/export/starexec/sandbox2/solver/bin/starexec_run_certified /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


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>app</name><arg><funapp><name>app</name><arg><funapp><name>.</name></funapp></arg><arg><funapp><name>1</name></funapp></arg></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>.</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>1</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>.</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>i</name></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>1</name></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>.</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>i</name></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>1</name></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>.</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>i</name></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>.</name></funapp></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></arg></funapp></lhs><rhs><var>z</var></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>.</name></funapp></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>.</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>i</name></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><var>z</var></arg></funapp></arg></funapp></lhs><rhs><var>z</var></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>.</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>.</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>.</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>.</name></funapp></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>i</name></funapp></arg><arg><funapp><name>1</name></funapp></arg></funapp></lhs><rhs><funapp><name>1</name></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>i</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>i</name></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>i</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>.</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>.</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>i</name></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>i</name></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><funapp><name>app</name><arg><var>f</var></arg><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>filter</name></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>filter</name></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>filter2</name></funapp></arg><arg><funapp><name>app</name><arg><var>f</var></arg><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>filter2</name></funapp></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>filter</name></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>filter2</name></funapp></arg><arg><funapp><name>false</name></funapp></arg></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>filter</name></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><uncurry><uncurryInformation><name>app</name><uncurriedSymbols><uncurriedSymbolEntry><name>.</name><arity>0</arity><name>.</name><name>.1</name><name>.2</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>1</name><arity>0</arity><name>1</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>i</name><arity>0</arity><name>i</name><name>i1</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>map</name><arity>0</arity><name>map</name><name>map1</name><name>map2</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>nil</name><arity>0</arity><name>nil</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>cons</name><arity>0</arity><name>cons</name><name>cons1</name><name>cons2</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>filter</name><arity>0</arity><name>filter</name><name>filter1</name><name>filter3</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>filter2</name><arity>0</arity><name>filter2</name><name>filter21</name><name>filter22</name><name>filter23</name><name>filter24</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>true</name><arity>0</arity><name>true</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>false</name><arity>0</arity><name>false</name></uncurriedSymbolEntry></uncurriedSymbols><uncurryRules><rules><rule><lhs><funapp><name>app</name><arg><funapp><name>.</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>.1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>.1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>.2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>i</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>i1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>map1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>map1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>map2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>cons1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>cons1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>cons2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>filter</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>filter1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>filter1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>filter3</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>filter2</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>filter21</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>filter21</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>filter22</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>filter22</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>filter23</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>filter23</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>filter24</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></uncurryRules><etaRules><rules/></etaRules></uncurryInformation><trs><rules><rule><lhs><funapp><name>.2</name><arg><funapp><name>1</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>.2</name><arg><var>x</var></arg><arg><funapp><name>1</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>.2</name><arg><funapp><name>i1</name><arg><var>x</var></arg></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>1</name></funapp></rhs></rule><rule><lhs><funapp><name>.2</name><arg><var>x</var></arg><arg><funapp><name>i1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>1</name></funapp></rhs></rule><rule><lhs><funapp><name>.2</name><arg><funapp><name>i1</name><arg><var>y</var></arg></funapp></arg><arg><funapp><name>.2</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></lhs><rhs><var>z</var></rhs></rule><rule><lhs><funapp><name>.2</name><arg><var>y</var></arg><arg><funapp><name>.2</name><arg><funapp><name>i1</name><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></arg></funapp></lhs><rhs><var>z</var></rhs></rule><rule><lhs><funapp><name>.2</name><arg><funapp><name>.2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>.2</name><arg><var>x</var></arg><arg><funapp><name>.2</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>i1</name><arg><funapp><name>1</name></funapp></arg></funapp></lhs><rhs><funapp><name>1</name></funapp></rhs></rule><rule><lhs><funapp><name>i1</name><arg><funapp><name>i1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>i1</name><arg><funapp><name>.2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>.2</name><arg><funapp><name>i1</name><arg><var>y</var></arg></funapp></arg><arg><funapp><name>i1</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>map2</name><arg><var>f</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>map2</name><arg><var>f</var></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons2</name><arg><funapp><name>app</name><arg><var>f</var></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>map2</name><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>filter3</name><arg><var>f</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>filter3</name><arg><var>f</var></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>filter24</name><arg><funapp><name>app</name><arg><var>f</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>filter24</name><arg><funapp><name>true</name></funapp></arg><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>filter3</name><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>filter24</name><arg><funapp><name>false</name></funapp></arg><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>filter3</name><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>.</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>.1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>.1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>.2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>i</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>i1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>map1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>map1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>map2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>cons1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>cons1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>cons2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>filter</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>filter1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>filter1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>filter3</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>filter2</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>filter21</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>filter21</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>filter22</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>filter22</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>filter23</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>filter23</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>filter24</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><pathOrder><statusPrecedence><statusPrecedenceEntry><name>.2</name><arity>2</arity><precedence>1</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>1</name><arity>0</arity><precedence>0</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>i1</name><arity>1</arity><precedence>5</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>map2</name><arity>2</arity><precedence>5</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>nil</name><arity>0</arity><precedence>2</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>cons2</name><arity>2</arity><precedence>3</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>app</name><arity>2</arity><precedence>5</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>filter3</name><arity>2</arity><precedence>5</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>filter24</name><arity>4</arity><precedence>5</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>true</name><arity>0</arity><precedence>6</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>false</name><arity>0</arity><precedence>7</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>.</name><arity>0</arity><precedence>8</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>i</name><arity>0</arity><precedence>9</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>map</name><arity>0</arity><precedence>10</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>map1</name><arity>1</arity><precedence>5</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>cons</name><arity>0</arity><precedence>11</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>filter</name><arity>0</arity><precedence>12</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>filter2</name><arity>0</arity><precedence>13</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>filter22</name><arity>2</arity><precedence>4</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>filter23</name><arity>3</arity><precedence>5</precedence><lex/></statusPrecedenceEntry></statusPrecedence><argumentFilter><argumentFilterEntry><name>.2</name><arity>2</arity><nonCollapsing><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>1</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>i1</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>map2</name><arity>2</arity><nonCollapsing><position>2</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>nil</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>cons2</name><arity>2</arity><nonCollapsing><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>app</name><arity>2</arity><nonCollapsing><position>2</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>filter3</name><arity>2</arity><nonCollapsing><position>2</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>filter24</name><arity>4</arity><nonCollapsing><position>4</position><position>2</position><position>1</position><position>3</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>true</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>false</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>.</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>.1</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>i</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>map</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>map1</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>cons</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>cons1</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>filter</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>filter1</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>filter2</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>filter21</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>filter22</name><arity>2</arity><nonCollapsing><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>filter23</name><arity>3</arity><nonCollapsing><position>3</position><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry></argumentFilter></pathOrder></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>app</name><arg><funapp><name>filter1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>filter3</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><knuthBendixOrder><w0>1</w0><precedenceWeight><precedenceWeightEntry><name>filter1</name><arity>1</arity><precedence>0</precedence><weight>1</weight></precedenceWeightEntry><precedenceWeightEntry><name>app</name><arity>2</arity><precedence>2</precedence><weight>0</weight></precedenceWeightEntry><precedenceWeightEntry><name>filter3</name><arity>2</arity><precedence>1</precedence><weight>1</weight></precedenceWeightEntry></precedenceWeight></knuthBendixOrder></redPair></orderingConstraintProof><trs><rules/></trs><trsTerminationProof><rIsEmpty/></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></uncurry></trsTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty
</version><strategy>Statistics for single proof: 100.00 % (4 real / 0 unknown / 0 assumptions / 4 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>