/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>f</name><arg><funapp><name>f</name><arg><funapp><name>a</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>f</name><arg><var>x</var></arg><arg><var>z</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>f</name><arg><funapp><name>b</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>c</name></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>y</var></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsNonterminationProof><uncurry><uncurryInformation><name>f</name><uncurriedSymbols><uncurriedSymbolEntry><name>a</name><arity>0</arity><name>a</name><name>a1</name><name>a2</name><name>a3</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>b</name><arity>0</arity><name>b</name><name>b1</name><name>b2</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>c</name><arity>0</arity><name>c</name><name>c1</name></uncurriedSymbolEntry></uncurriedSymbols><uncurryRules><rules><rule><lhs><funapp><name>f</name><arg><funapp><name>a</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>a1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>a1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>a2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>a2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>a3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>b</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>b1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>b1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>b2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>c</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>c1</name><arg><var>y1</var></arg></funapp></rhs></rule></rules></uncurryRules><etaRules><rules/></etaRules></uncurryInformation><trs><rules><rule><lhs><funapp><name>a3</name><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>f</name><arg><var>x</var></arg><arg><var>z</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>b2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>c1</name><arg><var>y</var></arg></funapp></lhs><rhs><var>y</var></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>a</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>a1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>a1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>a2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>a2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>a3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>b</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>b1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>b1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>b2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>c</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>c1</name><arg><var>y1</var></arg></funapp></rhs></rule></rules></trs><trsNonterminationProof><innermostLhssIncrease><innermostLhss><funapp><name>a3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp><funapp><name>b2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp><funapp><name>c1</name><arg><var>x0</var></arg></funapp><funapp><name>f</name><arg><funapp><name>a</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>f</name><arg><funapp><name>a1</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp><funapp><name>f</name><arg><funapp><name>a2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp><funapp><name>f</name><arg><funapp><name>b</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>f</name><arg><funapp><name>b1</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp><funapp><name>f</name><arg><funapp><name>c</name></funapp></arg><arg><var>x0</var></arg></funapp></innermostLhss><trsNonterminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><var>x</var></arg><arg><var>z</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>x</var></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>y</var></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>a2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>a3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>b1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>b2</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>c</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>c1</name></sharp><arg><var>y1</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>a2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>a3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><var>x</var></arg><arg><var>z</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>x</var></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>y</var></arg><arg><var>z</var></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>a3</name><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>f</name><arg><var>x</var></arg><arg><var>z</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>b2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>c1</name><arg><var>y</var></arg></funapp></lhs><rhs><var>y</var></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>a</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>a1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>a1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>a2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>a2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>a3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>b</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>b1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>b1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>b2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>c</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>c1</name><arg><var>y1</var></arg></funapp></rhs></rule></rules></trs><dpNonterminationProof><narrowingProc><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><var>x</var></arg><arg><var>z</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><positionInTerm><position>1</position></positionInTerm><narrowings><rules><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>a</name></funapp></arg><arg><var>y1</var></arg><arg><var>x0</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>a1</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x0</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>a1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>a2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>a2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>a3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>b</name></funapp></arg><arg><var>y1</var></arg><arg><var>x0</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>b1</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x0</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>b1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>b2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>c</name></funapp></arg><arg><var>y1</var></arg><arg><var>x0</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>c1</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x0</var></arg></funapp></arg></funapp></rhs></rule></rules></narrowings><dpNonterminationProof><dpRuleRemoval><dps><rules><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>x</var></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>a2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>a3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>y</var></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>a1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>a2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>a2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>a3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>b1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>b2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>c</name></funapp></arg><arg><var>y1</var></arg><arg><var>x0</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>c1</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x0</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>a3</name><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>f</name><arg><var>x</var></arg><arg><var>z</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>b2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>c1</name><arg><var>y</var></arg></funapp></lhs><rhs><var>y</var></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>a</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>a1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>a1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>a2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>a2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>a3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>b</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>b1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>b1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>b2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>c</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>c1</name><arg><var>y1</var></arg></funapp></rhs></rule></rules></trs><dpNonterminationProof><rewritingProc><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>a2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>a3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>1</position></positionInTerm><rule><lhs><funapp><name>a3</name><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>f</name><arg><var>x</var></arg><arg><var>z</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><var>x2</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>a2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><var>x2</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule><usableRules><rules><rule><lhs><funapp><name>f</name><arg><funapp><name>a2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>a3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a3</name><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>f</name><arg><var>x</var></arg><arg><var>z</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>a</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>a1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>a1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>a2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>b</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>b1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>b1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>b2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><funapp><name>c</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>c1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>c1</name><arg><var>y</var></arg></funapp></lhs><rhs><var>y</var></rhs></rule><rule><lhs><funapp><name>b2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule></rules></usableRules><dpNonterminationProof><rewritingProc><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>b1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>b2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>1</position></positionInTerm><rule><lhs><funapp><name>b2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><funapp><sharp><name>f</name></sharp><arg><var>x0</var></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>b1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>x0</var></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><usableRules><rules><rule><lhs><funapp><name>b2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule></rules></usableRules><dpNonterminationProof><rewritingProc><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>c</name></funapp></arg><arg><var>y1</var></arg><arg><var>x0</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>c1</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x0</var></arg></funapp></arg></funapp></rhs></rule><rewriteStep><positionInTerm><position>1</position></positionInTerm><rule><lhs><funapp><name>c1</name><arg><var>y</var></arg></funapp></lhs><rhs><var>y</var></rhs></rule><funapp><sharp><name>f</name></sharp><arg><var>x0</var></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x0</var></arg></funapp></arg></funapp></rewriteStep><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>c</name></funapp></arg><arg><var>y1</var></arg><arg><var>x0</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>x0</var></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x0</var></arg></funapp></arg></funapp></rhs></rule><usableRules><rules><rule><lhs><funapp><name>c1</name><arg><var>y</var></arg></funapp></lhs><rhs><var>y</var></rhs></rule></rules></usableRules><dpNonterminationProof><instantiationProc><dps><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>a2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>a3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>y</var></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>a1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>a2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>a2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><var>x2</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>b1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>x0</var></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>c</name></funapp></arg><arg><var>y1</var></arg><arg><var>x0</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>x0</var></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x0</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>a2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>a2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></rhs></rule></rules></dps><dpNonterminationProof><instantiationProc><dps><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>a2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>a3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>a1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>a2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>a2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><var>x2</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>b1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>x0</var></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>c</name></funapp></arg><arg><var>y1</var></arg><arg><var>x0</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>x0</var></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x0</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>a2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>a2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><var>x0</var></arg><arg><funapp><name>a2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>a2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></rhs></rule></rules></dps><dpNonterminationProof><instantiationProc><dps><rules><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>a1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>a2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>a2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>f</name><arg><funapp><name>f</name><arg><var>x0</var></arg><arg><var>x2</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>b1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>x0</var></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>c</name></funapp></arg><arg><var>y1</var></arg><arg><var>x0</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>x0</var></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x0</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>a2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>a2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><var>x0</var></arg><arg><funapp><name>a2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>a2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>a2</name><arg><funapp><name>a1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></lhs><rhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>a1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>a2</name><arg><funapp><name>a2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></lhs><rhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>a2</name><arg><var>y_0</var></arg><arg><var>y_1</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>a2</name><arg><funapp><name>b1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></lhs><rhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>b1</name><arg><var>y_0</var></arg></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>a2</name><arg><funapp><name>c</name></funapp></arg><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></lhs><rhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>c</name></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>a2</name><arg><var>x0</var></arg><arg><funapp><name>a2</name><arg><var>y_1</var></arg><arg><var>y_2</var></arg></funapp></arg></funapp></arg><arg><var>x2</var></arg></funapp></lhs><rhs><funapp><sharp><name>a3</name></sharp><arg><var>x0</var></arg><arg><funapp><name>a2</name><arg><var>y_1</var></arg><arg><var>y_2</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></rhs></rule></rules></dps><dpNonterminationProof><switchFullStrategyProc><wcrProof><joinableCriticalPairsBFS>0</joinableCriticalPairsBFS></wcrProof><dpNonterminationProof><loop><rewriteSequence><startTerm><funapp><sharp><name>a3</name></sharp><arg><funapp><name>c</name></funapp></arg><arg><funapp><name>c</name></funapp></arg><arg><funapp><name>f</name><arg><funapp><name>c</name></funapp></arg><arg><funapp><name>a2</name><arg><funapp><name>c</name></funapp></arg><arg><funapp><name>c</name></funapp></arg></funapp></arg></funapp></arg></funapp></startTerm><rewriteStep><positionInTerm><position>3</position></positionInTerm><rule><lhs><funapp><name>f</name><arg><funapp><name>c</name></funapp></arg><arg><var>y1'</var></arg></funapp></lhs><rhs><funapp><name>c1</name><arg><var>y1'</var></arg></funapp></rhs></rule><relative/><funapp><sharp><name>a3</name></sharp><arg><funapp><name>c</name></funapp></arg><arg><funapp><name>c</name></funapp></arg><arg><funapp><name>c1</name><arg><funapp><name>a2</name><arg><funapp><name>c</name></funapp></arg><arg><funapp><name>c</name></funapp></arg></funapp></arg></funapp></arg></funapp></rewriteStep><rewriteStep><positionInTerm><position>3</position></positionInTerm><rule><lhs><funapp><name>c1</name><arg><var>y</var></arg></funapp></lhs><rhs><var>y</var></rhs></rule><relative/><funapp><sharp><name>a3</name></sharp><arg><funapp><name>c</name></funapp></arg><arg><funapp><name>c</name></funapp></arg><arg><funapp><name>a2</name><arg><funapp><name>c</name></funapp></arg><arg><funapp><name>c</name></funapp></arg></funapp></arg></funapp></rewriteStep><rewriteStep><positionInTerm/><rule><lhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>c</name></funapp></arg><arg><var>y1</var></arg><arg><var>x0</var></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>x0</var></arg><arg><funapp><name>f</name><arg><var>y1</var></arg><arg><var>x0</var></arg></funapp></arg></funapp></rhs></rule><funapp><sharp><name>f</name></sharp><arg><funapp><name>a2</name><arg><funapp><name>c</name></funapp></arg><arg><funapp><name>c</name></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><funapp><name>c</name></funapp></arg><arg><funapp><name>a2</name><arg><funapp><name>c</name></funapp></arg><arg><funapp><name>c</name></funapp></arg></funapp></arg></funapp></arg></funapp></rewriteStep><rewriteStep><positionInTerm/><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>a2</name><arg><funapp><name>c</name></funapp></arg><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp></lhs><rhs><funapp><sharp><name>a3</name></sharp><arg><funapp><name>c</name></funapp></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></rhs></rule><funapp><sharp><name>a3</name></sharp><arg><funapp><name>c</name></funapp></arg><arg><funapp><name>c</name></funapp></arg><arg><funapp><name>f</name><arg><funapp><name>c</name></funapp></arg><arg><funapp><name>a2</name><arg><funapp><name>c</name></funapp></arg><arg><funapp><name>c</name></funapp></arg></funapp></arg></funapp></arg></funapp></rewriteStep></rewriteSequence><substitution/><box/></loop></dpNonterminationProof></switchFullStrategyProc></dpNonterminationProof></instantiationProc></dpNonterminationProof></instantiationProc></dpNonterminationProof></instantiationProc></dpNonterminationProof></rewritingProc></dpNonterminationProof></rewritingProc></dpNonterminationProof></rewritingProc></dpNonterminationProof></dpRuleRemoval></dpNonterminationProof></narrowingProc></dpNonterminationProof></dpRuleRemoval></dpNonterminationProof></dpTrans></trsNonterminationProof></innermostLhssIncrease></trsNonterminationProof></uncurry></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 % (14 real / 0 unknown / 0 assumptions / 14 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>