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


--------------------------------------------------------------------------------


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>f</name><arg><funapp><name>tt</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>isNat</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNat</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNat</name><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNat</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsNonterminationProof><innermostLhssIncrease><innermostLhss><funapp><name>f</name><arg><funapp><name>tt</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>isNat</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>isNat</name><arg><funapp><name>0</name></funapp></arg></funapp></innermostLhss><trsNonterminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>isNat</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><var>x</var></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpNonterminationProof><dpRuleRemoval><dps><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>isNat</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>f</name><arg><funapp><name>tt</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>isNat</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNat</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNat</name><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNat</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule></rules></trs><dpNonterminationProof><switchFullStrategyProc><wcrProof><joinableCriticalPairsBFS>10</joinableCriticalPairsBFS></wcrProof><dpNonterminationProof><nonLoop><patternRule><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>s</name><arg><var>zr0</var></arg></funapp></arg></funapp><substitution><substEntry><var>zr0</var><funapp><name>0</name></funapp></substEntry></substitution><substitution><substEntry><var>zr0</var><funapp><name>s</name><arg><var>zr0</var></arg></funapp></substEntry></substitution></patternTerm><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>zr0</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp><substitution><substEntry><var>zr0</var><funapp><name>0</name></funapp></substEntry></substitution><substitution><substEntry><var>zr0</var><funapp><name>s</name><arg><var>zr0</var></arg></funapp></substEntry></substitution></patternTerm><equivalence><patternRule><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>s</name><arg><var>zl0</var></arg></funapp></arg></funapp><substitution><substEntry><var>zl0</var><funapp><name>0</name></funapp></substEntry></substitution><substitution><substEntry><var>zl0</var><funapp><name>s</name><arg><var>zl0</var></arg></funapp></substEntry></substitution></patternTerm><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>zr0</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp><substitution><substEntry><var>zr0</var><funapp><name>0</name></funapp></substEntry></substitution><substitution><substEntry><var>zr0</var><funapp><name>s</name><arg><var>zr0</var></arg></funapp></substEntry></substitution></patternTerm><equivalence><patternRule><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>s</name><arg><var>zl0</var></arg></funapp></arg></funapp><substitution><substEntry><var>zl0</var><funapp><name>0</name></funapp></substEntry></substitution><substitution><substEntry><var>zl0</var><funapp><name>s</name><arg><var>zl0</var></arg></funapp></substEntry></substitution></patternTerm><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>zr1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp><substitution><substEntry><var>zr1</var><funapp><name>0</name></funapp></substEntry></substitution><substitution><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry></substitution></patternTerm><equivalence><patternRule><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>s</name><arg><var>zl1</var></arg></funapp></arg></funapp><substitution><substEntry><var>zl1</var><funapp><name>0</name></funapp></substEntry></substitution><substitution><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry></substitution></patternTerm><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>zr1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp><substitution><substEntry><var>zr1</var><funapp><name>0</name></funapp></substEntry></substitution><substitution><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry></substitution></patternTerm><equivalence><patternRule><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>s</name><arg><var>zl1</var></arg></funapp></arg></funapp><substitution><substEntry><var>zl1</var><funapp><name>0</name></funapp></substEntry></substitution><substitution><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry></substitution></patternTerm><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>zr1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp><substitution><substEntry><var>zr1</var><funapp><name>0</name></funapp></substEntry><substEntry><var>zl1</var><funapp><name>0</name></funapp></substEntry></substitution><substitution><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry></substitution></patternTerm><equivalence><patternRule><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>s</name><arg><var>zl1</var></arg></funapp></arg></funapp><substitution><substEntry><var>zr1</var><funapp><name>0</name></funapp></substEntry><substEntry><var>zl1</var><funapp><name>0</name></funapp></substEntry></substitution><substitution><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry></substitution></patternTerm><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>zr1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp><substitution><substEntry><var>zr1</var><funapp><name>0</name></funapp></substEntry><substEntry><var>zl1</var><funapp><name>0</name></funapp></substEntry></substitution><substitution><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry></substitution></patternTerm><narrowing><patternRule><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>s</name><arg><var>zl1</var></arg></funapp></arg></funapp><substitution><substEntry><var>zr1</var><funapp><name>0</name></funapp></substEntry><substEntry><var>zl1</var><funapp><name>0</name></funapp></substEntry></substitution><substitution><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry></substitution></patternTerm><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>isNat</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>zr1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp><substitution><substEntry><var>zl1</var><funapp><name>0</name></funapp></substEntry><substEntry><var>zr1</var><funapp><name>0</name></funapp></substEntry></substitution><substitution><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry></substitution></patternTerm><equivalence><patternRule><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>s</name><arg><var>zl1</var></arg></funapp></arg></funapp><substitution><substEntry><var>zr1</var><funapp><name>0</name></funapp></substEntry><substEntry><var>zl1</var><funapp><name>0</name></funapp></substEntry></substitution><substitution><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry></substitution></patternTerm><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>isNat</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>zr1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp><substitution><substEntry><var>zr1</var><funapp><name>0</name></funapp></substEntry></substitution><substitution><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry></substitution></patternTerm><equivalence><patternRule><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>s</name><arg><var>zl1</var></arg></funapp></arg></funapp><substitution><substEntry><var>zl1</var><funapp><name>0</name></funapp></substEntry></substitution><substitution><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry></substitution></patternTerm><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>isNat</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>zr1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp><substitution><substEntry><var>zr1</var><funapp><name>0</name></funapp></substEntry></substitution><substitution><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry></substitution></patternTerm><equivalence><patternRule><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>s</name><arg><var>zl1</var></arg></funapp></arg></funapp><substitution><substEntry><var>zl1</var><funapp><name>0</name></funapp></substEntry></substitution><substitution><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry></substitution></patternTerm><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>isNat</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>zr1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp><substitution><substEntry><var>zr1</var><funapp><name>0</name></funapp></substEntry></substitution><substitution><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry></substitution></patternTerm><equivalence><patternRule><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>s</name><arg><var>zl1</var></arg></funapp></arg></funapp><substitution><substEntry><var>zl1</var><funapp><name>0</name></funapp></substEntry></substitution><substitution><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry></substitution></patternTerm><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>isNat</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>zr1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp><substitution><substEntry><var>zr1</var><funapp><name>0</name></funapp></substEntry></substitution><substitution><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry></substitution></patternTerm><instantiation><patternRule><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>s</name><arg><var>zl1</var></arg></funapp></arg></funapp><substitution><substEntry><var>zl1</var><var>x0</var></substEntry></substitution><substitution><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry></substitution></patternTerm><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>isNat</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>zr1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp><substitution><substEntry><var>zr1</var><var>x0</var></substEntry></substitution><substitution><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry></substitution></patternTerm><equivalence><patternRule><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>s</name><arg><var>zl1</var></arg></funapp></arg></funapp><substitution><substEntry><var>zl1</var><var>x0</var></substEntry></substitution><substitution><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry></substitution></patternTerm><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>isNat</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>zr0</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp><substitution><substEntry><var>zr0</var><var>x0</var></substEntry></substitution><substitution><substEntry><var>zr0</var><funapp><name>s</name><arg><var>zr0</var></arg></funapp></substEntry></substitution></patternTerm><equivalence><patternRule><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>s</name><arg><var>zl0</var></arg></funapp></arg></funapp><substitution><substEntry><var>zl0</var><var>x0</var></substEntry></substitution><substitution><substEntry><var>zl0</var><funapp><name>s</name><arg><var>zl0</var></arg></funapp></substEntry></substitution></patternTerm><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>isNat</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>zr0</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp><substitution><substEntry><var>zr0</var><var>x0</var></substEntry></substitution><substitution><substEntry><var>zr0</var><funapp><name>s</name><arg><var>zr0</var></arg></funapp></substEntry></substitution></patternTerm><instantiation><patternRule><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>s</name><arg><var>zl0</var></arg></funapp></arg></funapp><substitution><substEntry><var>zl0</var><var>y0</var></substEntry></substitution><substitution><substEntry><var>zl0</var><funapp><name>s</name><arg><var>zl0</var></arg></funapp></substEntry></substitution></patternTerm><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>isNat</name><arg><var>y0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>zr0</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp><substitution><substEntry><var>zr0</var><var>y0</var></substEntry></substitution><substitution><substEntry><var>zr0</var><funapp><name>s</name><arg><var>zr0</var></arg></funapp></substEntry></substitution></patternTerm><equivalence><patternRule><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>s</name><arg><var>zl0</var></arg></funapp></arg></funapp><substitution><substEntry><var>zl0</var><var>y0</var></substEntry></substitution><substitution><substEntry><var>zl0</var><funapp><name>s</name><arg><var>zl0</var></arg></funapp></substEntry></substitution></patternTerm><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>isNat</name><arg><var>y0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>zs1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp><substitution><substEntry><var>zs1</var><var>y0</var></substEntry></substitution><substitution><substEntry><var>zs1</var><funapp><name>s</name><arg><var>zs1</var></arg></funapp></substEntry></substitution></patternTerm><equivalence><patternRule><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>s</name><arg><var>zs1</var></arg></funapp></arg></funapp><substitution><substEntry><var>zs1</var><var>y0</var></substEntry></substitution><substitution><substEntry><var>zs1</var><funapp><name>s</name><arg><var>zs1</var></arg></funapp></substEntry></substitution></patternTerm><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>isNat</name><arg><var>y0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>zs1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp><substitution><substEntry><var>zs1</var><var>y0</var></substEntry></substitution><substitution><substEntry><var>zs1</var><funapp><name>s</name><arg><var>zs1</var></arg></funapp></substEntry></substitution></patternTerm><narrowing><patternRule><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>s</name><arg><var>zs1</var></arg></funapp></arg></funapp><substitution><substEntry><var>zs1</var><var>y0</var></substEntry></substitution><substitution><substEntry><var>zs1</var><funapp><name>s</name><arg><var>zs1</var></arg></funapp></substEntry></substitution></patternTerm><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>isNat</name><arg><funapp><name>s</name><arg><var>zs1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>zs1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp><substitution><substEntry><var>zs1</var><var>y0</var></substEntry></substitution><substitution><substEntry><var>zs1</var><funapp><name>s</name><arg><var>zs1</var></arg></funapp></substEntry></substitution></patternTerm><instantiation><patternRule><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>s</name><arg><var>zs1</var></arg></funapp></arg></funapp><substitution/><substitution><substEntry><var>zs1</var><funapp><name>s</name><arg><var>zs1</var></arg></funapp></substEntry></substitution></patternTerm><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>isNat</name><arg><funapp><name>s</name><arg><var>zs1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>zs1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp><substitution/><substitution><substEntry><var>zs1</var><funapp><name>s</name><arg><var>zs1</var></arg></funapp></substEntry></substitution></patternTerm><instantiation><patternRule><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>s</name><arg><var>zs1</var></arg></funapp></arg></funapp><substitution/><substitution/></patternTerm><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>isNat</name><arg><funapp><name>s</name><arg><var>zs1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>zs1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp><substitution/><substitution/></patternTerm><instantiation><patternRule><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>x0</var></arg></funapp><substitution/><substitution/></patternTerm><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>isNat</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg></funapp></arg></funapp><substitution/><substitution/></patternTerm><instantiation><patternRule><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>x</var></arg></funapp><substitution/><substitution/></patternTerm><patternTerm><funapp><sharp><name>f</name></sharp><arg><funapp><name>isNat</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp><substitution/><substitution/></patternTerm><originalRule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>isNat</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><isPair>true</isPair></originalRule></patternRule><substitution><substEntry><var>x</var><var>x0</var></substEntry></substitution><base/></instantiation></patternRule><substitution><substEntry><var>x0</var><funapp><name>s</name><arg><var>zs1</var></arg></funapp></substEntry></substitution><base/></instantiation></patternRule><substitution><substEntry><var>zs1</var><funapp><name>s</name><arg><var>zs1</var></arg></funapp></substEntry></substitution><pumping/></instantiation></patternRule><substitution><substEntry><var>zs1</var><var>y0</var></substEntry></substitution><closing/></instantiation></patternRule><patternRule><patternTerm><funapp><name>isNat</name><arg><funapp><name>s</name><arg><var>zs1</var></arg></funapp></arg></funapp><substitution><substEntry><var>zs1</var><var>y0</var></substEntry></substitution><substitution><substEntry><var>zs1</var><funapp><name>s</name><arg><var>zs1</var></arg></funapp></substEntry></substitution></patternTerm><patternTerm><funapp><name>isNat</name><arg><var>y0</var></arg></funapp><substitution><substEntry><var>zs1</var><var>y0</var></substEntry></substitution><substitution><substEntry><var>zs1</var><funapp><name>s</name><arg><var>zs1</var></arg></funapp></substEntry></substitution></patternTerm><equivalence><patternRule><patternTerm><funapp><name>isNat</name><arg><funapp><name>s</name><arg><var>zs1</var></arg></funapp></arg></funapp><substitution><substEntry><var>zs1</var><var>y0</var></substEntry></substitution><substitution><substEntry><var>zs1</var><funapp><name>s</name><arg><var>zs1</var></arg></funapp></substEntry></substitution></patternTerm><patternTerm><funapp><name>isNat</name><arg><var>y0</var></arg></funapp><substitution/><substitution><substEntry><var>zs1</var><funapp><name>s</name><arg><var>zs1</var></arg></funapp></substEntry></substitution></patternTerm><equivalence><patternRule><patternTerm><funapp><name>isNat</name><arg><funapp><name>s</name><arg><var>zs1</var></arg></funapp></arg></funapp><substitution><substEntry><var>zs1</var><var>y0</var></substEntry></substitution><substitution><substEntry><var>zs1</var><funapp><name>s</name><arg><var>zs1</var></arg></funapp></substEntry></substitution></patternTerm><patternTerm><funapp><name>isNat</name><arg><var>y0</var></arg></funapp><substitution/><substitution/></patternTerm><equivalence><patternRule><patternTerm><funapp><name>isNat</name><arg><funapp><name>s</name><arg><var>zs0</var></arg></funapp></arg></funapp><substitution><substEntry><var>zs0</var><var>y0</var></substEntry></substitution><substitution><substEntry><var>zs0</var><funapp><name>s</name><arg><var>zs0</var></arg></funapp></substEntry></substitution></patternTerm><patternTerm><funapp><name>isNat</name><arg><var>y0</var></arg></funapp><substitution/><substitution/></patternTerm><instantiation><patternRule><patternTerm><funapp><name>isNat</name><arg><funapp><name>s</name><arg><var>zs0</var></arg></funapp></arg></funapp><substitution><substEntry><var>zs0</var><var>x</var></substEntry></substitution><substitution><substEntry><var>zs0</var><funapp><name>s</name><arg><var>zs0</var></arg></funapp></substEntry></substitution></patternTerm><patternTerm><funapp><name>isNat</name><arg><var>x</var></arg></funapp><substitution/><substitution/></patternTerm><equivalence><patternRule><patternTerm><funapp><name>isNat</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp><substitution/><substitution><substEntry><var>x</var><funapp><name>s</name><arg><var>x</var></arg></funapp></substEntry></substitution></patternTerm><patternTerm><funapp><name>isNat</name><arg><var>x</var></arg></funapp><substitution/><substitution/></patternTerm><initialPumping><patternRule><patternTerm><funapp><name>isNat</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp><substitution/><substitution/></patternTerm><patternTerm><funapp><name>isNat</name><arg><var>x</var></arg></funapp><substitution/><substitution/></patternTerm><originalRule><rule><lhs><funapp><name>isNat</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNat</name><arg><var>x</var></arg></funapp></rhs></rule><isPair>false</isPair></originalRule></patternRule><substitution><substEntry><var>x</var><funapp><name>s</name><arg><var>x</var></arg></funapp></substEntry></substitution><substitution/></initialPumping></patternRule><left/><patternEquivalence><domainRenaming><substitution><substEntry><var>x</var><var>zs0</var></substEntry></substitution></domainRenaming></patternEquivalence></equivalence></patternRule><substitution><substEntry><var>x</var><var>y0</var></substEntry></substitution><base/></instantiation></patternRule><left/><patternEquivalence><domainRenaming><substitution><substEntry><var>zs0</var><var>zs1</var></substEntry></substitution></domainRenaming></patternEquivalence></equivalence></patternRule><right/><patternEquivalence><irrelevant><substitution><substEntry><var>zs1</var><funapp><name>s</name><arg><var>zs1</var></arg></funapp></substEntry></substitution><substitution/></irrelevant></patternEquivalence></equivalence></patternRule><right/><patternEquivalence><irrelevant><substitution><substEntry><var>zs1</var><funapp><name>s</name><arg><var>zs1</var></arg></funapp></substEntry></substitution><substitution><substEntry><var>zs1</var><var>y0</var></substEntry></substitution></irrelevant></patternEquivalence></equivalence></patternRule><positionInTerm><position>1</position></positionInTerm></narrowing></patternRule><left/><patternEquivalence><domainRenaming><substitution><substEntry><var>zs1</var><var>zl0</var></substEntry></substitution></domainRenaming></patternEquivalence></equivalence></patternRule><right/><patternEquivalence><domainRenaming><substitution><substEntry><var>zs1</var><var>zr0</var></substEntry></substitution></domainRenaming></patternEquivalence></equivalence></patternRule><substitution><substEntry><var>y0</var><var>x0</var></substEntry></substitution><base/></instantiation></patternRule><left/><patternEquivalence><domainRenaming><substitution><substEntry><var>zl0</var><var>zl1</var></substEntry></substitution></domainRenaming></patternEquivalence></equivalence></patternRule><right/><patternEquivalence><domainRenaming><substitution><substEntry><var>zr0</var><var>zr1</var></substEntry></substitution></domainRenaming></patternEquivalence></equivalence></patternRule><substitution><substEntry><var>x0</var><funapp><name>0</name></funapp></substEntry></substitution><base/></instantiation></patternRule><left/><patternEquivalence><irrelevant><substitution><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry></substitution><substitution><substEntry><var>zl1</var><funapp><name>0</name></funapp></substEntry></substitution></irrelevant></patternEquivalence></equivalence></patternRule><right/><patternEquivalence><irrelevant><substitution><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry></substitution><substitution><substEntry><var>zr1</var><funapp><name>0</name></funapp></substEntry></substitution></irrelevant></patternEquivalence></equivalence></patternRule><left/><patternEquivalence><irrelevant><substitution><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry></substitution><substitution><substEntry><var>zr1</var><funapp><name>0</name></funapp></substEntry><substEntry><var>zl1</var><funapp><name>0</name></funapp></substEntry></substitution></irrelevant></patternEquivalence></equivalence></patternRule><right/><patternEquivalence><irrelevant><substitution><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry></substitution><substitution><substEntry><var>zl1</var><funapp><name>0</name></funapp></substEntry><substEntry><var>zr1</var><funapp><name>0</name></funapp></substEntry></substitution></irrelevant></patternEquivalence></equivalence></patternRule><patternRule><patternTerm><funapp><name>isNat</name><arg><funapp><name>0</name></funapp></arg></funapp><substitution><substEntry><var>zl1</var><funapp><name>0</name></funapp></substEntry><substEntry><var>zr1</var><funapp><name>0</name></funapp></substEntry></substitution><substitution><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry></substitution></patternTerm><patternTerm><funapp><name>tt</name></funapp><substitution><substEntry><var>zl1</var><funapp><name>0</name></funapp></substEntry><substEntry><var>zr1</var><funapp><name>0</name></funapp></substEntry></substitution><substitution><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry></substitution></patternTerm><equivalence><patternRule><patternTerm><funapp><name>isNat</name><arg><funapp><name>0</name></funapp></arg></funapp><substitution><substEntry><var>zl1</var><funapp><name>0</name></funapp></substEntry><substEntry><var>zr1</var><funapp><name>0</name></funapp></substEntry></substitution><substitution><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry></substitution></patternTerm><patternTerm><funapp><name>tt</name></funapp><substitution/><substitution><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry></substitution></patternTerm><equivalence><patternRule><patternTerm><funapp><name>isNat</name><arg><funapp><name>0</name></funapp></arg></funapp><substitution/><substitution><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry></substitution></patternTerm><patternTerm><funapp><name>tt</name></funapp><substitution/><substitution><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry></substitution></patternTerm><equivalence><patternRule><patternTerm><funapp><name>isNat</name><arg><funapp><name>0</name></funapp></arg></funapp><substitution/><substitution><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry></substitution></patternTerm><patternTerm><funapp><name>tt</name></funapp><substitution/><substitution/></patternTerm><equivalence><patternRule><patternTerm><funapp><name>isNat</name><arg><funapp><name>0</name></funapp></arg></funapp><substitution/><substitution/></patternTerm><patternTerm><funapp><name>tt</name></funapp><substitution/><substitution/></patternTerm><originalRule><rule><lhs><funapp><name>isNat</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><isPair>false</isPair></originalRule></patternRule><left/><patternEquivalence><irrelevant><substitution><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry></substitution><substitution/></irrelevant></patternEquivalence></equivalence></patternRule><right/><patternEquivalence><irrelevant><substitution><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry></substitution><substitution/></irrelevant></patternEquivalence></equivalence></patternRule><left/><patternEquivalence><irrelevant><substitution><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry></substitution><substitution><substEntry><var>zl1</var><funapp><name>0</name></funapp></substEntry><substEntry><var>zr1</var><funapp><name>0</name></funapp></substEntry></substitution></irrelevant></patternEquivalence></equivalence></patternRule><right/><patternEquivalence><irrelevant><substitution><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry></substitution><substitution><substEntry><var>zl1</var><funapp><name>0</name></funapp></substEntry><substEntry><var>zr1</var><funapp><name>0</name></funapp></substEntry></substitution></irrelevant></patternEquivalence></equivalence></patternRule><positionInTerm><position>1</position></positionInTerm></narrowing></patternRule><left/><patternEquivalence><irrelevant><substitution><substEntry><var>zl1</var><funapp><name>s</name><arg><var>zl1</var></arg></funapp></substEntry></substitution><substitution><substEntry><var>zl1</var><funapp><name>0</name></funapp></substEntry></substitution></irrelevant></patternEquivalence></equivalence></patternRule><right/><patternEquivalence><irrelevant><substitution><substEntry><var>zr1</var><funapp><name>s</name><arg><var>zr1</var></arg></funapp></substEntry></substitution><substitution><substEntry><var>zr1</var><funapp><name>0</name></funapp></substEntry></substitution></irrelevant></patternEquivalence></equivalence></patternRule><left/><patternEquivalence><domainRenaming><substitution><substEntry><var>zl1</var><var>zl0</var></substEntry></substitution></domainRenaming></patternEquivalence></equivalence></patternRule><right/><patternEquivalence><domainRenaming><substitution><substEntry><var>zr1</var><var>zr0</var></substEntry></substitution></domainRenaming></patternEquivalence></equivalence></patternRule><left/><patternEquivalence><domainRenaming><substitution><substEntry><var>zl0</var><var>zr0</var></substEntry></substitution></domainRenaming></patternEquivalence></equivalence></patternRule><substitution/><substitution/><natural>1</natural><natural>2</natural><positionInTerm/></nonLoop></dpNonterminationProof></switchFullStrategyProc></dpNonterminationProof></dpRuleRemoval></dpNonterminationProof></dpTrans></trsNonterminationProof></innermostLhssIncrease></trsNonterminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty
</version><strategy>Statistics for single proof: 100.00 % (5 real / 0 unknown / 0 assumptions / 5 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>