/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>U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><name>U12</name><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U12</name><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><name>snd</name><arg><funapp><name>splitAt</name><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U21</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U22</name><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U22</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>activate</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U31</name><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><name>U32</name><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U32</name><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><name>activate</name><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U41</name><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><name>U42</name><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U42</name><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><name>head</name><arg><funapp><name>afterNth</name><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U51</name><arg><funapp><name>tt</name></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U52</name><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U52</name><arg><funapp><name>tt</name></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>activate</name><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U61</name><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><name>U62</name><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U62</name><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><name>U63</name><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U63</name><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><name>U64</name><arg><funapp><name>splitAt</name><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U64</name><arg><funapp><name>pair</name><arg><var>YS</var></arg><arg><var>ZS</var></arg></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>pair</name><arg><funapp><name>cons</name><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg><arg><var>YS</var></arg></funapp></arg><arg><var>ZS</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U71</name><arg><funapp><name>tt</name></funapp></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><name>U72</name><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U72</name><arg><funapp><name>tt</name></funapp></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><name>activate</name><arg><var>XS</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U81</name><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><name>U82</name><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U82</name><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><name>fst</name><arg><funapp><name>splitAt</name><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>afterNth</name><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>fst</name><arg><funapp><name>pair</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>head</name><arg><funapp><name>cons</name><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U31</name><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>natsFrom</name><arg><var>N</var></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><var>N</var></arg><arg><funapp><name>n__natsFrom</name><arg><funapp><name>n__s</name><arg><var>N</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>sel</name><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><name>U41</name><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>snd</name><arg><funapp><name>pair</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U51</name><arg><funapp><name>tt</name></funapp></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>splitAt</name><arg><funapp><name>0</name></funapp></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><name>pair</name><arg><funapp><name>nil</name></funapp></arg><arg><var>XS</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>splitAt</name><arg><funapp><name>s</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U61</name><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>tail</name><arg><funapp><name>cons</name><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U71</name><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>take</name><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><name>U81</name><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>natsFrom</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__natsFrom</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>s</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__s</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__natsFrom</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>natsFrom</name><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><name>U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>U12</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U12</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>snd</name></sharp><arg><funapp><name>splitAt</name><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U12</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>splitAt</name></sharp><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U12</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U12</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>U22</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U22</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>U32</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U32</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U41</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>U42</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U41</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U41</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U42</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>head</name></sharp><arg><funapp><name>afterNth</name><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U42</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>afterNth</name></sharp><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U42</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U42</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>U52</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U52</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>U62</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U62</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>U63</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U62</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U62</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U62</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U63</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>U64</name></sharp><arg><funapp><name>splitAt</name><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U63</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>splitAt</name></sharp><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U63</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U63</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U63</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U64</name></sharp><arg><funapp><name>pair</name><arg><var>YS</var></arg><arg><var>ZS</var></arg></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>U72</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U72</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U81</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>U82</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U81</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U81</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U82</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>fst</name></sharp><arg><funapp><name>splitAt</name><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U82</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>splitAt</name></sharp><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U82</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U82</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>afterNth</name></sharp><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>fst</name></sharp><arg><funapp><name>pair</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>head</name></sharp><arg><funapp><name>cons</name><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sel</name></sharp><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>U41</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>snd</name></sharp><arg><funapp><name>pair</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>splitAt</name></sharp><arg><funapp><name>s</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>splitAt</name></sharp><arg><funapp><name>s</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>tail</name></sharp><arg><funapp><name>cons</name><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>tail</name></sharp><arg><funapp><name>cons</name><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>take</name></sharp><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>U81</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__natsFrom</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>natsFrom</name></sharp><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__natsFrom</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>sel</name></sharp><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>U41</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U41</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>U42</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U42</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>afterNth</name></sharp><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>afterNth</name></sharp><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>take</name></sharp><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>U81</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>U12</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U81</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>U82</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U82</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>fst</name></sharp><arg><funapp><name>splitAt</name><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U42</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>head</name></sharp><arg><funapp><name>afterNth</name><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U12</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>snd</name></sharp><arg><funapp><name>splitAt</name><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U12</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>splitAt</name></sharp><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U82</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>splitAt</name></sharp><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>fst</name></sharp><arg><funapp><name>pair</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>head</name></sharp><arg><funapp><name>cons</name><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>snd</name></sharp><arg><funapp><name>pair</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U62</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>U63</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U63</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>splitAt</name></sharp><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>splitAt</name></sharp><arg><funapp><name>s</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>U62</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><redPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>splitAt</name></sharp><arity>2</arity><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></interpret><interpret><sharp><name>U61</name></sharp><arity>4</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>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>U62</name></sharp><arity>4</arity><polynomial><sum><polynomial><coefficient><integer>-2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>U63</name></sharp><arity>4</arity><polynomial><sum><polynomial><coefficient><integer>-2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>activate</name><arity>1</arity><polynomial><variable>1</variable></polynomial></interpret><interpret><name>n__natsFrom</name><arity>1</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>natsFrom</name><arity>1</arity><polynomial><coefficient><integer>-2</integer></coefficient></polynomial></interpret><interpret><name>n__s</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></sum></polynomial></interpret><interpret><name>s</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></sum></polynomial></interpret><interpret><name>cons</name><arity>2</arity><polynomial><coefficient><integer>-2</integer></coefficient></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><coefficient><integer>2</integer></coefficient></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>U62</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>U63</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U63</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>splitAt</name></sharp><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__natsFrom</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>natsFrom</name><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>s</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__s</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>natsFrom</name><arg><var>N</var></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><var>N</var></arg><arg><funapp><name>n__natsFrom</name><arg><funapp><name>n__s</name><arg><var>N</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>natsFrom</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__natsFrom</name><arg><var>X</var></arg></funapp></rhs></rule></rules></usableRules><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>U62</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>U63</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U63</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>splitAt</name></sharp><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></redPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>tail</name></sharp><arg><funapp><name>cons</name><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>U22</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>U32</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>U52</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U63</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>U64</name></sharp><arg><funapp><name>splitAt</name><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>U72</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><funapp><name>activate</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U12</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U12</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U22</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U32</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U41</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U41</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U42</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U42</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U52</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U62</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U62</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U62</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U63</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U63</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U63</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U64</name></sharp><arg><funapp><name>pair</name><arg><var>YS</var></arg><arg><var>ZS</var></arg></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U72</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U81</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U81</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U82</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U82</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>splitAt</name></sharp><arg><funapp><name>s</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>tail</name></sharp><arg><funapp><name>cons</name><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>XS</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__natsFrom</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><monoRedPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>n__s</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>n__natsFrom</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>activate</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__natsFrom</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><trs><rules/></trs><usableRules><rules/></usableRules><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__natsFrom</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></monoRedPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__natsFrom</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>natsFrom</name></sharp><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></dpTrans></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 % (6 real / 0 unknown / 0 assumptions / 6 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>