KILLED proof of /export/starexec/sandbox2/benchmark/theBenchmark.trs # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). (0) CpxRelTRS ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__U101(tt, z0, z1) -> c(A__U102(a__isNaturalKind(z0), z0, z1), A__ISNATURALKIND(z0)) A__U101(z0, z1, z2) -> c1 A__U102(tt, z0, z1) -> c2(A__U103(a__isLNatKind(z1), z0, z1), A__ISLNATKIND(z1)) A__U102(z0, z1, z2) -> c3 A__U103(tt, z0, z1) -> c4(A__U104(a__isLNatKind(z1), z0, z1), A__ISLNATKIND(z1)) A__U103(z0, z1, z2) -> c5 A__U104(tt, z0, z1) -> c6(A__U105(a__isNatural(z0), z1), A__ISNATURAL(z0)) A__U104(z0, z1, z2) -> c7 A__U105(tt, z0) -> c8(A__U106(a__isLNat(z0)), A__ISLNAT(z0)) A__U105(z0, z1) -> c9 A__U106(tt) -> c10 A__U106(z0) -> c11 A__U11(tt, z0, z1) -> c12(A__U12(a__isNaturalKind(z0), z0, z1), A__ISNATURALKIND(z0)) A__U11(z0, z1, z2) -> c13 A__U111(tt, z0) -> c14(A__U112(a__isLNatKind(z0)), A__ISLNATKIND(z0)) A__U111(z0, z1) -> c15 A__U112(tt) -> c16 A__U112(z0) -> c17 A__U12(tt, z0, z1) -> c18(A__U13(a__isLNat(z1), z0, z1), A__ISLNAT(z1)) A__U12(z0, z1, z2) -> c19 A__U121(tt, z0) -> c20(A__U122(a__isLNatKind(z0)), A__ISLNATKIND(z0)) A__U121(z0, z1) -> c21 A__U122(tt) -> c22 A__U122(z0) -> c23 A__U13(tt, z0, z1) -> c24(A__U14(a__isLNatKind(z1), z0, z1), A__ISLNATKIND(z1)) A__U13(z0, z1, z2) -> c25 A__U131(tt) -> c26 A__U131(z0) -> c27 A__U14(tt, z0, z1) -> c28(A__SND(a__splitAt(mark(z0), mark(z1))), A__SPLITAT(mark(z0), mark(z1)), MARK(z0)) A__U14(tt, z0, z1) -> c29(A__SND(a__splitAt(mark(z0), mark(z1))), A__SPLITAT(mark(z0), mark(z1)), MARK(z1)) A__U14(z0, z1, z2) -> c30 A__U141(tt) -> c31 A__U141(z0) -> c32 A__U151(tt) -> c33 A__U151(z0) -> c34 A__U161(tt) -> c35 A__U161(z0) -> c36 A__U171(tt, z0) -> c37(A__U172(a__isLNatKind(z0)), A__ISLNATKIND(z0)) A__U171(z0, z1) -> c38 A__U172(tt) -> c39 A__U172(z0) -> c40 A__U181(tt, z0) -> c41(A__U182(a__isLNatKind(z0), z0), A__ISLNATKIND(z0)) A__U181(z0, z1) -> c42 A__U182(tt, z0) -> c43(A__U183(a__isLNat(z0)), A__ISLNAT(z0)) A__U182(z0, z1) -> c44 A__U183(tt) -> c45 A__U183(z0) -> c46 A__U191(tt, z0) -> c47(A__U192(a__isNaturalKind(z0), z0), A__ISNATURALKIND(z0)) A__U191(z0, z1) -> c48 A__U192(tt, z0) -> c49(A__U193(a__isNatural(z0)), A__ISNATURAL(z0)) A__U192(z0, z1) -> c50 A__U193(tt) -> c51 A__U193(z0) -> c52 A__U201(tt, z0, z1) -> c53(A__U202(a__isNaturalKind(z0), z0, z1), A__ISNATURALKIND(z0)) A__U201(z0, z1, z2) -> c54 A__U202(tt, z0, z1) -> c55(A__U203(a__isLNatKind(z1), z0, z1), A__ISLNATKIND(z1)) A__U202(z0, z1, z2) -> c56 A__U203(tt, z0, z1) -> c57(A__U204(a__isLNatKind(z1), z0, z1), A__ISLNATKIND(z1)) A__U203(z0, z1, z2) -> c58 A__U204(tt, z0, z1) -> c59(A__U205(a__isNatural(z0), z1), A__ISNATURAL(z0)) A__U204(z0, z1, z2) -> c60 A__U205(tt, z0) -> c61(A__U206(a__isLNat(z0)), A__ISLNAT(z0)) A__U205(z0, z1) -> c62 A__U206(tt) -> c63 A__U206(z0) -> c64 A__U21(tt, z0, z1) -> c65(A__U22(a__isLNatKind(z0), z0, z1), A__ISLNATKIND(z0)) A__U21(z0, z1, z2) -> c66 A__U211(tt) -> c67 A__U211(z0) -> c68 A__U22(tt, z0, z1) -> c69(A__U23(a__isLNat(z1), z0, z1), A__ISLNAT(z1)) A__U22(z0, z1, z2) -> c70 A__U221(tt) -> c71 A__U221(z0) -> c72 A__U23(tt, z0, z1) -> c73(A__U24(a__isLNatKind(z1), z0), A__ISLNATKIND(z1)) A__U23(z0, z1, z2) -> c74 A__U231(tt, z0) -> c75(A__U232(a__isLNatKind(z0)), A__ISLNATKIND(z0)) A__U231(z0, z1) -> c76 A__U232(tt) -> c77 A__U232(z0) -> c78 A__U24(tt, z0) -> c79(MARK(z0)) A__U24(z0, z1) -> c80 A__U241(tt, z0, z1) -> c81(A__U242(a__isLNatKind(z0), z0, z1), A__ISLNATKIND(z0)) A__U241(z0, z1, z2) -> c82 A__U242(tt, z0, z1) -> c83(A__U243(a__isLNatKind(z1), z0, z1), A__ISLNATKIND(z1)) A__U242(z0, z1, z2) -> c84 A__U243(tt, z0, z1) -> c85(A__U244(a__isLNatKind(z1), z0, z1), A__ISLNATKIND(z1)) A__U243(z0, z1, z2) -> c86 A__U244(tt, z0, z1) -> c87(A__U245(a__isLNat(z0), z1), A__ISLNAT(z0)) A__U244(z0, z1, z2) -> c88 A__U245(tt, z0) -> c89(A__U246(a__isLNat(z0)), A__ISLNAT(z0)) A__U245(z0, z1) -> c90 A__U246(tt) -> c91 A__U246(z0) -> c92 A__U251(tt, z0, z1) -> c93(A__U252(a__isNaturalKind(z0), z0, z1), A__ISNATURALKIND(z0)) A__U251(z0, z1, z2) -> c94 A__U252(tt, z0, z1) -> c95(A__U253(a__isLNatKind(z1), z0, z1), A__ISLNATKIND(z1)) A__U252(z0, z1, z2) -> c96 A__U253(tt, z0, z1) -> c97(A__U254(a__isLNatKind(z1), z0, z1), A__ISLNATKIND(z1)) A__U253(z0, z1, z2) -> c98 A__U254(tt, z0, z1) -> c99(A__U255(a__isNatural(z0), z1), A__ISNATURAL(z0)) A__U254(z0, z1, z2) -> c100 A__U255(tt, z0) -> c101(A__U256(a__isLNat(z0)), A__ISLNAT(z0)) A__U255(z0, z1) -> c102 A__U256(tt) -> c103 A__U256(z0) -> c104 A__U261(tt, z0) -> c105(A__U262(a__isLNatKind(z0)), A__ISLNATKIND(z0)) A__U261(z0, z1) -> c106 A__U262(tt) -> c107 A__U262(z0) -> c108 A__U271(tt, z0) -> c109(A__U272(a__isLNatKind(z0)), A__ISLNATKIND(z0)) A__U271(z0, z1) -> c110 A__U272(tt) -> c111 A__U272(z0) -> c112 A__U281(tt, z0) -> c113(A__U282(a__isNaturalKind(z0), z0), A__ISNATURALKIND(z0)) A__U281(z0, z1) -> c114 A__U282(tt, z0) -> c115(MARK(z0)) A__U282(z0, z1) -> c116 A__U291(tt, z0, z1) -> c117(A__U292(a__isNaturalKind(z0), z0, z1), A__ISNATURALKIND(z0)) A__U291(z0, z1, z2) -> c118 A__U292(tt, z0, z1) -> c119(A__U293(a__isLNat(z1), z0, z1), A__ISLNAT(z1)) A__U292(z0, z1, z2) -> c120 A__U293(tt, z0, z1) -> c121(A__U294(a__isLNatKind(z1), z0, z1), A__ISLNATKIND(z1)) A__U293(z0, z1, z2) -> c122 A__U294(tt, z0, z1) -> c123(A__HEAD(a__afterNth(mark(z0), mark(z1))), A__AFTERNTH(mark(z0), mark(z1)), MARK(z0)) A__U294(tt, z0, z1) -> c124(A__HEAD(a__afterNth(mark(z0), mark(z1))), A__AFTERNTH(mark(z0), mark(z1)), MARK(z1)) A__U294(z0, z1, z2) -> c125 A__U301(tt, z0, z1) -> c126(A__U302(a__isLNatKind(z0), z1), A__ISLNATKIND(z0)) A__U301(z0, z1, z2) -> c127 A__U302(tt, z0) -> c128(A__U303(a__isLNat(z0), z0), A__ISLNAT(z0)) A__U302(z0, z1) -> c129 A__U303(tt, z0) -> c130(A__U304(a__isLNatKind(z0), z0), A__ISLNATKIND(z0)) A__U303(z0, z1) -> c131 A__U304(tt, z0) -> c132(MARK(z0)) A__U304(z0, z1) -> c133 A__U31(tt, z0, z1) -> c134(A__U32(a__isNaturalKind(z0), z0, z1), A__ISNATURALKIND(z0)) A__U31(z0, z1, z2) -> c135 A__U311(tt, z0) -> c136(A__U312(a__isLNatKind(z0), z0), A__ISLNATKIND(z0)) A__U311(z0, z1) -> c137 A__U312(tt, z0) -> c138(MARK(z0)) A__U312(z0, z1) -> c139 A__U32(tt, z0, z1) -> c140(A__U33(a__isLNat(z1), z0, z1), A__ISLNAT(z1)) A__U32(z0, z1, z2) -> c141 A__U321(tt, z0, z1, z2) -> c142(A__U322(a__isNaturalKind(z0), z0, z1, z2), A__ISNATURALKIND(z0)) A__U321(z0, z1, z2, z3) -> c143 A__U322(tt, z0, z1, z2) -> c144(A__U323(a__isNatural(z1), z0, z1, z2), A__ISNATURAL(z1)) A__U322(z0, z1, z2, z3) -> c145 A__U323(tt, z0, z1, z2) -> c146(A__U324(a__isNaturalKind(z1), z0, z1, z2), A__ISNATURALKIND(z1)) A__U323(z0, z1, z2, z3) -> c147 A__U324(tt, z0, z1, z2) -> c148(A__U325(a__isLNat(z2), z0, z1, z2), A__ISLNAT(z2)) A__U324(z0, z1, z2, z3) -> c149 A__U325(tt, z0, z1, z2) -> c150(A__U326(a__isLNatKind(z2), z0, z1, z2), A__ISLNATKIND(z2)) A__U325(z0, z1, z2, z3) -> c151 A__U326(tt, z0, z1, z2) -> c152(A__U327(a__splitAt(mark(z0), mark(z2)), z1), A__SPLITAT(mark(z0), mark(z2)), MARK(z0)) A__U326(tt, z0, z1, z2) -> c153(A__U327(a__splitAt(mark(z0), mark(z2)), z1), A__SPLITAT(mark(z0), mark(z2)), MARK(z2)) A__U326(z0, z1, z2, z3) -> c154 A__U327(pair(z0, z1), z2) -> c155(MARK(z2)) A__U327(pair(z0, z1), z2) -> c156(MARK(z1)) A__U327(z0, z1) -> c157 A__U33(tt, z0, z1) -> c158(A__U34(a__isLNatKind(z1), z0), A__ISLNATKIND(z1)) A__U33(z0, z1, z2) -> c159 A__U331(tt, z0, z1) -> c160(A__U332(a__isNaturalKind(z0), z1), A__ISNATURALKIND(z0)) A__U331(z0, z1, z2) -> c161 A__U332(tt, z0) -> c162(A__U333(a__isLNat(z0), z0), A__ISLNAT(z0)) A__U332(z0, z1) -> c163 A__U333(tt, z0) -> c164(A__U334(a__isLNatKind(z0), z0), A__ISLNATKIND(z0)) A__U333(z0, z1) -> c165 A__U334(tt, z0) -> c166(MARK(z0)) A__U334(z0, z1) -> c167 A__U34(tt, z0) -> c168(MARK(z0)) A__U34(z0, z1) -> c169 A__U341(tt, z0, z1) -> c170(A__U342(a__isNaturalKind(z0), z0, z1), A__ISNATURALKIND(z0)) A__U341(z0, z1, z2) -> c171 A__U342(tt, z0, z1) -> c172(A__U343(a__isLNat(z1), z0, z1), A__ISLNAT(z1)) A__U342(z0, z1, z2) -> c173 A__U343(tt, z0, z1) -> c174(A__U344(a__isLNatKind(z1), z0, z1), A__ISLNATKIND(z1)) A__U343(z0, z1, z2) -> c175 A__U344(tt, z0, z1) -> c176(A__FST(a__splitAt(mark(z0), mark(z1))), A__SPLITAT(mark(z0), mark(z1)), MARK(z0)) A__U344(tt, z0, z1) -> c177(A__FST(a__splitAt(mark(z0), mark(z1))), A__SPLITAT(mark(z0), mark(z1)), MARK(z1)) A__U344(z0, z1, z2) -> c178 A__U41(tt, z0, z1) -> c179(A__U42(a__isNaturalKind(z0), z0, z1), A__ISNATURALKIND(z0)) A__U41(z0, z1, z2) -> c180 A__U42(tt, z0, z1) -> c181(A__U43(a__isLNatKind(z1), z0, z1), A__ISLNATKIND(z1)) A__U42(z0, z1, z2) -> c182 A__U43(tt, z0, z1) -> c183(A__U44(a__isLNatKind(z1), z0, z1), A__ISLNATKIND(z1)) A__U43(z0, z1, z2) -> c184 A__U44(tt, z0, z1) -> c185(A__U45(a__isNatural(z0), z1), A__ISNATURAL(z0)) A__U44(z0, z1, z2) -> c186 A__U45(tt, z0) -> c187(A__U46(a__isLNat(z0)), A__ISLNAT(z0)) A__U45(z0, z1) -> c188 A__U46(tt) -> c189 A__U46(z0) -> c190 A__U51(tt, z0, z1) -> c191(A__U52(a__isNaturalKind(z0), z0, z1), A__ISNATURALKIND(z0)) A__U51(z0, z1, z2) -> c192 A__U52(tt, z0, z1) -> c193(A__U53(a__isLNatKind(z1), z0, z1), A__ISLNATKIND(z1)) A__U52(z0, z1, z2) -> c194 A__U53(tt, z0, z1) -> c195(A__U54(a__isLNatKind(z1), z0, z1), A__ISLNATKIND(z1)) A__U53(z0, z1, z2) -> c196 A__U54(tt, z0, z1) -> c197(A__U55(a__isNatural(z0), z1), A__ISNATURAL(z0)) A__U54(z0, z1, z2) -> c198 A__U55(tt, z0) -> c199(A__U56(a__isLNat(z0)), A__ISLNAT(z0)) A__U55(z0, z1) -> c200 A__U56(tt) -> c201 A__U56(z0) -> c202 A__U61(tt, z0) -> c203(A__U62(a__isPLNatKind(z0), z0), A__ISPLNATKIND(z0)) A__U61(z0, z1) -> c204 A__U62(tt, z0) -> c205(A__U63(a__isPLNat(z0)), A__ISPLNAT(z0)) A__U62(z0, z1) -> c206 A__U63(tt) -> c207 A__U63(z0) -> c208 A__U71(tt, z0) -> c209(A__U72(a__isNaturalKind(z0), z0), A__ISNATURALKIND(z0)) A__U71(z0, z1) -> c210 A__U72(tt, z0) -> c211(A__U73(a__isNatural(z0)), A__ISNATURAL(z0)) A__U72(z0, z1) -> c212 A__U73(tt) -> c213 A__U73(z0) -> c214 A__U81(tt, z0) -> c215(A__U82(a__isPLNatKind(z0), z0), A__ISPLNATKIND(z0)) A__U81(z0, z1) -> c216 A__U82(tt, z0) -> c217(A__U83(a__isPLNat(z0)), A__ISPLNAT(z0)) A__U82(z0, z1) -> c218 A__U83(tt) -> c219 A__U83(z0) -> c220 A__U91(tt, z0) -> c221(A__U92(a__isLNatKind(z0), z0), A__ISLNATKIND(z0)) A__U91(z0, z1) -> c222 A__U92(tt, z0) -> c223(A__U93(a__isLNat(z0)), A__ISLNAT(z0)) A__U92(z0, z1) -> c224 A__U93(tt) -> c225 A__U93(z0) -> c226 A__AFTERNTH(z0, z1) -> c227(A__U11(a__isNatural(z0), z0, z1), A__ISNATURAL(z0)) A__AFTERNTH(z0, z1) -> c228 A__FST(pair(z0, z1)) -> c229(A__U21(a__isLNat(z0), z0, z1), A__ISLNAT(z0)) A__FST(z0) -> c230 A__HEAD(cons(z0, z1)) -> c231(A__U31(a__isNatural(z0), z0, z1), A__ISNATURAL(z0)) A__HEAD(z0) -> c232 A__ISLNAT(nil) -> c233 A__ISLNAT(afterNth(z0, z1)) -> c234(A__U41(a__isNaturalKind(z0), z0, z1), A__ISNATURALKIND(z0)) A__ISLNAT(cons(z0, z1)) -> c235(A__U51(a__isNaturalKind(z0), z0, z1), A__ISNATURALKIND(z0)) A__ISLNAT(fst(z0)) -> c236(A__U61(a__isPLNatKind(z0), z0), A__ISPLNATKIND(z0)) A__ISLNAT(natsFrom(z0)) -> c237(A__U71(a__isNaturalKind(z0), z0), A__ISNATURALKIND(z0)) A__ISLNAT(snd(z0)) -> c238(A__U81(a__isPLNatKind(z0), z0), A__ISPLNATKIND(z0)) A__ISLNAT(tail(z0)) -> c239(A__U91(a__isLNatKind(z0), z0), A__ISLNATKIND(z0)) A__ISLNAT(take(z0, z1)) -> c240(A__U101(a__isNaturalKind(z0), z0, z1), A__ISNATURALKIND(z0)) A__ISLNAT(z0) -> c241 A__ISLNATKIND(nil) -> c242 A__ISLNATKIND(afterNth(z0, z1)) -> c243(A__U111(a__isNaturalKind(z0), z1), A__ISNATURALKIND(z0)) A__ISLNATKIND(cons(z0, z1)) -> c244(A__U121(a__isNaturalKind(z0), z1), A__ISNATURALKIND(z0)) A__ISLNATKIND(fst(z0)) -> c245(A__U131(a__isPLNatKind(z0)), A__ISPLNATKIND(z0)) A__ISLNATKIND(natsFrom(z0)) -> c246(A__U141(a__isNaturalKind(z0)), A__ISNATURALKIND(z0)) A__ISLNATKIND(snd(z0)) -> c247(A__U151(a__isPLNatKind(z0)), A__ISPLNATKIND(z0)) A__ISLNATKIND(tail(z0)) -> c248(A__U161(a__isLNatKind(z0)), A__ISLNATKIND(z0)) A__ISLNATKIND(take(z0, z1)) -> c249(A__U171(a__isNaturalKind(z0), z1), A__ISNATURALKIND(z0)) A__ISLNATKIND(z0) -> c250 A__ISNATURAL(0) -> c251 A__ISNATURAL(head(z0)) -> c252(A__U181(a__isLNatKind(z0), z0), A__ISLNATKIND(z0)) A__ISNATURAL(s(z0)) -> c253(A__U191(a__isNaturalKind(z0), z0), A__ISNATURALKIND(z0)) A__ISNATURAL(sel(z0, z1)) -> c254(A__U201(a__isNaturalKind(z0), z0, z1), A__ISNATURALKIND(z0)) A__ISNATURAL(z0) -> c255 A__ISNATURALKIND(0) -> c256 A__ISNATURALKIND(head(z0)) -> c257(A__U211(a__isLNatKind(z0)), A__ISLNATKIND(z0)) A__ISNATURALKIND(s(z0)) -> c258(A__U221(a__isNaturalKind(z0)), A__ISNATURALKIND(z0)) A__ISNATURALKIND(sel(z0, z1)) -> c259(A__U231(a__isNaturalKind(z0), z1), A__ISNATURALKIND(z0)) A__ISNATURALKIND(z0) -> c260 A__ISPLNAT(pair(z0, z1)) -> c261(A__U241(a__isLNatKind(z0), z0, z1), A__ISLNATKIND(z0)) A__ISPLNAT(splitAt(z0, z1)) -> c262(A__U251(a__isNaturalKind(z0), z0, z1), A__ISNATURALKIND(z0)) A__ISPLNAT(z0) -> c263 A__ISPLNATKIND(pair(z0, z1)) -> c264(A__U261(a__isLNatKind(z0), z1), A__ISLNATKIND(z0)) A__ISPLNATKIND(splitAt(z0, z1)) -> c265(A__U271(a__isNaturalKind(z0), z1), A__ISNATURALKIND(z0)) A__ISPLNATKIND(z0) -> c266 A__NATSFROM(z0) -> c267(A__U281(a__isNatural(z0), z0), A__ISNATURAL(z0)) A__NATSFROM(z0) -> c268 A__SEL(z0, z1) -> c269(A__U291(a__isNatural(z0), z0, z1), A__ISNATURAL(z0)) A__SEL(z0, z1) -> c270 A__SND(pair(z0, z1)) -> c271(A__U301(a__isLNat(z0), z0, z1), A__ISLNAT(z0)) A__SND(z0) -> c272 A__SPLITAT(0, z0) -> c273(A__U311(a__isLNat(z0), z0), A__ISLNAT(z0)) A__SPLITAT(s(z0), cons(z1, z2)) -> c274(A__U321(a__isNatural(z0), z0, z1, z2), A__ISNATURAL(z0)) A__SPLITAT(z0, z1) -> c275 A__TAIL(cons(z0, z1)) -> c276(A__U331(a__isNatural(z0), z0, z1), A__ISNATURAL(z0)) A__TAIL(z0) -> c277 A__TAKE(z0, z1) -> c278(A__U341(a__isNatural(z0), z0, z1), A__ISNATURAL(z0)) A__TAKE(z0, z1) -> c279 MARK(U101(z0, z1, z2)) -> c280(A__U101(mark(z0), z1, z2), MARK(z0)) MARK(U102(z0, z1, z2)) -> c281(A__U102(mark(z0), z1, z2), MARK(z0)) MARK(isNaturalKind(z0)) -> c282(A__ISNATURALKIND(z0)) MARK(U103(z0, z1, z2)) -> c283(A__U103(mark(z0), z1, z2), MARK(z0)) MARK(isLNatKind(z0)) -> c284(A__ISLNATKIND(z0)) MARK(U104(z0, z1, z2)) -> c285(A__U104(mark(z0), z1, z2), MARK(z0)) MARK(U105(z0, z1)) -> c286(A__U105(mark(z0), z1), MARK(z0)) MARK(isNatural(z0)) -> c287(A__ISNATURAL(z0)) MARK(U106(z0)) -> c288(A__U106(mark(z0)), MARK(z0)) MARK(isLNat(z0)) -> c289(A__ISLNAT(z0)) MARK(U11(z0, z1, z2)) -> c290(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c291(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(U111(z0, z1)) -> c292(A__U111(mark(z0), z1), MARK(z0)) MARK(U112(z0)) -> c293(A__U112(mark(z0)), MARK(z0)) MARK(U13(z0, z1, z2)) -> c294(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U121(z0, z1)) -> c295(A__U121(mark(z0), z1), MARK(z0)) MARK(U122(z0)) -> c296(A__U122(mark(z0)), MARK(z0)) MARK(U14(z0, z1, z2)) -> c297(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U131(z0)) -> c298(A__U131(mark(z0)), MARK(z0)) MARK(snd(z0)) -> c299(A__SND(mark(z0)), MARK(z0)) MARK(splitAt(z0, z1)) -> c300(A__SPLITAT(mark(z0), mark(z1)), MARK(z0)) MARK(splitAt(z0, z1)) -> c301(A__SPLITAT(mark(z0), mark(z1)), MARK(z1)) MARK(U141(z0)) -> c302(A__U141(mark(z0)), MARK(z0)) MARK(U151(z0)) -> c303(A__U151(mark(z0)), MARK(z0)) MARK(U161(z0)) -> c304(A__U161(mark(z0)), MARK(z0)) MARK(U171(z0, z1)) -> c305(A__U171(mark(z0), z1), MARK(z0)) MARK(U172(z0)) -> c306(A__U172(mark(z0)), MARK(z0)) MARK(U181(z0, z1)) -> c307(A__U181(mark(z0), z1), MARK(z0)) MARK(U182(z0, z1)) -> c308(A__U182(mark(z0), z1), MARK(z0)) MARK(U183(z0)) -> c309(A__U183(mark(z0)), MARK(z0)) MARK(U191(z0, z1)) -> c310(A__U191(mark(z0), z1), MARK(z0)) MARK(U192(z0, z1)) -> c311(A__U192(mark(z0), z1), MARK(z0)) MARK(U193(z0)) -> c312(A__U193(mark(z0)), MARK(z0)) MARK(U201(z0, z1, z2)) -> c313(A__U201(mark(z0), z1, z2), MARK(z0)) MARK(U202(z0, z1, z2)) -> c314(A__U202(mark(z0), z1, z2), MARK(z0)) MARK(U203(z0, z1, z2)) -> c315(A__U203(mark(z0), z1, z2), MARK(z0)) MARK(U204(z0, z1, z2)) -> c316(A__U204(mark(z0), z1, z2), MARK(z0)) MARK(U205(z0, z1)) -> c317(A__U205(mark(z0), z1), MARK(z0)) MARK(U206(z0)) -> c318(A__U206(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2)) -> c319(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(U22(z0, z1, z2)) -> c320(A__U22(mark(z0), z1, z2), MARK(z0)) MARK(U211(z0)) -> c321(A__U211(mark(z0)), MARK(z0)) MARK(U23(z0, z1, z2)) -> c322(A__U23(mark(z0), z1, z2), MARK(z0)) MARK(U221(z0)) -> c323(A__U221(mark(z0)), MARK(z0)) MARK(U24(z0, z1)) -> c324(A__U24(mark(z0), z1), MARK(z0)) MARK(U231(z0, z1)) -> c325(A__U231(mark(z0), z1), MARK(z0)) MARK(U232(z0)) -> c326(A__U232(mark(z0)), MARK(z0)) MARK(U241(z0, z1, z2)) -> c327(A__U241(mark(z0), z1, z2), MARK(z0)) MARK(U242(z0, z1, z2)) -> c328(A__U242(mark(z0), z1, z2), MARK(z0)) MARK(U243(z0, z1, z2)) -> c329(A__U243(mark(z0), z1, z2), MARK(z0)) MARK(U244(z0, z1, z2)) -> c330(A__U244(mark(z0), z1, z2), MARK(z0)) MARK(U245(z0, z1)) -> c331(A__U245(mark(z0), z1), MARK(z0)) MARK(U246(z0)) -> c332(A__U246(mark(z0)), MARK(z0)) MARK(U251(z0, z1, z2)) -> c333(A__U251(mark(z0), z1, z2), MARK(z0)) MARK(U252(z0, z1, z2)) -> c334(A__U252(mark(z0), z1, z2), MARK(z0)) MARK(U253(z0, z1, z2)) -> c335(A__U253(mark(z0), z1, z2), MARK(z0)) MARK(U254(z0, z1, z2)) -> c336(A__U254(mark(z0), z1, z2), MARK(z0)) MARK(U255(z0, z1)) -> c337(A__U255(mark(z0), z1), MARK(z0)) MARK(U256(z0)) -> c338(A__U256(mark(z0)), MARK(z0)) MARK(U261(z0, z1)) -> c339(A__U261(mark(z0), z1), MARK(z0)) MARK(U262(z0)) -> c340(A__U262(mark(z0)), MARK(z0)) MARK(U271(z0, z1)) -> c341(A__U271(mark(z0), z1), MARK(z0)) MARK(U272(z0)) -> c342(A__U272(mark(z0)), MARK(z0)) MARK(U281(z0, z1)) -> c343(A__U281(mark(z0), z1), MARK(z0)) MARK(U282(z0, z1)) -> c344(A__U282(mark(z0), z1), MARK(z0)) MARK(natsFrom(z0)) -> c345(A__NATSFROM(mark(z0)), MARK(z0)) MARK(U291(z0, z1, z2)) -> c346(A__U291(mark(z0), z1, z2), MARK(z0)) MARK(U292(z0, z1, z2)) -> c347(A__U292(mark(z0), z1, z2), MARK(z0)) MARK(U293(z0, z1, z2)) -> c348(A__U293(mark(z0), z1, z2), MARK(z0)) MARK(U294(z0, z1, z2)) -> c349(A__U294(mark(z0), z1, z2), MARK(z0)) MARK(head(z0)) -> c350(A__HEAD(mark(z0)), MARK(z0)) MARK(afterNth(z0, z1)) -> c351(A__AFTERNTH(mark(z0), mark(z1)), MARK(z0)) MARK(afterNth(z0, z1)) -> c352(A__AFTERNTH(mark(z0), mark(z1)), MARK(z1)) MARK(U301(z0, z1, z2)) -> c353(A__U301(mark(z0), z1, z2), MARK(z0)) MARK(U302(z0, z1)) -> c354(A__U302(mark(z0), z1), MARK(z0)) MARK(U303(z0, z1)) -> c355(A__U303(mark(z0), z1), MARK(z0)) MARK(U304(z0, z1)) -> c356(A__U304(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1, z2)) -> c357(A__U31(mark(z0), z1, z2), MARK(z0)) MARK(U32(z0, z1, z2)) -> c358(A__U32(mark(z0), z1, z2), MARK(z0)) MARK(U311(z0, z1)) -> c359(A__U311(mark(z0), z1), MARK(z0)) MARK(U312(z0, z1)) -> c360(A__U312(mark(z0), z1), MARK(z0)) MARK(U33(z0, z1, z2)) -> c361(A__U33(mark(z0), z1, z2), MARK(z0)) MARK(U321(z0, z1, z2, z3)) -> c362(A__U321(mark(z0), z1, z2, z3), MARK(z0)) MARK(U322(z0, z1, z2, z3)) -> c363(A__U322(mark(z0), z1, z2, z3), MARK(z0)) MARK(U323(z0, z1, z2, z3)) -> c364(A__U323(mark(z0), z1, z2, z3), MARK(z0)) MARK(U324(z0, z1, z2, z3)) -> c365(A__U324(mark(z0), z1, z2, z3), MARK(z0)) MARK(U325(z0, z1, z2, z3)) -> c366(A__U325(mark(z0), z1, z2, z3), MARK(z0)) MARK(U326(z0, z1, z2, z3)) -> c367(A__U326(mark(z0), z1, z2, z3), MARK(z0)) MARK(U327(z0, z1)) -> c368(A__U327(mark(z0), z1), MARK(z0)) MARK(U34(z0, z1)) -> c369(A__U34(mark(z0), z1), MARK(z0)) MARK(U331(z0, z1, z2)) -> c370(A__U331(mark(z0), z1, z2), MARK(z0)) MARK(U332(z0, z1)) -> c371(A__U332(mark(z0), z1), MARK(z0)) MARK(U333(z0, z1)) -> c372(A__U333(mark(z0), z1), MARK(z0)) MARK(U334(z0, z1)) -> c373(A__U334(mark(z0), z1), MARK(z0)) MARK(U341(z0, z1, z2)) -> c374(A__U341(mark(z0), z1, z2), MARK(z0)) MARK(U342(z0, z1, z2)) -> c375(A__U342(mark(z0), z1, z2), MARK(z0)) MARK(U343(z0, z1, z2)) -> c376(A__U343(mark(z0), z1, z2), MARK(z0)) MARK(U344(z0, z1, z2)) -> c377(A__U344(mark(z0), z1, z2), MARK(z0)) MARK(fst(z0)) -> c378(A__FST(mark(z0)), MARK(z0)) MARK(U41(z0, z1, z2)) -> c379(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c380(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(U43(z0, z1, z2)) -> c381(A__U43(mark(z0), z1, z2), MARK(z0)) MARK(U44(z0, z1, z2)) -> c382(A__U44(mark(z0), z1, z2), MARK(z0)) MARK(U45(z0, z1)) -> c383(A__U45(mark(z0), z1), MARK(z0)) MARK(U46(z0)) -> c384(A__U46(mark(z0)), MARK(z0)) MARK(U51(z0, z1, z2)) -> c385(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c386(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(U53(z0, z1, z2)) -> c387(A__U53(mark(z0), z1, z2), MARK(z0)) MARK(U54(z0, z1, z2)) -> c388(A__U54(mark(z0), z1, z2), MARK(z0)) MARK(U55(z0, z1)) -> c389(A__U55(mark(z0), z1), MARK(z0)) MARK(U56(z0)) -> c390(A__U56(mark(z0)), MARK(z0)) MARK(U61(z0, z1)) -> c391(A__U61(mark(z0), z1), MARK(z0)) MARK(U62(z0, z1)) -> c392(A__U62(mark(z0), z1), MARK(z0)) MARK(isPLNatKind(z0)) -> c393(A__ISPLNATKIND(z0)) MARK(U63(z0)) -> c394(A__U63(mark(z0)), MARK(z0)) MARK(isPLNat(z0)) -> c395(A__ISPLNAT(z0)) MARK(U71(z0, z1)) -> c396(A__U71(mark(z0), z1), MARK(z0)) MARK(U72(z0, z1)) -> c397(A__U72(mark(z0), z1), MARK(z0)) MARK(U73(z0)) -> c398(A__U73(mark(z0)), MARK(z0)) MARK(U81(z0, z1)) -> c399(A__U81(mark(z0), z1), MARK(z0)) MARK(U82(z0, z1)) -> c400(A__U82(mark(z0), z1), MARK(z0)) MARK(U83(z0)) -> c401(A__U83(mark(z0)), MARK(z0)) MARK(U91(z0, z1)) -> c402(A__U91(mark(z0), z1), MARK(z0)) MARK(U92(z0, z1)) -> c403(A__U92(mark(z0), z1), MARK(z0)) MARK(U93(z0)) -> c404(A__U93(mark(z0)), MARK(z0)) MARK(tail(z0)) -> c405(A__TAIL(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c406(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c407(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(sel(z0, z1)) -> c408(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c409(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c410 MARK(cons(z0, z1)) -> c411(MARK(z0)) MARK(s(z0)) -> c412(MARK(z0)) MARK(pair(z0, z1)) -> c413(MARK(z0)) MARK(pair(z0, z1)) -> c414(MARK(z1)) MARK(nil) -> c415 MARK(0) -> c416 The (relative) TRS S consists of the following rules: a__U101(tt, z0, z1) -> a__U102(a__isNaturalKind(z0), z0, z1) a__U101(z0, z1, z2) -> U101(z0, z1, z2) a__U102(tt, z0, z1) -> a__U103(a__isLNatKind(z1), z0, z1) a__U102(z0, z1, z2) -> U102(z0, z1, z2) a__U103(tt, z0, z1) -> a__U104(a__isLNatKind(z1), z0, z1) a__U103(z0, z1, z2) -> U103(z0, z1, z2) a__U104(tt, z0, z1) -> a__U105(a__isNatural(z0), z1) a__U104(z0, z1, z2) -> U104(z0, z1, z2) a__U105(tt, z0) -> a__U106(a__isLNat(z0)) a__U105(z0, z1) -> U105(z0, z1) a__U106(tt) -> tt a__U106(z0) -> U106(z0) a__U11(tt, z0, z1) -> a__U12(a__isNaturalKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U111(tt, z0) -> a__U112(a__isLNatKind(z0)) a__U111(z0, z1) -> U111(z0, z1) a__U112(tt) -> tt a__U112(z0) -> U112(z0) a__U12(tt, z0, z1) -> a__U13(a__isLNat(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U121(tt, z0) -> a__U122(a__isLNatKind(z0)) a__U121(z0, z1) -> U121(z0, z1) a__U122(tt) -> tt a__U122(z0) -> U122(z0) a__U13(tt, z0, z1) -> a__U14(a__isLNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U131(tt) -> tt a__U131(z0) -> U131(z0) a__U14(tt, z0, z1) -> a__snd(a__splitAt(mark(z0), mark(z1))) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U141(tt) -> tt a__U141(z0) -> U141(z0) a__U151(tt) -> tt a__U151(z0) -> U151(z0) a__U161(tt) -> tt a__U161(z0) -> U161(z0) a__U171(tt, z0) -> a__U172(a__isLNatKind(z0)) a__U171(z0, z1) -> U171(z0, z1) a__U172(tt) -> tt a__U172(z0) -> U172(z0) a__U181(tt, z0) -> a__U182(a__isLNatKind(z0), z0) a__U181(z0, z1) -> U181(z0, z1) a__U182(tt, z0) -> a__U183(a__isLNat(z0)) a__U182(z0, z1) -> U182(z0, z1) a__U183(tt) -> tt a__U183(z0) -> U183(z0) a__U191(tt, z0) -> a__U192(a__isNaturalKind(z0), z0) a__U191(z0, z1) -> U191(z0, z1) a__U192(tt, z0) -> a__U193(a__isNatural(z0)) a__U192(z0, z1) -> U192(z0, z1) a__U193(tt) -> tt a__U193(z0) -> U193(z0) a__U201(tt, z0, z1) -> a__U202(a__isNaturalKind(z0), z0, z1) a__U201(z0, z1, z2) -> U201(z0, z1, z2) a__U202(tt, z0, z1) -> a__U203(a__isLNatKind(z1), z0, z1) a__U202(z0, z1, z2) -> U202(z0, z1, z2) a__U203(tt, z0, z1) -> a__U204(a__isLNatKind(z1), z0, z1) a__U203(z0, z1, z2) -> U203(z0, z1, z2) a__U204(tt, z0, z1) -> a__U205(a__isNatural(z0), z1) a__U204(z0, z1, z2) -> U204(z0, z1, z2) a__U205(tt, z0) -> a__U206(a__isLNat(z0)) a__U205(z0, z1) -> U205(z0, z1) a__U206(tt) -> tt a__U206(z0) -> U206(z0) a__U21(tt, z0, z1) -> a__U22(a__isLNatKind(z0), z0, z1) a__U21(z0, z1, z2) -> U21(z0, z1, z2) a__U211(tt) -> tt a__U211(z0) -> U211(z0) a__U22(tt, z0, z1) -> a__U23(a__isLNat(z1), z0, z1) a__U22(z0, z1, z2) -> U22(z0, z1, z2) a__U221(tt) -> tt a__U221(z0) -> U221(z0) a__U23(tt, z0, z1) -> a__U24(a__isLNatKind(z1), z0) a__U23(z0, z1, z2) -> U23(z0, z1, z2) a__U231(tt, z0) -> a__U232(a__isLNatKind(z0)) a__U231(z0, z1) -> U231(z0, z1) a__U232(tt) -> tt a__U232(z0) -> U232(z0) a__U24(tt, z0) -> mark(z0) a__U24(z0, z1) -> U24(z0, z1) a__U241(tt, z0, z1) -> a__U242(a__isLNatKind(z0), z0, z1) a__U241(z0, z1, z2) -> U241(z0, z1, z2) a__U242(tt, z0, z1) -> a__U243(a__isLNatKind(z1), z0, z1) a__U242(z0, z1, z2) -> U242(z0, z1, z2) a__U243(tt, z0, z1) -> a__U244(a__isLNatKind(z1), z0, z1) a__U243(z0, z1, z2) -> U243(z0, z1, z2) a__U244(tt, z0, z1) -> a__U245(a__isLNat(z0), z1) a__U244(z0, z1, z2) -> U244(z0, z1, z2) a__U245(tt, z0) -> a__U246(a__isLNat(z0)) a__U245(z0, z1) -> U245(z0, z1) a__U246(tt) -> tt a__U246(z0) -> U246(z0) a__U251(tt, z0, z1) -> a__U252(a__isNaturalKind(z0), z0, z1) a__U251(z0, z1, z2) -> U251(z0, z1, z2) a__U252(tt, z0, z1) -> a__U253(a__isLNatKind(z1), z0, z1) a__U252(z0, z1, z2) -> U252(z0, z1, z2) a__U253(tt, z0, z1) -> a__U254(a__isLNatKind(z1), z0, z1) a__U253(z0, z1, z2) -> U253(z0, z1, z2) a__U254(tt, z0, z1) -> a__U255(a__isNatural(z0), z1) a__U254(z0, z1, z2) -> U254(z0, z1, z2) a__U255(tt, z0) -> a__U256(a__isLNat(z0)) a__U255(z0, z1) -> U255(z0, z1) a__U256(tt) -> tt a__U256(z0) -> U256(z0) a__U261(tt, z0) -> a__U262(a__isLNatKind(z0)) a__U261(z0, z1) -> U261(z0, z1) a__U262(tt) -> tt a__U262(z0) -> U262(z0) a__U271(tt, z0) -> a__U272(a__isLNatKind(z0)) a__U271(z0, z1) -> U271(z0, z1) a__U272(tt) -> tt a__U272(z0) -> U272(z0) a__U281(tt, z0) -> a__U282(a__isNaturalKind(z0), z0) a__U281(z0, z1) -> U281(z0, z1) a__U282(tt, z0) -> cons(mark(z0), natsFrom(s(z0))) a__U282(z0, z1) -> U282(z0, z1) a__U291(tt, z0, z1) -> a__U292(a__isNaturalKind(z0), z0, z1) a__U291(z0, z1, z2) -> U291(z0, z1, z2) a__U292(tt, z0, z1) -> a__U293(a__isLNat(z1), z0, z1) a__U292(z0, z1, z2) -> U292(z0, z1, z2) a__U293(tt, z0, z1) -> a__U294(a__isLNatKind(z1), z0, z1) a__U293(z0, z1, z2) -> U293(z0, z1, z2) a__U294(tt, z0, z1) -> a__head(a__afterNth(mark(z0), mark(z1))) a__U294(z0, z1, z2) -> U294(z0, z1, z2) a__U301(tt, z0, z1) -> a__U302(a__isLNatKind(z0), z1) a__U301(z0, z1, z2) -> U301(z0, z1, z2) a__U302(tt, z0) -> a__U303(a__isLNat(z0), z0) a__U302(z0, z1) -> U302(z0, z1) a__U303(tt, z0) -> a__U304(a__isLNatKind(z0), z0) a__U303(z0, z1) -> U303(z0, z1) a__U304(tt, z0) -> mark(z0) a__U304(z0, z1) -> U304(z0, z1) a__U31(tt, z0, z1) -> a__U32(a__isNaturalKind(z0), z0, z1) a__U31(z0, z1, z2) -> U31(z0, z1, z2) a__U311(tt, z0) -> a__U312(a__isLNatKind(z0), z0) a__U311(z0, z1) -> U311(z0, z1) a__U312(tt, z0) -> pair(nil, mark(z0)) a__U312(z0, z1) -> U312(z0, z1) a__U32(tt, z0, z1) -> a__U33(a__isLNat(z1), z0, z1) a__U32(z0, z1, z2) -> U32(z0, z1, z2) a__U321(tt, z0, z1, z2) -> a__U322(a__isNaturalKind(z0), z0, z1, z2) a__U321(z0, z1, z2, z3) -> U321(z0, z1, z2, z3) a__U322(tt, z0, z1, z2) -> a__U323(a__isNatural(z1), z0, z1, z2) a__U322(z0, z1, z2, z3) -> U322(z0, z1, z2, z3) a__U323(tt, z0, z1, z2) -> a__U324(a__isNaturalKind(z1), z0, z1, z2) a__U323(z0, z1, z2, z3) -> U323(z0, z1, z2, z3) a__U324(tt, z0, z1, z2) -> a__U325(a__isLNat(z2), z0, z1, z2) a__U324(z0, z1, z2, z3) -> U324(z0, z1, z2, z3) a__U325(tt, z0, z1, z2) -> a__U326(a__isLNatKind(z2), z0, z1, z2) a__U325(z0, z1, z2, z3) -> U325(z0, z1, z2, z3) a__U326(tt, z0, z1, z2) -> a__U327(a__splitAt(mark(z0), mark(z2)), z1) a__U326(z0, z1, z2, z3) -> U326(z0, z1, z2, z3) a__U327(pair(z0, z1), z2) -> pair(cons(mark(z2), z0), mark(z1)) a__U327(z0, z1) -> U327(z0, z1) a__U33(tt, z0, z1) -> a__U34(a__isLNatKind(z1), z0) a__U33(z0, z1, z2) -> U33(z0, z1, z2) a__U331(tt, z0, z1) -> a__U332(a__isNaturalKind(z0), z1) a__U331(z0, z1, z2) -> U331(z0, z1, z2) a__U332(tt, z0) -> a__U333(a__isLNat(z0), z0) a__U332(z0, z1) -> U332(z0, z1) a__U333(tt, z0) -> a__U334(a__isLNatKind(z0), z0) a__U333(z0, z1) -> U333(z0, z1) a__U334(tt, z0) -> mark(z0) a__U334(z0, z1) -> U334(z0, z1) a__U34(tt, z0) -> mark(z0) a__U34(z0, z1) -> U34(z0, z1) a__U341(tt, z0, z1) -> a__U342(a__isNaturalKind(z0), z0, z1) a__U341(z0, z1, z2) -> U341(z0, z1, z2) a__U342(tt, z0, z1) -> a__U343(a__isLNat(z1), z0, z1) a__U342(z0, z1, z2) -> U342(z0, z1, z2) a__U343(tt, z0, z1) -> a__U344(a__isLNatKind(z1), z0, z1) a__U343(z0, z1, z2) -> U343(z0, z1, z2) a__U344(tt, z0, z1) -> a__fst(a__splitAt(mark(z0), mark(z1))) a__U344(z0, z1, z2) -> U344(z0, z1, z2) a__U41(tt, z0, z1) -> a__U42(a__isNaturalKind(z0), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> a__U43(a__isLNatKind(z1), z0, z1) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__U43(tt, z0, z1) -> a__U44(a__isLNatKind(z1), z0, z1) a__U43(z0, z1, z2) -> U43(z0, z1, z2) a__U44(tt, z0, z1) -> a__U45(a__isNatural(z0), z1) a__U44(z0, z1, z2) -> U44(z0, z1, z2) a__U45(tt, z0) -> a__U46(a__isLNat(z0)) a__U45(z0, z1) -> U45(z0, z1) a__U46(tt) -> tt a__U46(z0) -> U46(z0) a__U51(tt, z0, z1) -> a__U52(a__isNaturalKind(z0), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> a__U53(a__isLNatKind(z1), z0, z1) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U53(tt, z0, z1) -> a__U54(a__isLNatKind(z1), z0, z1) a__U53(z0, z1, z2) -> U53(z0, z1, z2) a__U54(tt, z0, z1) -> a__U55(a__isNatural(z0), z1) a__U54(z0, z1, z2) -> U54(z0, z1, z2) a__U55(tt, z0) -> a__U56(a__isLNat(z0)) a__U55(z0, z1) -> U55(z0, z1) a__U56(tt) -> tt a__U56(z0) -> U56(z0) a__U61(tt, z0) -> a__U62(a__isPLNatKind(z0), z0) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt, z0) -> a__U63(a__isPLNat(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> a__U72(a__isNaturalKind(z0), z0) a__U71(z0, z1) -> U71(z0, z1) a__U72(tt, z0) -> a__U73(a__isNatural(z0)) a__U72(z0, z1) -> U72(z0, z1) a__U73(tt) -> tt a__U73(z0) -> U73(z0) a__U81(tt, z0) -> a__U82(a__isPLNatKind(z0), z0) a__U81(z0, z1) -> U81(z0, z1) a__U82(tt, z0) -> a__U83(a__isPLNat(z0)) a__U82(z0, z1) -> U82(z0, z1) a__U83(tt) -> tt a__U83(z0) -> U83(z0) a__U91(tt, z0) -> a__U92(a__isLNatKind(z0), z0) a__U91(z0, z1) -> U91(z0, z1) a__U92(tt, z0) -> a__U93(a__isLNat(z0)) a__U92(z0, z1) -> U92(z0, z1) a__U93(tt) -> tt a__U93(z0) -> U93(z0) a__afterNth(z0, z1) -> a__U11(a__isNatural(z0), z0, z1) a__afterNth(z0, z1) -> afterNth(z0, z1) a__fst(pair(z0, z1)) -> a__U21(a__isLNat(z0), z0, z1) a__fst(z0) -> fst(z0) a__head(cons(z0, z1)) -> a__U31(a__isNatural(z0), z0, z1) a__head(z0) -> head(z0) a__isLNat(nil) -> tt a__isLNat(afterNth(z0, z1)) -> a__U41(a__isNaturalKind(z0), z0, z1) a__isLNat(cons(z0, z1)) -> a__U51(a__isNaturalKind(z0), z0, z1) a__isLNat(fst(z0)) -> a__U61(a__isPLNatKind(z0), z0) a__isLNat(natsFrom(z0)) -> a__U71(a__isNaturalKind(z0), z0) a__isLNat(snd(z0)) -> a__U81(a__isPLNatKind(z0), z0) a__isLNat(tail(z0)) -> a__U91(a__isLNatKind(z0), z0) a__isLNat(take(z0, z1)) -> a__U101(a__isNaturalKind(z0), z0, z1) a__isLNat(z0) -> isLNat(z0) a__isLNatKind(nil) -> tt a__isLNatKind(afterNth(z0, z1)) -> a__U111(a__isNaturalKind(z0), z1) a__isLNatKind(cons(z0, z1)) -> a__U121(a__isNaturalKind(z0), z1) a__isLNatKind(fst(z0)) -> a__U131(a__isPLNatKind(z0)) a__isLNatKind(natsFrom(z0)) -> a__U141(a__isNaturalKind(z0)) a__isLNatKind(snd(z0)) -> a__U151(a__isPLNatKind(z0)) a__isLNatKind(tail(z0)) -> a__U161(a__isLNatKind(z0)) a__isLNatKind(take(z0, z1)) -> a__U171(a__isNaturalKind(z0), z1) a__isLNatKind(z0) -> isLNatKind(z0) a__isNatural(0) -> tt a__isNatural(head(z0)) -> a__U181(a__isLNatKind(z0), z0) a__isNatural(s(z0)) -> a__U191(a__isNaturalKind(z0), z0) a__isNatural(sel(z0, z1)) -> a__U201(a__isNaturalKind(z0), z0, z1) a__isNatural(z0) -> isNatural(z0) a__isNaturalKind(0) -> tt a__isNaturalKind(head(z0)) -> a__U211(a__isLNatKind(z0)) a__isNaturalKind(s(z0)) -> a__U221(a__isNaturalKind(z0)) a__isNaturalKind(sel(z0, z1)) -> a__U231(a__isNaturalKind(z0), z1) a__isNaturalKind(z0) -> isNaturalKind(z0) a__isPLNat(pair(z0, z1)) -> a__U241(a__isLNatKind(z0), z0, z1) a__isPLNat(splitAt(z0, z1)) -> a__U251(a__isNaturalKind(z0), z0, z1) a__isPLNat(z0) -> isPLNat(z0) a__isPLNatKind(pair(z0, z1)) -> a__U261(a__isLNatKind(z0), z1) a__isPLNatKind(splitAt(z0, z1)) -> a__U271(a__isNaturalKind(z0), z1) a__isPLNatKind(z0) -> isPLNatKind(z0) a__natsFrom(z0) -> a__U281(a__isNatural(z0), z0) a__natsFrom(z0) -> natsFrom(z0) a__sel(z0, z1) -> a__U291(a__isNatural(z0), z0, z1) a__sel(z0, z1) -> sel(z0, z1) a__snd(pair(z0, z1)) -> a__U301(a__isLNat(z0), z0, z1) a__snd(z0) -> snd(z0) a__splitAt(0, z0) -> a__U311(a__isLNat(z0), z0) a__splitAt(s(z0), cons(z1, z2)) -> a__U321(a__isNatural(z0), z0, z1, z2) a__splitAt(z0, z1) -> splitAt(z0, z1) a__tail(cons(z0, z1)) -> a__U331(a__isNatural(z0), z0, z1) a__tail(z0) -> tail(z0) a__take(z0, z1) -> a__U341(a__isNatural(z0), z0, z1) a__take(z0, z1) -> take(z0, z1) mark(U101(z0, z1, z2)) -> a__U101(mark(z0), z1, z2) mark(U102(z0, z1, z2)) -> a__U102(mark(z0), z1, z2) mark(isNaturalKind(z0)) -> a__isNaturalKind(z0) mark(U103(z0, z1, z2)) -> a__U103(mark(z0), z1, z2) mark(isLNatKind(z0)) -> a__isLNatKind(z0) mark(U104(z0, z1, z2)) -> a__U104(mark(z0), z1, z2) mark(U105(z0, z1)) -> a__U105(mark(z0), z1) mark(isNatural(z0)) -> a__isNatural(z0) mark(U106(z0)) -> a__U106(mark(z0)) mark(isLNat(z0)) -> a__isLNat(z0) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(U111(z0, z1)) -> a__U111(mark(z0), z1) mark(U112(z0)) -> a__U112(mark(z0)) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U121(z0, z1)) -> a__U121(mark(z0), z1) mark(U122(z0)) -> a__U122(mark(z0)) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U131(z0)) -> a__U131(mark(z0)) mark(snd(z0)) -> a__snd(mark(z0)) mark(splitAt(z0, z1)) -> a__splitAt(mark(z0), mark(z1)) mark(U141(z0)) -> a__U141(mark(z0)) mark(U151(z0)) -> a__U151(mark(z0)) mark(U161(z0)) -> a__U161(mark(z0)) mark(U171(z0, z1)) -> a__U171(mark(z0), z1) mark(U172(z0)) -> a__U172(mark(z0)) mark(U181(z0, z1)) -> a__U181(mark(z0), z1) mark(U182(z0, z1)) -> a__U182(mark(z0), z1) mark(U183(z0)) -> a__U183(mark(z0)) mark(U191(z0, z1)) -> a__U191(mark(z0), z1) mark(U192(z0, z1)) -> a__U192(mark(z0), z1) mark(U193(z0)) -> a__U193(mark(z0)) mark(U201(z0, z1, z2)) -> a__U201(mark(z0), z1, z2) mark(U202(z0, z1, z2)) -> a__U202(mark(z0), z1, z2) mark(U203(z0, z1, z2)) -> a__U203(mark(z0), z1, z2) mark(U204(z0, z1, z2)) -> a__U204(mark(z0), z1, z2) mark(U205(z0, z1)) -> a__U205(mark(z0), z1) mark(U206(z0)) -> a__U206(mark(z0)) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2) mark(U211(z0)) -> a__U211(mark(z0)) mark(U23(z0, z1, z2)) -> a__U23(mark(z0), z1, z2) mark(U221(z0)) -> a__U221(mark(z0)) mark(U24(z0, z1)) -> a__U24(mark(z0), z1) mark(U231(z0, z1)) -> a__U231(mark(z0), z1) mark(U232(z0)) -> a__U232(mark(z0)) mark(U241(z0, z1, z2)) -> a__U241(mark(z0), z1, z2) mark(U242(z0, z1, z2)) -> a__U242(mark(z0), z1, z2) mark(U243(z0, z1, z2)) -> a__U243(mark(z0), z1, z2) mark(U244(z0, z1, z2)) -> a__U244(mark(z0), z1, z2) mark(U245(z0, z1)) -> a__U245(mark(z0), z1) mark(U246(z0)) -> a__U246(mark(z0)) mark(U251(z0, z1, z2)) -> a__U251(mark(z0), z1, z2) mark(U252(z0, z1, z2)) -> a__U252(mark(z0), z1, z2) mark(U253(z0, z1, z2)) -> a__U253(mark(z0), z1, z2) mark(U254(z0, z1, z2)) -> a__U254(mark(z0), z1, z2) mark(U255(z0, z1)) -> a__U255(mark(z0), z1) mark(U256(z0)) -> a__U256(mark(z0)) mark(U261(z0, z1)) -> a__U261(mark(z0), z1) mark(U262(z0)) -> a__U262(mark(z0)) mark(U271(z0, z1)) -> a__U271(mark(z0), z1) mark(U272(z0)) -> a__U272(mark(z0)) mark(U281(z0, z1)) -> a__U281(mark(z0), z1) mark(U282(z0, z1)) -> a__U282(mark(z0), z1) mark(natsFrom(z0)) -> a__natsFrom(mark(z0)) mark(U291(z0, z1, z2)) -> a__U291(mark(z0), z1, z2) mark(U292(z0, z1, z2)) -> a__U292(mark(z0), z1, z2) mark(U293(z0, z1, z2)) -> a__U293(mark(z0), z1, z2) mark(U294(z0, z1, z2)) -> a__U294(mark(z0), z1, z2) mark(head(z0)) -> a__head(mark(z0)) mark(afterNth(z0, z1)) -> a__afterNth(mark(z0), mark(z1)) mark(U301(z0, z1, z2)) -> a__U301(mark(z0), z1, z2) mark(U302(z0, z1)) -> a__U302(mark(z0), z1) mark(U303(z0, z1)) -> a__U303(mark(z0), z1) mark(U304(z0, z1)) -> a__U304(mark(z0), z1) mark(U31(z0, z1, z2)) -> a__U31(mark(z0), z1, z2) mark(U32(z0, z1, z2)) -> a__U32(mark(z0), z1, z2) mark(U311(z0, z1)) -> a__U311(mark(z0), z1) mark(U312(z0, z1)) -> a__U312(mark(z0), z1) mark(U33(z0, z1, z2)) -> a__U33(mark(z0), z1, z2) mark(U321(z0, z1, z2, z3)) -> a__U321(mark(z0), z1, z2, z3) mark(U322(z0, z1, z2, z3)) -> a__U322(mark(z0), z1, z2, z3) mark(U323(z0, z1, z2, z3)) -> a__U323(mark(z0), z1, z2, z3) mark(U324(z0, z1, z2, z3)) -> a__U324(mark(z0), z1, z2, z3) mark(U325(z0, z1, z2, z3)) -> a__U325(mark(z0), z1, z2, z3) mark(U326(z0, z1, z2, z3)) -> a__U326(mark(z0), z1, z2, z3) mark(U327(z0, z1)) -> a__U327(mark(z0), z1) mark(U34(z0, z1)) -> a__U34(mark(z0), z1) mark(U331(z0, z1, z2)) -> a__U331(mark(z0), z1, z2) mark(U332(z0, z1)) -> a__U332(mark(z0), z1) mark(U333(z0, z1)) -> a__U333(mark(z0), z1) mark(U334(z0, z1)) -> a__U334(mark(z0), z1) mark(U341(z0, z1, z2)) -> a__U341(mark(z0), z1, z2) mark(U342(z0, z1, z2)) -> a__U342(mark(z0), z1, z2) mark(U343(z0, z1, z2)) -> a__U343(mark(z0), z1, z2) mark(U344(z0, z1, z2)) -> a__U344(mark(z0), z1, z2) mark(fst(z0)) -> a__fst(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(U43(z0, z1, z2)) -> a__U43(mark(z0), z1, z2) mark(U44(z0, z1, z2)) -> a__U44(mark(z0), z1, z2) mark(U45(z0, z1)) -> a__U45(mark(z0), z1) mark(U46(z0)) -> a__U46(mark(z0)) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(U53(z0, z1, z2)) -> a__U53(mark(z0), z1, z2) mark(U54(z0, z1, z2)) -> a__U54(mark(z0), z1, z2) mark(U55(z0, z1)) -> a__U55(mark(z0), z1) mark(U56(z0)) -> a__U56(mark(z0)) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(isPLNatKind(z0)) -> a__isPLNatKind(z0) mark(U63(z0)) -> a__U63(mark(z0)) mark(isPLNat(z0)) -> a__isPLNat(z0) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(U73(z0)) -> a__U73(mark(z0)) mark(U81(z0, z1)) -> a__U81(mark(z0), z1) mark(U82(z0, z1)) -> a__U82(mark(z0), z1) mark(U83(z0)) -> a__U83(mark(z0)) mark(U91(z0, z1)) -> a__U91(mark(z0), z1) mark(U92(z0, z1)) -> a__U92(mark(z0), z1) mark(U93(z0)) -> a__U93(mark(z0)) mark(tail(z0)) -> a__tail(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(tt) -> tt mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) mark(nil) -> nil mark(0) -> 0 Rewrite Strategy: INNERMOST