapp><name>ok</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>tail</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>tail</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>tail</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></component></depGraphProc></dpProof></dpTrans></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></proof><origin><proofOrigin><tool><name>ttt2</name><version>ttt2 1.17 [hg: a28b6edf8379]</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[5] | arctic -dp -ur -dim 2 -ib 2 -ob 2[8] | arctic -dp -ur -dim 3 -ib 1 -ob 1[8] | arctic -dp -ur -dim 4 -ib 1 -ob 1[8] | fail) || (arctic -bz -dp -ur -dim 1 -ib 4 -ob 3[5] | arctic -bz -dp -ur -dim 2 -ib 2 -ob 2[8] | arctic -bz -dp -ur -dim 3 -ib 1 -ob 1[8] | arctic -bz -dp -ur -dim 4 -ib 1 -ob 1[8] | fail) || fail) } restore) )*[29])) || (bounds -cert || fail;(bounds -rfc -qc))))! || (( unfold || fail)*[7])!)[42])! || ((((( (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[5] | arctic -dp -ur -dim 2 -ib 2 -ob 2[8] | arctic -dp -ur -dim 3 -ib 1 -ob 1[8] | arctic -dp -ur -dim 4 -ib 1 -ob 1[8] | fail) || (arctic -bz -dp -ur -dim 1 -ib 4 -ob 3[5] | arctic -bz -dp -ur -dim 2 -ib 2 -ob 2[8] | arctic -bz -dp -ur -dim 3 -ib 1 -ob 1[8] | arctic -bz -dp -ur -dim 4 -ib 1 -ob 1[8] | fail) || fail) } restore) )*[29])) || (bounds -cert || fail;(bounds -rfc -qc))))! || (( unfold || fail)*[7])!)[42])! || (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[5] | arctic -dp -ur -dim 2 -ib 2 -ob 2[8] | arctic -dp -ur -dim 3 -ib 1 -ob 1[8] | arctic -dp -ur -dim 4 -ib 1 -ob 1[8] | fail) || (arctic -bz -dp -ur -dim 1 -ib 4 -ob 3[5] | arctic -bz -dp -ur -dim 2 -ib 2 -ob 2[8] | arctic -bz -dp -ur -dim 3 -ib 1 -ob 1[8] | arctic -bz -dp -ur -dim 4 -ib 1 -ob 1[8] | fail) || fail) } restore) )*[29])) || (bounds -cert || fail;(bounds -rfc -qc))))![42])! ) 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[5] | arctic -dp -ur -dim 2 -ib 2 -ob 2[8] | arctic -dp -ur -dim 3 -ib 1 -ob 1[8] | arctic -dp -ur -dim 4 -ib 1 -ob 1[8] | fail) || (arctic -bz -dp -ur -dim 1 -ib 4 -ob 3[5] | arctic -bz -dp -ur -dim 2 -ib 2 -ob 2[8] | arctic -bz -dp -ur -dim 3 -ib 1 -ob 1[8] | arctic -bz -dp -ur -dim 4 -ib 1 -ob 1[8] | fail) || fail) } restore) )*[29])) || (bounds -cert || fail;(bounds -rfc -qc))))! || (( unfold || fail)*[7])!)[42])))</strategy></tool></proofOrigin></origin></certificationProblem> popout

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