NO
<?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>fact</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>if</name><arg><funapp><name>zero</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>n__s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>n__prod</name><arg><var>X</var></arg><arg><funapp><name>fact</name><arg><funapp><name>p</name><arg><var>X</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>add</name><arg><funapp><name>0</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>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>add</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>prod</name><arg><funapp><name>0</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>prod</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>add</name><arg><var>Y</var></arg><arg><funapp><name>prod</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>if</name><arg><funapp><name>true</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>activate</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>if</name><arg><funapp><name>false</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>activate</name><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>zero</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>zero</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>p</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>s</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__s</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>prod</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>n__prod</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__prod</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>prod</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule></rules></trs><strategy><outermost/></strategy></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsNonterminationProof><loop><rewriteSequence><startTerm><funapp><name>fact</name><arg><var>X</var></arg></funapp></startTerm><rewriteStep><positionInTerm/><rule><lhs><funapp><name>fact</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>if</name><arg><funapp><name>zero</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>n__s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>n__prod</name><arg><var>X</var></arg><arg><funapp><name>fact</name><arg><funapp><name>p</name><arg><var>X</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><funapp><name>if</name><arg><funapp><name>zero</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>n__s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>n__prod</name><arg><var>X</var></arg><arg><funapp><name>fact</name><arg><funapp><name>p</name><arg><var>X</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rewriteStep></rewriteSequence><substitution><substEntry><var>X</var><funapp><name>p</name><arg><var>X</var></arg></funapp></substEntry></substitution><funContext><name>if</name><before><funapp><name>zero</name><arg><var>X</var></arg></funapp><funapp><name>n__s</name><arg><funapp><name>0</name></funapp></arg></funapp></before><funContext><name>n__prod</name><before><var>X</var></before><box/><after/></funContext><after/></funContext></loop></trsNonterminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
</version><strategy>Statistics for single proof: 100.00 % (1 real / 0 unknown / 0 assumptions / 1 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>