/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>a</name><arg><funapp><name>f</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>a</name><arg><funapp><name>s</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a</name><arg><funapp><name>d</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>a</name><arg><funapp><name>d</name></funapp></arg><arg><funapp><name>a</name><arg><funapp><name>s</name></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a</name><arg><funapp><name>s</name></funapp></arg><arg><funapp><name>a</name><arg><funapp><name>s</name></funapp></arg><arg><funapp><name>a</name><arg><funapp><name>d</name></funapp></arg><arg><funapp><name>a</name><arg><funapp><name>p</name></funapp></arg><arg><funapp><name>a</name><arg><funapp><name>s</name></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a</name><arg><funapp><name>f</name></funapp></arg><arg><funapp><name>a</name><arg><funapp><name>s</name></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a</name><arg><funapp><name>d</name></funapp></arg><arg><funapp><name>a</name><arg><funapp><name>f</name></funapp></arg><arg><funapp><name>a</name><arg><funapp><name>p</name></funapp></arg><arg><funapp><name>a</name><arg><funapp><name>s</name></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a</name><arg><funapp><name>p</name></funapp></arg><arg><funapp><name>a</name><arg><funapp><name>s</name></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><uncurry><uncurryInformation><name>a</name><uncurriedSymbols><uncurriedSymbolEntry><name>f</name><arity>0</arity><name>f</name><name>f1</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>0</name><arity>0</arity><name>0</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>s</name><arity>0</arity><name>s</name><name>s1</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>d</name><arity>0</arity><name>d</name><name>d1</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>p</name><arity>0</arity><name>p</name><name>p1</name></uncurriedSymbolEntry></uncurriedSymbols><uncurryRules><rules><rule><lhs><funapp><name>a</name><arg><funapp><name>f</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>f1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a</name><arg><funapp><name>s</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a</name><arg><funapp><name>d</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>d1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a</name><arg><funapp><name>p</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>p1</name><arg><var>y1</var></arg></funapp></rhs></rule></rules></uncurryRules><etaRules><rules/></etaRules></uncurryInformation><trs><rules><rule><lhs><funapp><name>f1</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>d1</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>d1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><funapp><name>s1</name><arg><funapp><name>d1</name><arg><funapp><name>p1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>d1</name><arg><funapp><name>f1</name><arg><funapp><name>p1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>p1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>a</name><arg><funapp><name>f</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>f1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a</name><arg><funapp><name>s</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a</name><arg><funapp><name>d</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>d1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a</name><arg><funapp><name>p</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>p1</name><arg><var>y1</var></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>f1</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>s1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>d1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>p1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>a</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>f</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>s</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>d</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>p</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>d1</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>d1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><funapp><name>s1</name><arg><funapp><name>d1</name><arg><funapp><name>p1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>d1</name><arg><funapp><name>f1</name><arg><funapp><name>p1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>p1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>a</name><arg><funapp><name>s</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a</name><arg><funapp><name>p</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>p1</name><arg><var>y1</var></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>d1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>s1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>p1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>f1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>a</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>s</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>p</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>d1</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>d1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><funapp><name>s1</name><arg><funapp><name>d1</name><arg><funapp><name>p1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>d1</name><arg><funapp><name>f1</name><arg><funapp><name>p1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>p1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>a</name><arg><funapp><name>p</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>p1</name><arg><var>y1</var></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><pathOrder><statusPrecedence><statusPrecedenceEntry><name>0</name><arity>0</arity><precedence>0</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>f1</name><arity>1</arity><precedence>1</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>a</name><arity>2</arity><precedence>2</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>p</name><arity>0</arity><precedence>3</precedence><mul/></statusPrecedenceEntry></statusPrecedence><argumentFilter><argumentFilterEntry><name>d1</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>0</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>s1</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>p1</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>f1</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>a</name><arity>2</arity><nonCollapsing><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>p</name><arity>0</arity><nonCollapsing/></argumentFilterEntry></argumentFilter></pathOrder></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>d1</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>d1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><funapp><name>s1</name><arg><funapp><name>d1</name><arg><funapp><name>p1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>d1</name><arg><funapp><name>f1</name><arg><funapp><name>p1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>p1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule></rules></trs><trsTerminationProof><switchInnermost><wcrProof><joinableCriticalPairsBFS>10</joinableCriticalPairsBFS></wcrProof><trsTerminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><name>d1</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>d1</name></sharp><arg><funapp><name>p1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>d1</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>p1</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f1</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>d1</name></sharp><arg><funapp><name>f1</name><arg><funapp><name>p1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f1</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f1</name></sharp><arg><funapp><name>p1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f1</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>p1</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>f1</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f1</name></sharp><arg><funapp><name>p1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>p1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule></rules></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>p1</name><arg><funapp><name>s1</name><arg><var>x0</var></arg></funapp></arg></funapp></innermostLhss><dpProof><monoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>p1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>s1</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>f1</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>f1</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f1</name></sharp><arg><funapp><name>p1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules/></trs><dpProof><switchToTRS><trsTerminationProof><bounds><type><match/></type><bound>1</bound><finalStates><state>0</state><state>1</state><state>2</state></finalStates><treeAutomaton><finalStates><state>0</state><state>1</state><state>2</state></finalStates><transitions><transition><lhs><sharp><name>f1</name></sharp><height>0</height><state>0</state></lhs><rhs><state>0</state></rhs></transition><transition><lhs><sharp><name>f1</name></sharp><height>0</height><state>1</state></lhs><rhs><state>0</state></rhs></transition><transition><lhs><sharp><name>f1</name></sharp><height>0</height><state>2</state></lhs><rhs><state>0</state></rhs></transition><transition><lhs><name>s1</name><height>0</height><state>0</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>s1</name><height>0</height><state>1</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>s1</name><height>0</height><state>2</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>p1</name><height>0</height><state>0</state></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>p1</name><height>0</height><state>1</state></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>p1</name><height>0</height><state>2</state></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>s1</name><height>1</height><state>0</state></lhs><rhs><state>4</state></rhs></transition><transition><lhs><name>p1</name><height>1</height><state>4</state></lhs><rhs><state>3</state></rhs></transition><transition><lhs><sharp><name>f1</name></sharp><height>1</height><state>3</state></lhs><rhs><state>0</state></rhs></transition><transition><lhs><name>s1</name><height>1</height><state>1</state></lhs><rhs><state>4</state></rhs></transition><transition><lhs><name>s1</name><height>1</height><state>2</state></lhs><rhs><state>4</state></rhs></transition></transitions></treeAutomaton></bounds></trsTerminationProof></switchToTRS></dpProof></monoRedPairProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>f1</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>d1</name></sharp><arg><funapp><name>f1</name><arg><funapp><name>p1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>d1</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>d1</name></sharp><arg><funapp><name>p1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>p1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule></rules></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>p1</name><arg><funapp><name>s1</name><arg><var>x0</var></arg></funapp></arg></funapp></innermostLhss><dpProof><monoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>p1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>s1</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>d1</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>d1</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>d1</name></sharp><arg><funapp><name>p1</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules/></trs><dpProof><switchToTRS><trsTerminationProof><bounds><type><match/></type><bound>1</bound><finalStates><state>0</state><state>1</state><state>2</state></finalStates><treeAutomaton><finalStates><state>0</state><state>1</state><state>2</state></finalStates><transitions><transition><lhs><sharp><name>d1</name></sharp><height>0</height><state>0</state></lhs><rhs><state>0</state></rhs></transition><transition><lhs><sharp><name>d1</name></sharp><height>0</height><state>1</state></lhs><rhs><state>0</state></rhs></transition><transition><lhs><sharp><name>d1</name></sharp><height>0</height><state>2</state></lhs><rhs><state>0</state></rhs></transition><transition><lhs><name>s1</name><height>0</height><state>0</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>s1</name><height>0</height><state>1</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>s1</name><height>0</height><state>2</state></lhs><rhs><state>1</state></rhs></transition><transition><lhs><name>p1</name><height>0</height><state>0</state></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>p1</name><height>0</height><state>1</state></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>p1</name><height>0</height><state>2</state></lhs><rhs><state>2</state></rhs></transition><transition><lhs><name>s1</name><height>1</height><state>0</state></lhs><rhs><state>4</state></rhs></transition><transition><lhs><name>p1</name><height>1</height><state>4</state></lhs><rhs><state>3</state></rhs></transition><transition><lhs><sharp><name>d1</name></sharp><height>1</height><state>3</state></lhs><rhs><state>0</state></rhs></transition><transition><lhs><name>s1</name><height>1</height><state>1</state></lhs><rhs><state>4</state></rhs></transition><transition><lhs><name>s1</name><height>1</height><state>2</state></lhs><rhs><state>4</state></rhs></transition></transitions></treeAutomaton></bounds></trsTerminationProof></switchToTRS></dpProof></monoRedPairProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>d1</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>p1</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>f1</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>p1</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></dpTrans></trsTerminationProof></switchInnermost></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></uncurry></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 % (17 real / 0 unknown / 0 assumptions / 17 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>