/export/starexec/sandbox/solver/bin/starexec_run_certified /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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>ap</name><arg><funapp><name>ap</name><arg><funapp><name>map</name></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>ap</name><arg><funapp><name>ap</name><arg><funapp><name>ap</name><arg><funapp><name>if</name></funapp></arg><arg><funapp><name>ap</name><arg><funapp><name>isEmpty</name></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ap</name><arg><funapp><name>ap</name><arg><funapp><name>ap</name><arg><funapp><name>if</name></funapp></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>null</name></funapp></rhs></rule><rule><lhs><funapp><name>ap</name><arg><funapp><name>ap</name><arg><funapp><name>ap</name><arg><funapp><name>if</name></funapp></arg><arg><funapp><name>null</name></funapp></arg></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>ap</name><arg><funapp><name>ap</name><arg><funapp><name>cons</name></funapp></arg><arg><funapp><name>ap</name><arg><var>f</var></arg><arg><funapp><name>ap</name><arg><funapp><name>last</name></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>ap</name><arg><funapp><name>ap</name><arg><funapp><name>if2</name></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>ap</name><arg><funapp><name>ap</name><arg><funapp><name>if2</name></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>ap</name><arg><funapp><name>ap</name><arg><funapp><name>map</name></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><funapp><name>ap</name><arg><funapp><name>dropLast</name></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>ap</name><arg><funapp><name>isEmpty</name></funapp></arg><arg><funapp><name>null</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>ap</name><arg><funapp><name>isEmpty</name></funapp></arg><arg><funapp><name>ap</name><arg><funapp><name>ap</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>null</name></funapp></rhs></rule><rule><lhs><funapp><name>ap</name><arg><funapp><name>last</name></funapp></arg><arg><funapp><name>ap</name><arg><funapp><name>ap</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>null</name></funapp></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>ap</name><arg><funapp><name>last</name></funapp></arg><arg><funapp><name>ap</name><arg><funapp><name>ap</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>ap</name><arg><funapp><name>ap</name><arg><funapp><name>cons</name></funapp></arg><arg><var>y</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ap</name><arg><funapp><name>last</name></funapp></arg><arg><funapp><name>ap</name><arg><funapp><name>ap</name><arg><funapp><name>cons</name></funapp></arg><arg><var>y</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>ap</name><arg><funapp><name>dropLast</name></funapp></arg><arg><funapp><name>ap</name><arg><funapp><name>ap</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>null</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>null</name></funapp></rhs></rule><rule><lhs><funapp><name>ap</name><arg><funapp><name>dropLast</name></funapp></arg><arg><funapp><name>ap</name><arg><funapp><name>ap</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>ap</name><arg><funapp><name>ap</name><arg><funapp><name>cons</name></funapp></arg><arg><var>y</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>ap</name><arg><funapp><name>ap</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>ap</name><arg><funapp><name>dropLast</name></funapp></arg><arg><funapp><name>ap</name><arg><funapp><name>ap</name><arg><funapp><name>cons</name></funapp></arg><arg><var>y</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><uncurry><uncurryInformation><name>ap</name><uncurriedSymbols><uncurriedSymbolEntry><name>map</name><arity>0</arity><name>map</name><name>map1</name><name>map2</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>if</name><arity>0</arity><name>if</name><name>if1</name><name>if3</name><name>if4</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>isEmpty</name><arity>0</arity><name>isEmpty</name><name>isEmpty1</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>true</name><arity>0</arity><name>true</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>null</name><arity>0</arity><name>null</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>cons</name><arity>0</arity><name>cons</name><name>cons1</name><name>cons2</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>last</name><arity>0</arity><name>last</name><name>last1</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>if2</name><arity>0</arity><name>if2</name><name>if21</name><name>if22</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>dropLast</name><arity>0</arity><name>dropLast</name><name>dropLast1</name></uncurriedSymbolEntry></uncurriedSymbols><uncurryRules><rules><rule><lhs><funapp><name>ap</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>ap</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>ap</name><arg><funapp><name>if</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ap</name><arg><funapp><name>if1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if3</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ap</name><arg><funapp><name>if3</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if4</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ap</name><arg><funapp><name>isEmpty</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>isEmpty1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ap</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>ap</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>ap</name><arg><funapp><name>last</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>last1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ap</name><arg><funapp><name>if2</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if21</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ap</name><arg><funapp><name>if21</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if22</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ap</name><arg><funapp><name>dropLast</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>dropLast1</name><arg><var>y1</var></arg></funapp></rhs></rule></rules></uncurryRules><etaRules><rules/></etaRules></uncurryInformation><trs><rules><rule><lhs><funapp><name>map2</name><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>if4</name><arg><funapp><name>isEmpty1</name><arg><var>xs</var></arg></funapp></arg><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>if4</name><arg><funapp><name>true</name></funapp></arg><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>null</name></funapp></rhs></rule><rule><lhs><funapp><name>if4</name><arg><funapp><name>null</name></funapp></arg><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>cons2</name><arg><funapp><name>ap</name><arg><var>f</var></arg><arg><funapp><name>last1</name><arg><var>xs</var></arg></funapp></arg></funapp></arg><arg><funapp><name>if22</name><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>if22</name><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>map2</name><arg><var>f</var></arg><arg><funapp><name>dropLast1</name><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isEmpty1</name><arg><funapp><name>null</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>isEmpty1</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>null</name></funapp></rhs></rule><rule><lhs><funapp><name>last1</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>null</name></funapp></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>last1</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>last1</name><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>dropLast1</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>null</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>null</name></funapp></rhs></rule><rule><lhs><funapp><name>dropLast1</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>dropLast1</name><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>ap</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>ap</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>ap</name><arg><funapp><name>if</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ap</name><arg><funapp><name>if1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if3</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ap</name><arg><funapp><name>if3</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if4</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ap</name><arg><funapp><name>isEmpty</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>isEmpty1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ap</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>ap</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>ap</name><arg><funapp><name>last</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>last1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ap</name><arg><funapp><name>if2</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if21</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ap</name><arg><funapp><name>if21</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if22</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>ap</name><arg><funapp><name>dropLast</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>dropLast1</name><arg><var>y1</var></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><switchInnermost><wcrProof><joinableCriticalPairsBFS>10</joinableCriticalPairsBFS></wcrProof><trsTerminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><name>map2</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>if4</name></sharp><arg><funapp><name>isEmpty1</name><arg><var>xs</var></arg></funapp></arg><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>map2</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>isEmpty1</name></sharp><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if4</name></sharp><arg><funapp><name>null</name></funapp></arg><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>ap</name></sharp><arg><var>f</var></arg><arg><funapp><name>last1</name><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if4</name></sharp><arg><funapp><name>null</name></funapp></arg><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>last1</name></sharp><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if4</name></sharp><arg><funapp><name>null</name></funapp></arg><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>if22</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if22</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>map2</name></sharp><arg><var>f</var></arg><arg><funapp><name>dropLast1</name><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if22</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>dropLast1</name></sharp><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>last1</name></sharp><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>last1</name></sharp><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dropLast1</name></sharp><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>dropLast1</name></sharp><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>ap</name></sharp><arg><funapp><name>map1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>map2</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>ap</name></sharp><arg><funapp><name>if3</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>if4</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>ap</name></sharp><arg><funapp><name>isEmpty</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>isEmpty1</name></sharp><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>ap</name></sharp><arg><funapp><name>last</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>last1</name></sharp><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>ap</name></sharp><arg><funapp><name>if21</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>if22</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>ap</name></sharp><arg><funapp><name>dropLast</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>dropLast1</name></sharp><arg><var>y1</var></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>if4</name></sharp><arg><funapp><name>null</name></funapp></arg><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>ap</name></sharp><arg><var>f</var></arg><arg><funapp><name>last1</name><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>ap</name></sharp><arg><funapp><name>map1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>map2</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>map2</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>if4</name></sharp><arg><funapp><name>isEmpty1</name><arg><var>xs</var></arg></funapp></arg><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if4</name></sharp><arg><funapp><name>null</name></funapp></arg><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>if22</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if22</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>map2</name></sharp><arg><var>f</var></arg><arg><funapp><name>dropLast1</name><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>ap</name></sharp><arg><funapp><name>if3</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>if4</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>ap</name></sharp><arg><funapp><name>if21</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>if22</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>dropLast1</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>null</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>null</name></funapp></rhs></rule><rule><lhs><funapp><name>dropLast1</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>dropLast1</name><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isEmpty1</name><arg><funapp><name>null</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>isEmpty1</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>null</name></funapp></rhs></rule><rule><lhs><funapp><name>last1</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>null</name></funapp></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>last1</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>last1</name><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>isEmpty1</name><arg><funapp><name>null</name></funapp></arg></funapp><funapp><name>isEmpty1</name><arg><funapp><name>cons2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>last1</name><arg><funapp><name>cons2</name><arg><var>x0</var></arg><arg><funapp><name>null</name></funapp></arg></funapp></arg></funapp><funapp><name>last1</name><arg><funapp><name>cons2</name><arg><var>x0</var></arg><arg><funapp><name>cons2</name><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>dropLast1</name><arg><funapp><name>cons2</name><arg><var>x0</var></arg><arg><funapp><name>null</name></funapp></arg></funapp></arg></funapp><funapp><name>dropLast1</name><arg><funapp><name>cons2</name><arg><var>x0</var></arg><arg><funapp><name>cons2</name><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></innermostLhss><dpProof><narrowingProc><rule><lhs><funapp><sharp><name>map2</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>if4</name></sharp><arg><funapp><name>isEmpty1</name><arg><var>xs</var></arg></funapp></arg><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><positionInTerm><position>1</position></positionInTerm><narrowings><rules><rule><lhs><funapp><sharp><name>map2</name></sharp><arg><var>y0</var></arg><arg><funapp><name>null</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>if4</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>y0</var></arg><arg><funapp><name>null</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>map2</name></sharp><arg><var>y0</var></arg><arg><funapp><name>cons2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>if4</name></sharp><arg><funapp><name>null</name></funapp></arg><arg><var>y0</var></arg><arg><funapp><name>cons2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></narrowings><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>ap</name></sharp><arg><funapp><name>map1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>map2</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>map2</name></sharp><arg><var>y0</var></arg><arg><funapp><name>cons2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>if4</name></sharp><arg><funapp><name>null</name></funapp></arg><arg><var>y0</var></arg><arg><funapp><name>cons2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if4</name></sharp><arg><funapp><name>null</name></funapp></arg><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>ap</name></sharp><arg><var>f</var></arg><arg><funapp><name>last1</name><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>ap</name></sharp><arg><funapp><name>if3</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>if4</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>if4</name></sharp><arg><funapp><name>null</name></funapp></arg><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>if22</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if22</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>map2</name></sharp><arg><var>f</var></arg><arg><funapp><name>dropLast1</name><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>ap</name></sharp><arg><funapp><name>if21</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>if22</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>dropLast1</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>null</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>null</name></funapp></rhs></rule><rule><lhs><funapp><name>dropLast1</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>dropLast1</name><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>last1</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>null</name></funapp></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>last1</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>last1</name><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>last1</name><arg><funapp><name>cons2</name><arg><var>x0</var></arg><arg><funapp><name>null</name></funapp></arg></funapp></arg></funapp><funapp><name>last1</name><arg><funapp><name>cons2</name><arg><var>x0</var></arg><arg><funapp><name>cons2</name><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp><funapp><name>dropLast1</name><arg><funapp><name>cons2</name><arg><var>x0</var></arg><arg><funapp><name>null</name></funapp></arg></funapp></arg></funapp><funapp><name>dropLast1</name><arg><funapp><name>cons2</name><arg><var>x0</var></arg><arg><funapp><name>cons2</name><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></innermostLhss><dpProof><monoRedPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>dropLast1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>cons2</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>null</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>last1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>ap</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>map1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>map2</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>if4</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>if3</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>if22</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>if21</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>map2</name></sharp><arg><var>y0</var></arg><arg><funapp><name>cons2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>if4</name></sharp><arg><funapp><name>null</name></funapp></arg><arg><var>y0</var></arg><arg><funapp><name>cons2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if4</name></sharp><arg><funapp><name>null</name></funapp></arg><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>ap</name></sharp><arg><var>f</var></arg><arg><funapp><name>last1</name><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if4</name></sharp><arg><funapp><name>null</name></funapp></arg><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>if22</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if22</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>map2</name></sharp><arg><var>f</var></arg><arg><funapp><name>dropLast1</name><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>dropLast1</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>null</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>null</name></funapp></rhs></rule><rule><lhs><funapp><name>dropLast1</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>dropLast1</name><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>last1</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>null</name></funapp></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>last1</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>last1</name><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>dropLast1</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>null</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>null</name></funapp></rhs></rule><rule><lhs><funapp><name>dropLast1</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>dropLast1</name><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>last1</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>null</name></funapp></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>last1</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>last1</name><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>if4</name></sharp><arg><funapp><name>null</name></funapp></arg><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>if22</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if22</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>map2</name></sharp><arg><var>f</var></arg><arg><funapp><name>dropLast1</name><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>map2</name></sharp><arg><var>y0</var></arg><arg><funapp><name>cons2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>if4</name></sharp><arg><funapp><name>null</name></funapp></arg><arg><var>y0</var></arg><arg><funapp><name>cons2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>dropLast1</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>null</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>null</name></funapp></rhs></rule><rule><lhs><funapp><name>dropLast1</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>dropLast1</name><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>dropLast1</name><arg><funapp><name>cons2</name><arg><var>x0</var></arg><arg><funapp><name>null</name></funapp></arg></funapp></arg></funapp><funapp><name>dropLast1</name><arg><funapp><name>cons2</name><arg><var>x0</var></arg><arg><funapp><name>cons2</name><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp></arg></funapp></innermostLhss><dpProof><monoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>dropLast1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>cons2</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>null</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>if4</name></sharp><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>if22</name></sharp><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>map2</name></sharp><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>if4</name></sharp><arg><funapp><name>null</name></funapp></arg><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>if22</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if22</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>map2</name></sharp><arg><var>f</var></arg><arg><funapp><name>dropLast1</name><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>map2</name></sharp><arg><var>y0</var></arg><arg><funapp><name>cons2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>if4</name></sharp><arg><funapp><name>null</name></funapp></arg><arg><var>y0</var></arg><arg><funapp><name>cons2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>dropLast1</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>dropLast1</name><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><dpProof><redPairProc><orderingConstraintProof><redPair><interpretation><type><matrixInterpretation><domain><integers/></domain><dimension>2</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><sharp><name>if4</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>null</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>if22</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>map2</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>dropLast1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>cons2</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>if4</name></sharp><arg><funapp><name>null</name></funapp></arg><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>if22</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if22</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>map2</name></sharp><arg><var>f</var></arg><arg><funapp><name>dropLast1</name><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>if4</name></sharp><arg><funapp><name>null</name></funapp></arg><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>if22</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>if22</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>map2</name></sharp><arg><var>f</var></arg><arg><funapp><name>dropLast1</name><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></redPairProc></dpProof></monoRedPairProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>if4</name></sharp><arg><funapp><name>null</name></funapp></arg><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>ap</name></sharp><arg><var>f</var></arg><arg><funapp><name>last1</name><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></monoRedPairUrProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>map2</name></sharp><arg><var>y0</var></arg><arg><funapp><name>null</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>if4</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>y0</var></arg><arg><funapp><name>null</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></narrowingProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>if4</name></sharp><arg><funapp><name>null</name></funapp></arg><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>last1</name></sharp><arg><var>xs</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>ap</name></sharp><arg><funapp><name>last</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>last1</name></sharp><arg><var>y1</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>if22</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>dropLast1</name></sharp><arg><var>xs</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>ap</name></sharp><arg><funapp><name>dropLast</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>dropLast1</name></sharp><arg><var>y1</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>map2</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>isEmpty1</name></sharp><arg><var>xs</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>last1</name></sharp><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>last1</name></sharp><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss/><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>last1</name></sharp><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>last1</name></sharp><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>dropLast1</name></sharp><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>dropLast1</name></sharp><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss/><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>dropLast1</name></sharp><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>dropLast1</name></sharp><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>ap</name></sharp><arg><funapp><name>isEmpty</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>isEmpty1</name></sharp><arg><var>y1</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></dpTrans></trsTerminationProof></switchInnermost></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 % (23 real / 0 unknown / 0 assumptions / 23 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>