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__terms</name><arg><var>N</var></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>recip</name><arg><funapp><name>a__sqr</name><arg><funapp><name>mark</name><arg><var>N</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>terms</name><arg><funapp><name>s</name><arg><var>N</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__sqr</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>a__sqr</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>a__add</name><arg><funapp><name>a__sqr</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>a__dbl</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__dbl</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>a__dbl</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>a__dbl</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__add</name><arg><funapp><name>0</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__add</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>a__add</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>mark</name><arg><var>Y</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__first</name><arg><funapp><name>0</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>a__first</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>Y</var></arg><arg><var>Z</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>mark</name><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>first</name><arg><var>X</var></arg><arg><var>Z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__half</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>a__half</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>a__half</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>a__half</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__half</name><arg><funapp><name>dbl</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>terms</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__terms</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>sqr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__sqr</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>add</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__add</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>dbl</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__dbl</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>first</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__first</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>half</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__half</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>recip</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>recip</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>a__terms</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>terms</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__sqr</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>sqr</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__add</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>add</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__dbl</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>dbl</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__first</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>first</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__half</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>half</name><arg><var>X</var></arg></funapp></rhs></rule></rules></trs><strategy><innermost/></strategy></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><name>a__terms</name></sharp><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>a__sqr</name></sharp><arg><funapp><name>mark</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__terms</name></sharp><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__sqr</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__add</name></sharp><arg><funapp><name>a__sqr</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>a__dbl</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__sqr</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__sqr</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__sqr</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__sqr</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__dbl</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__dbl</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__dbl</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__dbl</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__add</name></sharp><arg><funapp><name>0</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__add</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>a__add</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>mark</name><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__add</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__add</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__first</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>Y</var></arg><arg><var>Z</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__half</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__half</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__half</name></sharp><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__half</name></sharp><arg><funapp><name>dbl</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>terms</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__terms</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>terms</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>sqr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__sqr</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>sqr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>add</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__add</name></sharp><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>add</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>add</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>dbl</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__dbl</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>dbl</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>first</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__first</name></sharp><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>mark</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>first</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>first</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>half</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__half</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>half</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>recip</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpProof><redPairProc><orderingConstraintProof><redPair><pathOrder><statusPrecedence><statusPrecedenceEntry><sharp><name>a__terms</name></sharp><arity>1</arity><precedence>6</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><sharp><name>a__sqr</name></sharp><arity>1</arity><precedence>6</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><sharp><name>mark</name></sharp><arity>1</arity><precedence>0</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>s</name><arity>1</arity><precedence>1</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><sharp><name>a__add</name></sharp><arity>2</arity><precedence>2</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>a__sqr</name><arity>1</arity><precedence>6</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>a__dbl</name><arity>1</arity><precedence>6</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><sharp><name>a__dbl</name></sharp><arity>1</arity><precedence>3</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>0</name><arity>0</arity><precedence>6</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><sharp><name>a__first</name></sharp><arity>2</arity><precedence>0</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><sharp><name>a__half</name></sharp><arity>1</arity><precedence>0</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>dbl</name><arity>1</arity><precedence>6</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>terms</name><arity>1</arity><precedence>6</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>sqr</name><arity>1</arity><precedence>6</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>add</name><arity>2</arity><precedence>4</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>first</name><arity>2</arity><precedence>7</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>a__terms</name><arity>1</arity><precedence>6</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>a__add</name><arity>2</arity><precedence>4</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>a__first</name><arity>2</arity><precedence>7</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>nil</name><arity>0</arity><precedence>5</precedence><mul/></statusPrecedenceEntry></statusPrecedence><argumentFilter><argumentFilterEntry><sharp><name>a__terms</name></sharp><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><sharp><name>a__sqr</name></sharp><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>mark</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><sharp><name>mark</name></sharp><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>s</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><sharp><name>a__add</name></sharp><arity>2</arity><nonCollapsing><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>a__sqr</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>a__dbl</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><sharp><name>a__dbl</name></sharp><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>0</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><sharp><name>a__first</name></sharp><arity>2</arity><nonCollapsing><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>cons</name><arity>2</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><sharp><name>a__half</name></sharp><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>dbl</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>terms</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>sqr</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>add</name><arity>2</arity><nonCollapsing><position>2</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>first</name><arity>2</arity><nonCollapsing><position>2</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>half</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>recip</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>a__terms</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>a__add</name><arity>2</arity><nonCollapsing><position>2</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>a__half</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>a__first</name><arity>2</arity><nonCollapsing><position>2</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>nil</name><arity>0</arity><nonCollapsing/></argumentFilterEntry></argumentFilter></pathOrder></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>a__terms</name></sharp><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>a__sqr</name></sharp><arg><funapp><name>mark</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__first</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>Y</var></arg><arg><var>Z</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>half</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__half</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>half</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>recip</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>a__first</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>Y</var></arg><arg><var>Z</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>half</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>recip</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss/><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>half</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>recip</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>a__terms</name></sharp><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>a__sqr</name></sharp><arg><funapp><name>mark</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>half</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__half</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></redPairProc></dpProof></dpTrans></trsTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
</version><strategy>Statistics for single proof: 100.00 % (6 real / 0 unknown / 0 assumptions / 6 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>