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<?xml version='1.0' ?><certificationProblem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" noNamespaceSchemaLocation="cpf3.xsd"><cpfVersion>3.0</cpfVersion><lookupTables /><input><trsInput><trs><rules><rule><funapp><name>monus</name><funapp><name>0</name></funapp><var>y</var></funapp><funapp><name>0</name></funapp></rule><rule><funapp><name>monus</name><var>x</var><funapp><name>0</name></funapp></funapp><var>x</var></rule><rule><funapp><name>monus</name><funapp><name>s</name><var>x</var></funapp><funapp><name>s</name><var>y</var></funapp></funapp><funapp><name>monus</name><var>x</var><var>y</var></funapp></rule><rule><funapp><name>div</name><funapp><name>0</name></funapp><funapp><name>s</name><var>y</var></funapp></funapp><funapp><name>0</name></funapp></rule><rule><funapp><name>div</name><funapp><name>s</name><var>x</var></funapp><funapp><name>s</name><var>y</var></funapp></funapp><funapp><name>s</name><funapp><name>div</name><funapp><name>monus</name><var>x</var><var>y</var></funapp><funapp><name>s</name><var>y</var></funapp></funapp></funapp></rule></rules></trs></trsInput></input><property><termination /></property><answer><yes /></answer><proof><trsTerminationProof><ruleRemoval><monotonicSemanticPathOrder><generalizedWeightedPathOrder><precedenceList><precedenceListEntry><name>monus</name><arity>2</arity><precedence>0</precedence></precedenceListEntry><precedenceListEntry><name>0</name><arity>0</arity><precedence>1</precedence></precedenceListEntry><precedenceListEntry><name>s</name><arity>1</arity><precedence>0</precedence></precedenceListEntry><precedenceListEntry><name>div</name><arity>2</arity><precedence>2</precedence></precedenceListEntry></precedenceList><interpretation><type><polynomial><domain><naturals /></domain><degree>1</degree></polynomial></type><interpret><name>monus</name><arity>2</arity><sum><integer>0</integer><product><integer>1</integer><variable>1</variable></product><product><integer>0</integer><variable>2</variable></product></sum></interpret><interpret><sharp><name>monus</name></sharp><arity>2</arity><sum><integer>5</integer><product><integer>1</integer><variable>1</variable></product><product><integer>0</integer><variable>2</variable></product></sum></interpret><interpret><name>0</name><arity>0</arity><integer>1</integer></interpret><interpret><sharp><name>0</name></sharp><arity>0</arity><integer>5</integer></interpret><interpret><name>s</name><arity>1</arity><sum><integer>3</integer><product><integer>1</integer><variable>1</variable></product></sum></interpret><interpret><sharp><name>s</name></sharp><arity>1</arity><sum><integer>0</integer><product><integer>0</integer><variable>1</variable></product></sum></interpret><interpret><name>div</name><arity>2</arity><sum><integer>1</integer><product><integer>1</integer><variable>1</variable></product><product><integer>0</integer><variable>2</variable></product></sum></interpret><interpret><sharp><name>div</name></sharp><arity>2</arity><sum><integer>0</integer><product><integer>1</integer><variable>1</variable></product><product><integer>1</integer><variable>2</variable></product></sum></interpret></interpretation></generalizedWeightedPathOrder></monotonicSemanticPathOrder><trs><rules /></trs><trsTerminationProof><rIsEmpty /></trsTerminationProof></ruleRemoval></trsTerminationProof></proof></certificationProblem> |
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