/export/starexec/sandbox/solver/bin/starexec_run_certified /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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<?xml version="1.0" encoding="UTF-8" standalone="no"?><?xml-stylesheet type="text/xsl" href="cpfHTML.xsl"?><certificationProblem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" 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><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>a</name></sharp><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>a</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>a</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>a</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>a</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>a</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>a</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><monoRedPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></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>b</name><numberLabel><number>1</number></numberLabel></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>b</name><numberLabel><number>0</number></numberLabel></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>a</name><numberLabel><number>1</number></numberLabel></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><sharp><name>a</name></sharp><numberLabel><number>0</number></numberLabel></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><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>a</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>a</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>a</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>a</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>a</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>a</name></sharp><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><monoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></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>b</name><numberLabel><number>1</number></numberLabel></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>b</name><numberLabel><number>0</number></numberLabel></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>a</name><numberLabel><number>1</number></numberLabel></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><sharp><name>a</name></sharp><numberLabel><number>0</number></numberLabel></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><dps><rules/></dps><trs><rules><rule><lhs><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><dpProof><pIsEmpty/></dpProof></monoRedPairProc></dpProof></monoRedPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>a</name></sharp><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>a</name></sharp><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>a</name></sharp><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>a</name></sharp><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>a</name></sharp><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>a</name></sharp><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><monoRedPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></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>b</name><numberLabel><number>0</number></numberLabel></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>b</name><numberLabel><number>1</number></numberLabel></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>a</name><numberLabel><number>0</number></numberLabel></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><sharp><name>a</name></sharp><numberLabel><number>1</number></numberLabel></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><dps><rules><rule><lhs><funapp><labeledSymbol><sharp><name>a</name></sharp><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>a</name></sharp><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>a</name></sharp><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>a</name></sharp><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><labeledSymbol><sharp><name>a</name></sharp><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><sharp><name>a</name></sharp><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><monoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></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>b</name><numberLabel><number>0</number></numberLabel></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>b</name><numberLabel><number>1</number></numberLabel></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>a</name><numberLabel><number>0</number></numberLabel></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><sharp><name>a</name></sharp><numberLabel><number>1</number></numberLabel></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><dps><rules/></dps><trs><rules><rule><lhs><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>b</name><numberLabel><number>0</number></numberLabel></labeledSymbol><arg><funapp><labeledSymbol><name>a</name><numberLabel><number>1</number></numberLabel></labeledSymbol><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><dpProof><pIsEmpty/></dpProof></monoRedPairProc></dpProof></monoRedPairUrProc></dpProof></component></depGraphProc></dpProof></semlabProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>a</name></sharp><arg><funapp><name>b</name><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><funapp><name>b</name><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a</name></sharp><arg><funapp><name>b</name><arg><funapp><name>b</name><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><funapp><name>b</name><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><funapp><name>a</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>a</name></sharp><arg><funapp><name>b</name><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><funapp><name>b</name><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a</name></sharp><arg><funapp><name>b</name><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><funapp><name>b</name><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><funapp><name>a</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>a</name></sharp><arg><funapp><name>b</name><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><funapp><name>b</name><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a</name></sharp><arg><funapp><name>b</name><arg><funapp><name>b</name><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><funapp><name>a</name><arg><funapp><name>b</name><arg><funapp><name>a</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></dpTrans></trsTerminationProof></stringReversal></trsTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished
</version><strategy>Statistics for single proof: 100.00 % (11 real / 0 unknown / 0 assumptions / 11 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>