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><rule><lhs><funapp><name>U91</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>U92</name><arg><funapp><name>isLNatKind</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U92</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>U93</name><arg><funapp><name>isLNat</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U93</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></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>isNatural</name></funapp></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>isLNat</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>head</name><arg><funapp><name>cons</name><arg><var>N</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U31</name><arg><funapp><name>isNatural</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isLNat</name></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isLNat</name></funapp></lhs><rhs><funapp><name>U41</name><arg><funapp><name>isNaturalKind</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isLNat</name></funapp></lhs><rhs><funapp><name>U51</name><arg><funapp><name>isNaturalKind</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isLNat</name></funapp></lhs><rhs><funapp><name>U61</name><arg><funapp><name>isPLNatKind</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isLNat</name></funapp></lhs><rhs><funapp><name>U71</name><arg><funapp><name>isNaturalKind</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isLNat</name></funapp></lhs><rhs><funapp><name>U81</name><arg><funapp><name>isPLNatKind</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isLNat</name></funapp></lhs><rhs><funapp><name>U91</name><arg><funapp><name>isLNatKind</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isLNat</name></funapp></lhs><rhs><funapp><name>U101</name><arg><funapp><name>isNaturalKind</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isLNatKind</name></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isLNatKind</name></funapp></lhs><rhs><funapp><name>U111</name><arg><funapp><name>isNaturalKind</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isLNatKind</name></funapp></lhs><rhs><funapp><name>U121</name><arg><funapp><name>isNaturalKind</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isLNatKind</name></funapp></lhs><rhs><funapp><name>U131</name><arg><funapp><name>isPLNatKind</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isLNatKind</name></funapp></lhs><rhs><funapp><name>U141</name><arg><funapp><name>isNaturalKind</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isLNatKind</name></funapp></lhs><rhs><funapp><name>U151</name><arg><funapp><name>isPLNatKind</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isLNatKind</name></funapp></lhs><rhs><funapp><name>U161</name><arg><funapp><name>isLNatKind</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isLNatKind</name></funapp></lhs><rhs><funapp><name>U171</name><arg><funapp><name>isNaturalKind</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNatural</name></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isNatural</name></funapp></lhs><rhs><funapp><name>U181</name><arg><funapp><name>isLNatKind</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNatural</name></funapp></lhs><rhs><funapp><name>U191</name><arg><funapp><name>isNaturalKind</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNatural</name></funapp></lhs><rhs><funapp><name>U201</name><arg><funapp><name>isNaturalKind</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNaturalKind</name></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isNaturalKind</name></funapp></lhs><rhs><funapp><name>U211</name><arg><funapp><name>isLNatKind</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNaturalKind</name></funapp></lhs><rhs><funapp><name>U221</name><arg><funapp><name>isNaturalKind</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNaturalKind</name></funapp></lhs><rhs><funapp><name>U231</name><arg><funapp><name>isNaturalKind</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isPLNat</name></funapp></lhs><rhs><funapp><name>U241</name><arg><funapp><name>isLNatKind</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isPLNat</name></funapp></lhs><rhs><funapp><name>U251</name><arg><funapp><name>isNaturalKind</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isPLNatKind</name></funapp></lhs><rhs><funapp><name>U261</name><arg><funapp><name>isLNatKind</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isPLNatKind</name></funapp></lhs><rhs><funapp><name>U271</name><arg><funapp><name>isNaturalKind</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>natsFrom</name><arg><var>N</var></arg></funapp></lhs><rhs><funapp><name>U281</name><arg><funapp><name>isNatural</name></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>U291</name><arg><funapp><name>isNatural</name></funapp></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>U301</name><arg><funapp><name>isLNat</name></funapp></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>U311</name><arg><funapp><name>isLNat</name></funapp></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></funapp></arg></funapp></lhs><rhs><funapp><name>U321</name><arg><funapp><name>isNatural</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>tail</name><arg><funapp><name>cons</name><arg><var>N</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U331</name><arg><funapp><name>isNatural</name></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>U341</name><arg><funapp><name>isNatural</name></funapp></arg></funapp></rhs></rule></rules></trs><strategy><outermost/></strategy></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsNonterminationProof><loop><rewriteSequence><startTerm><funapp><name>U14</name><arg><funapp><name>tt</name></funapp></arg></funapp></startTerm><rewriteStep><positionInTerm/><rule><lhs><funapp><name>U14</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>snd</name><arg><funapp><name>splitAt</name><arg><var>N</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><funapp><name>snd</name><arg><funapp><name>splitAt</name><arg><funapp><name>U14</name><arg><funapp><name>tt</name></funapp></arg></funapp></arg><arg><funapp><name>U14</name><arg><funapp><name>tt</name></funapp></arg></funapp></arg></funapp></arg></funapp></rewriteStep></rewriteSequence><substitution/><funContext><name>snd</name><before/><funContext><name>splitAt</name><before/><box/><after><funapp><name>U14</name><arg><funapp><name>tt</name></funapp></arg></funapp></after></funContext><after/></funContext></loop></trsNonterminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
</version><strategy>Statistics for single proof: 100.00 % (1 real / 0 unknown / 0 assumptions / 1 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>