details

property	value
status	complete
benchmark	z013.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n003.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	6.40277791023 seconds
cpu usage	12.148444846
max memory	1.53944064E9

stage attributes

key	value
certification-result	CERTIFIED
output-size	61395
starexec-result	YES
certification-time	0.1

output

/export/starexec/sandbox2/solver/bin/starexec_run_certified /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES <?xml version="1.0" encoding="UTF-8" standalone="no"?><?xml-stylesheet type="text/xsl" href="cpfHTML.xsl"?><certificationProblem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="cpf.xsd"><input><trsInput><trs><rules><rule><lhs><funapp><name>g</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>g</name><arg><funapp><name>f</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>g</name><arg><funapp><name>f</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>g</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>g</name><arg><funapp><name>g</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>g</name><arg><funapp><name>f</name><arg><funapp><name>g</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>g</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>g</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><flatContextClosure><flatContexts><funContext><name>g</name><before/><box/><after/></funContext><funContext><name>c</name><before/><box/><after/></funContext><funContext><name>f</name><before/><box/><after/></funContext></flatContexts><trs><rules><rule><lhs><funapp><name>g</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>g</name><arg><funapp><name>f</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>g</name><arg><funapp><name>f</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>g</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>c</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>g</name><arg><funapp><name>g</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>g</name><arg><funapp><name>f</name><arg><funapp><name>g</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>g</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>g</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>g</name><arg><funapp><name>g</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>c</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>g</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c</name><arg><funapp><name>g</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>g</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>g</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><semlab><model><rootLabeling/></model><trs><rules><rule><lhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>c</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>c</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>c</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>c</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>c</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>c</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><labeledSymbol><name>g</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>c</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>c</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>c</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><redPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>c</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>c</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>c</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><labeledSymbol><name>g</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules/></dps><dpProof><pIsEmpty/></dpProof></redPairProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>c</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>c</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><funapp><labeledSymbol><name>g</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><labeledSymbol><name>g</name><symbolLabel><name>f</name></symbolLabel></labeledSymbol></sharp><arg><funapp><labeledSymbol><name>f</name><symbolLabel><name>g</name></symbolLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></dpTrans></trsTerminationProof></ruleRemoval></trsTerminationProof></semlab></trsTerminationProof></flatContextClosure></trsTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (7 real / 0 unknown / 0 assumptions / 7 total proof steps)</strategy><url>http://aprove.informatik.rwth-aachen.de</url></tool><toolUser><firstName>John</firstName><lastName>Doe</lastName></toolUser></proofOrigin><inputOrigin/></origin></certificationProblem> popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to SRS Standard Certified