/export/starexec/sandbox/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- MAYBE We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. 0 : [] --> o U101 : [o * o * o] --> o U102 : [o * o * o] --> o U103 : [o * o * o] --> o U104 : [o * o * o] --> o U105 : [o * o] --> o U106 : [o] --> o U11 : [o * o * o] --> o U111 : [o * o] --> o U112 : [o] --> o U12 : [o * o * o] --> o U121 : [o * o] --> o U122 : [o] --> o U13 : [o * o * o] --> o U131 : [o] --> o U14 : [o * o * o] --> o U141 : [o] --> o U151 : [o] --> o U161 : [o] --> o U171 : [o * o] --> o U172 : [o] --> o U181 : [o * o] --> o U182 : [o * o] --> o U183 : [o] --> o U191 : [o * o] --> o U192 : [o * o] --> o U193 : [o] --> o U201 : [o * o * o] --> o U202 : [o * o * o] --> o U203 : [o * o * o] --> o U204 : [o * o * o] --> o U205 : [o * o] --> o U206 : [o] --> o U21 : [o * o * o] --> o U211 : [o] --> o U22 : [o * o * o] --> o U221 : [o] --> o U23 : [o * o * o] --> o U231 : [o * o] --> o U232 : [o] --> o U24 : [o * o] --> o U241 : [o * o * o] --> o U242 : [o * o * o] --> o U243 : [o * o * o] --> o U244 : [o * o * o] --> o U245 : [o * o] --> o U246 : [o] --> o U251 : [o * o * o] --> o U252 : [o * o * o] --> o U253 : [o * o * o] --> o U254 : [o * o * o] --> o U255 : [o * o] --> o U256 : [o] --> o U261 : [o * o] --> o U262 : [o] --> o U271 : [o * o] --> o U272 : [o] --> o U281 : [o * o] --> o U282 : [o * o] --> o U291 : [o * o * o] --> o U292 : [o * o * o] --> o U293 : [o * o * o] --> o U294 : [o * o * o] --> o U301 : [o * o * o] --> o U302 : [o * o] --> o U303 : [o * o] --> o U304 : [o * o] --> o U31 : [o * o * o] --> o U311 : [o * o] --> o U312 : [o * o] --> o U32 : [o * o * o] --> o U321 : [o * o * o * o] --> o U322 : [o * o * o * o] --> o U323 : [o * o * o * o] --> o U324 : [o * o * o * o] --> o U325 : [o * o * o * o] --> o U326 : [o * o * o * o] --> o U327 : [o * o] --> o U33 : [o * o * o] --> o U331 : [o * o * o] --> o U332 : [o * o] --> o U333 : [o * o] --> o U334 : [o * o] --> o U34 : [o * o] --> o U341 : [o * o * o] --> o U342 : [o * o * o] --> o U343 : [o * o * o] --> o U344 : [o * o * o] --> o U41 : [o * o * o] --> o U42 : [o * o * o] --> o U43 : [o * o * o] --> o U44 : [o * o * o] --> o U45 : [o * o] --> o U46 : [o] --> o U51 : [o * o * o] --> o U52 : [o * o * o] --> o U53 : [o * o * o] --> o U54 : [o * o * o] --> o U55 : [o * o] --> o U56 : [o] --> o U61 : [o * o] --> o U62 : [o * o] --> o U63 : [o] --> o U71 : [o * o] --> o U72 : [o * o] --> o U73 : [o] --> o U81 : [o * o] --> o U82 : [o * o] --> o U83 : [o] --> o U91 : [o * o] --> o U92 : [o * o] --> o U93 : [o] --> o active : [o] --> o afterNth : [o * o] --> o cons : [o * o] --> o fst : [o] --> o head : [o] --> o isLNat : [o] --> o isLNatKind : [o] --> o isNatural : [o] --> o isNaturalKind : [o] --> o isPLNat : [o] --> o isPLNatKind : [o] --> o mark : [o] --> o natsFrom : [o] --> o nil : [] --> o pair : [o * o] --> o s : [o] --> o sel : [o * o] --> o snd : [o] --> o splitAt : [o * o] --> o tail : [o] --> o take : [o * o] --> o tt : [] --> o active(U101(tt, X, Y)) => mark(U102(isNaturalKind(X), X, Y)) active(U102(tt, X, Y)) => mark(U103(isLNatKind(Y), X, Y)) active(U103(tt, X, Y)) => mark(U104(isLNatKind(Y), X, Y)) active(U104(tt, X, Y)) => mark(U105(isNatural(X), Y)) active(U105(tt, X)) => mark(U106(isLNat(X))) active(U106(tt)) => mark(tt) active(U11(tt, X, Y)) => mark(U12(isNaturalKind(X), X, Y)) active(U111(tt, X)) => mark(U112(isLNatKind(X))) active(U112(tt)) => mark(tt) active(U12(tt, X, Y)) => mark(U13(isLNat(Y), X, Y)) active(U121(tt, X)) => mark(U122(isLNatKind(X))) active(U122(tt)) => mark(tt) active(U13(tt, X, Y)) => mark(U14(isLNatKind(Y), X, Y)) active(U131(tt)) => mark(tt) active(U14(tt, X, Y)) => mark(snd(splitAt(X, Y))) active(U141(tt)) => mark(tt) active(U151(tt)) => mark(tt) active(U161(tt)) => mark(tt) active(U171(tt, X)) => mark(U172(isLNatKind(X))) active(U172(tt)) => mark(tt) active(U181(tt, X)) => mark(U182(isLNatKind(X), X)) active(U182(tt, X)) => mark(U183(isLNat(X))) active(U183(tt)) => mark(tt) active(U191(tt, X)) => mark(U192(isNaturalKind(X), X)) active(U192(tt, X)) => mark(U193(isNatural(X))) active(U193(tt)) => mark(tt) active(U201(tt, X, Y)) => mark(U202(isNaturalKind(X), X, Y)) active(U202(tt, X, Y)) => mark(U203(isLNatKind(Y), X, Y)) active(U203(tt, X, Y)) => mark(U204(isLNatKind(Y), X, Y)) active(U204(tt, X, Y)) => mark(U205(isNatural(X), Y)) active(U205(tt, X)) => mark(U206(isLNat(X))) active(U206(tt)) => mark(tt) active(U21(tt, X, Y)) => mark(U22(isLNatKind(X), X, Y)) active(U211(tt)) => mark(tt) active(U22(tt, X, Y)) => mark(U23(isLNat(Y), X, Y)) active(U221(tt)) => mark(tt) active(U23(tt, X, Y)) => mark(U24(isLNatKind(Y), X)) active(U231(tt, X)) => mark(U232(isLNatKind(X))) active(U232(tt)) => mark(tt) active(U24(tt, X)) => mark(X) active(U241(tt, X, Y)) => mark(U242(isLNatKind(X), X, Y)) active(U242(tt, X, Y)) => mark(U243(isLNatKind(Y), X, Y)) active(U243(tt, X, Y)) => mark(U244(isLNatKind(Y), X, Y)) active(U244(tt, X, Y)) => mark(U245(isLNat(X), Y)) active(U245(tt, X)) => mark(U246(isLNat(X))) active(U246(tt)) => mark(tt) active(U251(tt, X, Y)) => mark(U252(isNaturalKind(X), X, Y)) active(U252(tt, X, Y)) => mark(U253(isLNatKind(Y), X, Y)) active(U253(tt, X, Y)) => mark(U254(isLNatKind(Y), X, Y)) active(U254(tt, X, Y)) => mark(U255(isNatural(X), Y)) active(U255(tt, X)) => mark(U256(isLNat(X))) active(U256(tt)) => mark(tt) active(U261(tt, X)) => mark(U262(isLNatKind(X))) active(U262(tt)) => mark(tt) active(U271(tt, X)) => mark(U272(isLNatKind(X))) active(U272(tt)) => mark(tt) active(U281(tt, X)) => mark(U282(isNaturalKind(X), X)) active(U282(tt, X)) => mark(cons(X, natsFrom(s(X)))) active(U291(tt, X, Y)) => mark(U292(isNaturalKind(X), X, Y)) active(U292(tt, X, Y)) => mark(U293(isLNat(Y), X, Y)) active(U293(tt, X, Y)) => mark(U294(isLNatKind(Y), X, Y)) active(U294(tt, X, Y)) => mark(head(afterNth(X, Y))) active(U301(tt, X, Y)) => mark(U302(isLNatKind(X), Y)) active(U302(tt, X)) => mark(U303(isLNat(X), X)) active(U303(tt, X)) => mark(U304(isLNatKind(X), X)) active(U304(tt, X)) => mark(X) active(U31(tt, X, Y)) => mark(U32(isNaturalKind(X), X, Y)) active(U311(tt, X)) => mark(U312(isLNatKind(X), X)) active(U312(tt, X)) => mark(pair(nil, X)) active(U32(tt, X, Y)) => mark(U33(isLNat(Y), X, Y)) active(U321(tt, X, Y, Z)) => mark(U322(isNaturalKind(X), X, Y, Z)) active(U322(tt, X, Y, Z)) => mark(U323(isNatural(Y), X, Y, Z)) active(U323(tt, X, Y, Z)) => mark(U324(isNaturalKind(Y), X, Y, Z)) active(U324(tt, X, Y, Z)) => mark(U325(isLNat(Z), X, Y, Z)) active(U325(tt, X, Y, Z)) => mark(U326(isLNatKind(Z), X, Y, Z)) active(U326(tt, X, Y, Z)) => mark(U327(splitAt(X, Z), Y)) active(U327(pair(X, Y), Z)) => mark(pair(cons(Z, X), Y)) active(U33(tt, X, Y)) => mark(U34(isLNatKind(Y), X)) active(U331(tt, X, Y)) => mark(U332(isNaturalKind(X), Y)) active(U332(tt, X)) => mark(U333(isLNat(X), X)) active(U333(tt, X)) => mark(U334(isLNatKind(X), X)) active(U334(tt, X)) => mark(X) active(U34(tt, X)) => mark(X) active(U341(tt, X, Y)) => mark(U342(isNaturalKind(X), X, Y)) active(U342(tt, X, Y)) => mark(U343(isLNat(Y), X, Y)) active(U343(tt, X, Y)) => mark(U344(isLNatKind(Y), X, Y)) active(U344(tt, X, Y)) => mark(fst(splitAt(X, Y))) active(U41(tt, X, Y)) => mark(U42(isNaturalKind(X), X, Y)) active(U42(tt, X, Y)) => mark(U43(isLNatKind(Y), X, Y)) active(U43(tt, X, Y)) => mark(U44(isLNatKind(Y), X, Y)) active(U44(tt, X, Y)) => mark(U45(isNatural(X), Y)) active(U45(tt, X)) => mark(U46(isLNat(X))) active(U46(tt)) => mark(tt) active(U51(tt, X, Y)) => mark(U52(isNaturalKind(X), X, Y)) active(U52(tt, X, Y)) => mark(U53(isLNatKind(Y), X, Y)) active(U53(tt, X, Y)) => mark(U54(isLNatKind(Y), X, Y)) active(U54(tt, X, Y)) => mark(U55(isNatural(X), Y)) active(U55(tt, X)) => mark(U56(isLNat(X))) active(U56(tt)) => mark(tt) active(U61(tt, X)) => mark(U62(isPLNatKind(X), X)) active(U62(tt, X)) => mark(U63(isPLNat(X))) active(U63(tt)) => mark(tt) active(U71(tt, X)) => mark(U72(isNaturalKind(X), X)) active(U72(tt, X)) => mark(U73(isNatural(X))) active(U73(tt)) => mark(tt) active(U81(tt, X)) => mark(U82(isPLNatKind(X), X)) active(U82(tt, X)) => mark(U83(isPLNat(X))) active(U83(tt)) => mark(tt) active(U91(tt, X)) => mark(U92(isLNatKind(X), X)) active(U92(tt, X)) => mark(U93(isLNat(X))) active(U93(tt)) => mark(tt) active(afterNth(X, Y)) => mark(U11(isNatural(X), X, Y)) active(fst(pair(X, Y))) => mark(U21(isLNat(X), X, Y)) active(head(cons(X, Y))) => mark(U31(isNatural(X), X, Y)) active(isLNat(nil)) => mark(tt) active(isLNat(afterNth(X, Y))) => mark(U41(isNaturalKind(X), X, Y)) active(isLNat(cons(X, Y))) => mark(U51(isNaturalKind(X), X, Y)) active(isLNat(fst(X))) => mark(U61(isPLNatKind(X), X)) active(isLNat(natsFrom(X))) => mark(U71(isNaturalKind(X), X)) active(isLNat(snd(X))) => mark(U81(isPLNatKind(X), X)) active(isLNat(tail(X))) => mark(U91(isLNatKind(X), X)) active(isLNat(take(X, Y))) => mark(U101(isNaturalKind(X), X, Y)) active(isLNatKind(nil)) => mark(tt) active(isLNatKind(afterNth(X, Y))) => mark(U111(isNaturalKind(X), Y)) active(isLNatKind(cons(X, Y))) => mark(U121(isNaturalKind(X), Y)) active(isLNatKind(fst(X))) => mark(U131(isPLNatKind(X))) active(isLNatKind(natsFrom(X))) => mark(U141(isNaturalKind(X))) active(isLNatKind(snd(X))) => mark(U151(isPLNatKind(X))) active(isLNatKind(tail(X))) => mark(U161(isLNatKind(X))) active(isLNatKind(take(X, Y))) => mark(U171(isNaturalKind(X), Y)) active(isNatural(0)) => mark(tt) active(isNatural(head(X))) => mark(U181(isLNatKind(X), X)) active(isNatural(s(X))) => mark(U191(isNaturalKind(X), X)) active(isNatural(sel(X, Y))) => mark(U201(isNaturalKind(X), X, Y)) active(isNaturalKind(0)) => mark(tt) active(isNaturalKind(head(X))) => mark(U211(isLNatKind(X))) active(isNaturalKind(s(X))) => mark(U221(isNaturalKind(X))) active(isNaturalKind(sel(X, Y))) => mark(U231(isNaturalKind(X), Y)) active(isPLNat(pair(X, Y))) => mark(U241(isLNatKind(X), X, Y)) active(isPLNat(splitAt(X, Y))) => mark(U251(isNaturalKind(X), X, Y)) active(isPLNatKind(pair(X, Y))) => mark(U261(isLNatKind(X), Y)) active(isPLNatKind(splitAt(X, Y))) => mark(U271(isNaturalKind(X), Y)) active(natsFrom(X)) => mark(U281(isNatural(X), X)) active(sel(X, Y)) => mark(U291(isNatural(X), X, Y)) active(snd(pair(X, Y))) => mark(U301(isLNat(X), X, Y)) active(splitAt(0, X)) => mark(U311(isLNat(X), X)) active(splitAt(s(X), cons(Y, Z))) => mark(U321(isNatural(X), X, Y, Z)) active(tail(cons(X, Y))) => mark(U331(isNatural(X), X, Y)) active(take(X, Y)) => mark(U341(isNatural(X), X, Y)) mark(U101(X, Y, Z)) => active(U101(mark(X), Y, Z)) mark(tt) => active(tt) mark(U102(X, Y, Z)) => active(U102(mark(X), Y, Z)) mark(isNaturalKind(X)) => active(isNaturalKind(X)) mark(U103(X, Y, Z)) => active(U103(mark(X), Y, Z)) mark(isLNatKind(X)) => active(isLNatKind(X)) mark(U104(X, Y, Z)) => active(U104(mark(X), Y, Z)) mark(U105(X, Y)) => active(U105(mark(X), Y)) mark(isNatural(X)) => active(isNatural(X)) mark(U106(X)) => active(U106(mark(X))) mark(isLNat(X)) => active(isLNat(X)) mark(U11(X, Y, Z)) => active(U11(mark(X), Y, Z)) mark(U12(X, Y, Z)) => active(U12(mark(X), Y, Z)) mark(U111(X, Y)) => active(U111(mark(X), Y)) mark(U112(X)) => active(U112(mark(X))) mark(U13(X, Y, Z)) => active(U13(mark(X), Y, Z)) mark(U121(X, Y)) => active(U121(mark(X), Y)) mark(U122(X)) => active(U122(mark(X))) mark(U14(X, Y, Z)) => active(U14(mark(X), Y, Z)) mark(U131(X)) => active(U131(mark(X))) mark(snd(X)) => active(snd(mark(X))) mark(splitAt(X, Y)) => active(splitAt(mark(X), mark(Y))) mark(U141(X)) => active(U141(mark(X))) mark(U151(X)) => active(U151(mark(X))) mark(U161(X)) => active(U161(mark(X))) mark(U171(X, Y)) => active(U171(mark(X), Y)) mark(U172(X)) => active(U172(mark(X))) mark(U181(X, Y)) => active(U181(mark(X), Y)) mark(U182(X, Y)) => active(U182(mark(X), Y)) mark(U183(X)) => active(U183(mark(X))) mark(U191(X, Y)) => active(U191(mark(X), Y)) mark(U192(X, Y)) => active(U192(mark(X), Y)) mark(U193(X)) => active(U193(mark(X))) mark(U201(X, Y, Z)) => active(U201(mark(X), Y, Z)) mark(U202(X, Y, Z)) => active(U202(mark(X), Y, Z)) mark(U203(X, Y, Z)) => active(U203(mark(X), Y, Z)) mark(U204(X, Y, Z)) => active(U204(mark(X), Y, Z)) mark(U205(X, Y)) => active(U205(mark(X), Y)) mark(U206(X)) => active(U206(mark(X))) mark(U21(X, Y, Z)) => active(U21(mark(X), Y, Z)) mark(U22(X, Y, Z)) => active(U22(mark(X), Y, Z)) mark(U211(X)) => active(U211(mark(X))) mark(U23(X, Y, Z)) => active(U23(mark(X), Y, Z)) mark(U221(X)) => active(U221(mark(X))) mark(U24(X, Y)) => active(U24(mark(X), Y)) mark(U231(X, Y)) => active(U231(mark(X), Y)) mark(U232(X)) => active(U232(mark(X))) mark(U241(X, Y, Z)) => active(U241(mark(X), Y, Z)) mark(U242(X, Y, Z)) => active(U242(mark(X), Y, Z)) mark(U243(X, Y, Z)) => active(U243(mark(X), Y, Z)) mark(U244(X, Y, Z)) => active(U244(mark(X), Y, Z)) mark(U245(X, Y)) => active(U245(mark(X), Y)) mark(U246(X)) => active(U246(mark(X))) mark(U251(X, Y, Z)) => active(U251(mark(X), Y, Z)) mark(U252(X, Y, Z)) => active(U252(mark(X), Y, Z)) mark(U253(X, Y, Z)) => active(U253(mark(X), Y, Z)) mark(U254(X, Y, Z)) => active(U254(mark(X), Y, Z)) mark(U255(X, Y)) => active(U255(mark(X), Y)) mark(U256(X)) => active(U256(mark(X))) mark(U261(X, Y)) => active(U261(mark(X), Y)) mark(U262(X)) => active(U262(mark(X))) mark(U271(X, Y)) => active(U271(mark(X), Y)) mark(U272(X)) => active(U272(mark(X))) mark(U281(X, Y)) => active(U281(mark(X), Y)) mark(U282(X, Y)) => active(U282(mark(X), Y)) mark(cons(X, Y)) => active(cons(mark(X), Y)) mark(natsFrom(X)) => active(natsFrom(mark(X))) mark(s(X)) => active(s(mark(X))) mark(U291(X, Y, Z)) => active(U291(mark(X), Y, Z)) mark(U292(X, Y, Z)) => active(U292(mark(X), Y, Z)) mark(U293(X, Y, Z)) => active(U293(mark(X), Y, Z)) mark(U294(X, Y, Z)) => active(U294(mark(X), Y, Z)) mark(head(X)) => active(head(mark(X))) mark(afterNth(X, Y)) => active(afterNth(mark(X), mark(Y))) mark(U301(X, Y, Z)) => active(U301(mark(X), Y, Z)) mark(U302(X, Y)) => active(U302(mark(X), Y)) mark(U303(X, Y)) => active(U303(mark(X), Y)) mark(U304(X, Y)) => active(U304(mark(X), Y)) mark(U31(X, Y, Z)) => active(U31(mark(X), Y, Z)) mark(U32(X, Y, Z)) => active(U32(mark(X), Y, Z)) mark(U311(X, Y)) => active(U311(mark(X), Y)) mark(U312(X, Y)) => active(U312(mark(X), Y)) mark(pair(X, Y)) => active(pair(mark(X), mark(Y))) mark(nil) => active(nil) mark(U33(X, Y, Z)) => active(U33(mark(X), Y, Z)) mark(U321(X, Y, Z, U)) => active(U321(mark(X), Y, Z, U)) mark(U322(X, Y, Z, U)) => active(U322(mark(X), Y, Z, U)) mark(U323(X, Y, Z, U)) => active(U323(mark(X), Y, Z, U)) mark(U324(X, Y, Z, U)) => active(U324(mark(X), Y, Z, U)) mark(U325(X, Y, Z, U)) => active(U325(mark(X), Y, Z, U)) mark(U326(X, Y, Z, U)) => active(U326(mark(X), Y, Z, U)) mark(U327(X, Y)) => active(U327(mark(X), Y)) mark(U34(X, Y)) => active(U34(mark(X), Y)) mark(U331(X, Y, Z)) => active(U331(mark(X), Y, Z)) mark(U332(X, Y)) => active(U332(mark(X), Y)) mark(U333(X, Y)) => active(U333(mark(X), Y)) mark(U334(X, Y)) => active(U334(mark(X), Y)) mark(U341(X, Y, Z)) => active(U341(mark(X), Y, Z)) mark(U342(X, Y, Z)) => active(U342(mark(X), Y, Z)) mark(U343(X, Y, Z)) => active(U343(mark(X), Y, Z)) mark(U344(X, Y, Z)) => active(U344(mark(X), Y, Z)) mark(fst(X)) => active(fst(mark(X))) mark(U41(X, Y, Z)) => active(U41(mark(X), Y, Z)) mark(U42(X, Y, Z)) => active(U42(mark(X), Y, Z)) mark(U43(X, Y, Z)) => active(U43(mark(X), Y, Z)) mark(U44(X, Y, Z)) => active(U44(mark(X), Y, Z)) mark(U45(X, Y)) => active(U45(mark(X), Y)) mark(U46(X)) => active(U46(mark(X))) mark(U51(X, Y, Z)) => active(U51(mark(X), Y, Z)) mark(U52(X, Y, Z)) => active(U52(mark(X), Y, Z)) mark(U53(X, Y, Z)) => active(U53(mark(X), Y, Z)) mark(U54(X, Y, Z)) => active(U54(mark(X), Y, Z)) mark(U55(X, Y)) => active(U55(mark(X), Y)) mark(U56(X)) => active(U56(mark(X))) mark(U61(X, Y)) => active(U61(mark(X), Y)) mark(U62(X, Y)) => active(U62(mark(X), Y)) mark(isPLNatKind(X)) => active(isPLNatKind(X)) mark(U63(X)) => active(U63(mark(X))) mark(isPLNat(X)) => active(isPLNat(X)) mark(U71(X, Y)) => active(U71(mark(X), Y)) mark(U72(X, Y)) => active(U72(mark(X), Y)) mark(U73(X)) => active(U73(mark(X))) mark(U81(X, Y)) => active(U81(mark(X), Y)) mark(U82(X, Y)) => active(U82(mark(X), Y)) mark(U83(X)) => active(U83(mark(X))) mark(U91(X, Y)) => active(U91(mark(X), Y)) mark(U92(X, Y)) => active(U92(mark(X), Y)) mark(U93(X)) => active(U93(mark(X))) mark(tail(X)) => active(tail(mark(X))) mark(take(X, Y)) => active(take(mark(X), mark(Y))) mark(0) => active(0) mark(sel(X, Y)) => active(sel(mark(X), mark(Y))) U101(mark(X), Y, Z) => U101(X, Y, Z) U101(X, mark(Y), Z) => U101(X, Y, Z) U101(X, Y, mark(Z)) => U101(X, Y, Z) U101(active(X), Y, Z) => U101(X, Y, Z) U101(X, active(Y), Z) => U101(X, Y, Z) U101(X, Y, active(Z)) => U101(X, Y, Z) U102(mark(X), Y, Z) => U102(X, Y, Z) U102(X, mark(Y), Z) => U102(X, Y, Z) U102(X, Y, mark(Z)) => U102(X, Y, Z) U102(active(X), Y, Z) => U102(X, Y, Z) U102(X, active(Y), Z) => U102(X, Y, Z) U102(X, Y, active(Z)) => U102(X, Y, Z) isNaturalKind(mark(X)) => isNaturalKind(X) isNaturalKind(active(X)) => isNaturalKind(X) U103(mark(X), Y, Z) => U103(X, Y, Z) U103(X, mark(Y), Z) => U103(X, Y, Z) U103(X, Y, mark(Z)) => U103(X, Y, Z) U103(active(X), Y, Z) => U103(X, Y, Z) U103(X, active(Y), Z) => U103(X, Y, Z) U103(X, Y, active(Z)) => U103(X, Y, Z) isLNatKind(mark(X)) => isLNatKind(X) isLNatKind(active(X)) => isLNatKind(X) U104(mark(X), Y, Z) => U104(X, Y, Z) U104(X, mark(Y), Z) => U104(X, Y, Z) U104(X, Y, mark(Z)) => U104(X, Y, Z) U104(active(X), Y, Z) => U104(X, Y, Z) U104(X, active(Y), Z) => U104(X, Y, Z) U104(X, Y, active(Z)) => U104(X, Y, Z) U105(mark(X), Y) => U105(X, Y) U105(X, mark(Y)) => U105(X, Y) U105(active(X), Y) => U105(X, Y) U105(X, active(Y)) => U105(X, Y) isNatural(mark(X)) => isNatural(X) isNatural(active(X)) => isNatural(X) U106(mark(X)) => U106(X) U106(active(X)) => U106(X) isLNat(mark(X)) => isLNat(X) isLNat(active(X)) => isLNat(X) U11(mark(X), Y, Z) => U11(X, Y, Z) U11(X, mark(Y), Z) => U11(X, Y, Z) U11(X, Y, mark(Z)) => U11(X, Y, Z) U11(active(X), Y, Z) => U11(X, Y, Z) U11(X, active(Y), Z) => U11(X, Y, Z) U11(X, Y, active(Z)) => U11(X, Y, Z) U12(mark(X), Y, Z) => U12(X, Y, Z) U12(X, mark(Y), Z) => U12(X, Y, Z) U12(X, Y, mark(Z)) => U12(X, Y, Z) U12(active(X), Y, Z) => U12(X, Y, Z) U12(X, active(Y), Z) => U12(X, Y, Z) U12(X, Y, active(Z)) => U12(X, Y, Z) U111(mark(X), Y) => U111(X, Y) U111(X, mark(Y)) => U111(X, Y) U111(active(X), Y) => U111(X, Y) U111(X, active(Y)) => U111(X, Y) U112(mark(X)) => U112(X) U112(active(X)) => U112(X) U13(mark(X), Y, Z) => U13(X, Y, Z) U13(X, mark(Y), Z) => U13(X, Y, Z) U13(X, Y, mark(Z)) => U13(X, Y, Z) U13(active(X), Y, Z) => U13(X, Y, Z) U13(X, active(Y), Z) => U13(X, Y, Z) U13(X, Y, active(Z)) => U13(X, Y, Z) U121(mark(X), Y) => U121(X, Y) U121(X, mark(Y)) => U121(X, Y) U121(active(X), Y) => U121(X, Y) U121(X, active(Y)) => U121(X, Y) U122(mark(X)) => U122(X) U122(active(X)) => U122(X) U14(mark(X), Y, Z) => U14(X, Y, Z) U14(X, mark(Y), Z) => U14(X, Y, Z) U14(X, Y, mark(Z)) => U14(X, Y, Z) U14(active(X), Y, Z) => U14(X, Y, Z) U14(X, active(Y), Z) => U14(X, Y, Z) U14(X, Y, active(Z)) => U14(X, Y, Z) U131(mark(X)) => U131(X) U131(active(X)) => U131(X) snd(mark(X)) => snd(X) snd(active(X)) => snd(X) splitAt(mark(X), Y) => splitAt(X, Y) splitAt(X, mark(Y)) => splitAt(X, Y) splitAt(active(X), Y) => splitAt(X, Y) splitAt(X, active(Y)) => splitAt(X, Y) U141(mark(X)) => U141(X) U141(active(X)) => U141(X) U151(mark(X)) => U151(X) U151(active(X)) => U151(X) U161(mark(X)) => U161(X) U161(active(X)) => U161(X) U171(mark(X), Y) => U171(X, Y) U171(X, mark(Y)) => U171(X, Y) U171(active(X), Y) => U171(X, Y) U171(X, active(Y)) => U171(X, Y) U172(mark(X)) => U172(X) U172(active(X)) => U172(X) U181(mark(X), Y) => U181(X, Y) U181(X, mark(Y)) => U181(X, Y) U181(active(X), Y) => U181(X, Y) U181(X, active(Y)) => U181(X, Y) U182(mark(X), Y) => U182(X, Y) U182(X, mark(Y)) => U182(X, Y) U182(active(X), Y) => U182(X, Y) U182(X, active(Y)) => U182(X, Y) U183(mark(X)) => U183(X) U183(active(X)) => U183(X) U191(mark(X), Y) => U191(X, Y) U191(X, mark(Y)) => U191(X, Y) U191(active(X), Y) => U191(X, Y) U191(X, active(Y)) => U191(X, Y) U192(mark(X), Y) => U192(X, Y) U192(X, mark(Y)) => U192(X, Y) U192(active(X), Y) => U192(X, Y) U192(X, active(Y)) => U192(X, Y) U193(mark(X)) => U193(X) U193(active(X)) => U193(X) U201(mark(X), Y, Z) => U201(X, Y, Z) U201(X, mark(Y), Z) => U201(X, Y, Z) U201(X, Y, mark(Z)) => U201(X, Y, Z) U201(active(X), Y, Z) => U201(X, Y, Z) U201(X, active(Y), Z) => U201(X, Y, Z) U201(X, Y, active(Z)) => U201(X, Y, Z) U202(mark(X), Y, Z) => U202(X, Y, Z) U202(X, mark(Y), Z) => U202(X, Y, Z) U202(X, Y, mark(Z)) => U202(X, Y, Z) U202(active(X), Y, Z) => U202(X, Y, Z) U202(X, active(Y), Z) => U202(X, Y, Z) U202(X, Y, active(Z)) => U202(X, Y, Z) U203(mark(X), Y, Z) => U203(X, Y, Z) U203(X, mark(Y), Z) => U203(X, Y, Z) U203(X, Y, mark(Z)) => U203(X, Y, Z) U203(active(X), Y, Z) => U203(X, Y, Z) U203(X, active(Y), Z) => U203(X, Y, Z) U203(X, Y, active(Z)) => U203(X, Y, Z) U204(mark(X), Y, Z) => U204(X, Y, Z) U204(X, mark(Y), Z) => U204(X, Y, Z) U204(X, Y, mark(Z)) => U204(X, Y, Z) U204(active(X), Y, Z) => U204(X, Y, Z) U204(X, active(Y), Z) => U204(X, Y, Z) U204(X, Y, active(Z)) => U204(X, Y, Z) U205(mark(X), Y) => U205(X, Y) U205(X, mark(Y)) => U205(X, Y) U205(active(X), Y) => U205(X, Y) U205(X, active(Y)) => U205(X, Y) U206(mark(X)) => U206(X) U206(active(X)) => U206(X) U21(mark(X), Y, Z) => U21(X, Y, Z) U21(X, mark(Y), Z) => U21(X, Y, Z) U21(X, Y, mark(Z)) => U21(X, Y, Z) U21(active(X), Y, Z) => U21(X, Y, Z) U21(X, active(Y), Z) => U21(X, Y, Z) U21(X, Y, active(Z)) => U21(X, Y, Z) U22(mark(X), Y, Z) => U22(X, Y, Z) U22(X, mark(Y), Z) => U22(X, Y, Z) U22(X, Y, mark(Z)) => U22(X, Y, Z) U22(active(X), Y, Z) => U22(X, Y, Z) U22(X, active(Y), Z) => U22(X, Y, Z) U22(X, Y, active(Z)) => U22(X, Y, Z) U211(mark(X)) => U211(X) U211(active(X)) => U211(X) U23(mark(X), Y, Z) => U23(X, Y, Z) U23(X, mark(Y), Z) => U23(X, Y, Z) U23(X, Y, mark(Z)) => U23(X, Y, Z) U23(active(X), Y, Z) => U23(X, Y, Z) U23(X, active(Y), Z) => U23(X, Y, Z) U23(X, Y, active(Z)) => U23(X, Y, Z) U221(mark(X)) => U221(X) U221(active(X)) => U221(X) U24(mark(X), Y) => U24(X, Y) U24(X, mark(Y)) => U24(X, Y) U24(active(X), Y) => U24(X, Y) U24(X, active(Y)) => U24(X, Y) U231(mark(X), Y) => U231(X, Y) U231(X, mark(Y)) => U231(X, Y) U231(active(X), Y) => U231(X, Y) U231(X, active(Y)) => U231(X, Y) U232(mark(X)) => U232(X) U232(active(X)) => U232(X) U241(mark(X), Y, Z) => U241(X, Y, Z) U241(X, mark(Y), Z) => U241(X, Y, Z) U241(X, Y, mark(Z)) => U241(X, Y, Z) U241(active(X), Y, Z) => U241(X, Y, Z) U241(X, active(Y), Z) => U241(X, Y, Z) U241(X, Y, active(Z)) => U241(X, Y, Z) U242(mark(X), Y, Z) => U242(X, Y, Z) U242(X, mark(Y), Z) => U242(X, Y, Z) U242(X, Y, mark(Z)) => U242(X, Y, Z) U242(active(X), Y, Z) => U242(X, Y, Z) U242(X, active(Y), Z) => U242(X, Y, Z) U242(X, Y, active(Z)) => U242(X, Y, Z) U243(mark(X), Y, Z) => U243(X, Y, Z) U243(X, mark(Y), Z) => U243(X, Y, Z) U243(X, Y, mark(Z)) => U243(X, Y, Z) U243(active(X), Y, Z) => U243(X, Y, Z) U243(X, active(Y), Z) => U243(X, Y, Z) U243(X, Y, active(Z)) => U243(X, Y, Z) U244(mark(X), Y, Z) => U244(X, Y, Z) U244(X, mark(Y), Z) => U244(X, Y, Z) U244(X, Y, mark(Z)) => U244(X, Y, Z) U244(active(X), Y, Z) => U244(X, Y, Z) U244(X, active(Y), Z) => U244(X, Y, Z) U244(X, Y, active(Z)) => U244(X, Y, Z) U245(mark(X), Y) => U245(X, Y) U245(X, mark(Y)) => U245(X, Y) U245(active(X), Y) => U245(X, Y) U245(X, active(Y)) => U245(X, Y) U246(mark(X)) => U246(X) U246(active(X)) => U246(X) U251(mark(X), Y, Z) => U251(X, Y, Z) U251(X, mark(Y), Z) => U251(X, Y, Z) U251(X, Y, mark(Z)) => U251(X, Y, Z) U251(active(X), Y, Z) => U251(X, Y, Z) U251(X, active(Y), Z) => U251(X, Y, Z) U251(X, Y, active(Z)) => U251(X, Y, Z) U252(mark(X), Y, Z) => U252(X, Y, Z) U252(X, mark(Y), Z) => U252(X, Y, Z) U252(X, Y, mark(Z)) => U252(X, Y, Z) U252(active(X), Y, Z) => U252(X, Y, Z) U252(X, active(Y), Z) => U252(X, Y, Z) U252(X, Y, active(Z)) => U252(X, Y, Z) U253(mark(X), Y, Z) => U253(X, Y, Z) U253(X, mark(Y), Z) => U253(X, Y, Z) U253(X, Y, mark(Z)) => U253(X, Y, Z) U253(active(X), Y, Z) => U253(X, Y, Z) U253(X, active(Y), Z) => U253(X, Y, Z) U253(X, Y, active(Z)) => U253(X, Y, Z) U254(mark(X), Y, Z) => U254(X, Y, Z) U254(X, mark(Y), Z) => U254(X, Y, Z) U254(X, Y, mark(Z)) => U254(X, Y, Z) U254(active(X), Y, Z) => U254(X, Y, Z) U254(X, active(Y), Z) => U254(X, Y, Z) U254(X, Y, active(Z)) => U254(X, Y, Z) U255(mark(X), Y) => U255(X, Y) U255(X, mark(Y)) => U255(X, Y) U255(active(X), Y) => U255(X, Y) U255(X, active(Y)) => U255(X, Y) U256(mark(X)) => U256(X) U256(active(X)) => U256(X) U261(mark(X), Y) => U261(X, Y) U261(X, mark(Y)) => U261(X, Y) U261(active(X), Y) => U261(X, Y) U261(X, active(Y)) => U261(X, Y) U262(mark(X)) => U262(X) U262(active(X)) => U262(X) U271(mark(X), Y) => U271(X, Y) U271(X, mark(Y)) => U271(X, Y) U271(active(X), Y) => U271(X, Y) U271(X, active(Y)) => U271(X, Y) U272(mark(X)) => U272(X) U272(active(X)) => U272(X) U281(mark(X), Y) => U281(X, Y) U281(X, mark(Y)) => U281(X, Y) U281(active(X), Y) => U281(X, Y) U281(X, active(Y)) => U281(X, Y) U282(mark(X), Y) => U282(X, Y) U282(X, mark(Y)) => U282(X, Y) U282(active(X), Y) => U282(X, Y) U282(X, active(Y)) => U282(X, Y) cons(mark(X), Y) => cons(X, Y) cons(X, mark(Y)) => cons(X, Y) cons(active(X), Y) => cons(X, Y) cons(X, active(Y)) => cons(X, Y) natsFrom(mark(X)) => natsFrom(X) natsFrom(active(X)) => natsFrom(X) s(mark(X)) => s(X) s(active(X)) => s(X) U291(mark(X), Y, Z) => U291(X, Y, Z) U291(X, mark(Y), Z) => U291(X, Y, Z) U291(X, Y, mark(Z)) => U291(X, Y, Z) U291(active(X), Y, Z) => U291(X, Y, Z) U291(X, active(Y), Z) => U291(X, Y, Z) U291(X, Y, active(Z)) => U291(X, Y, Z) U292(mark(X), Y, Z) => U292(X, Y, Z) U292(X, mark(Y), Z) => U292(X, Y, Z) U292(X, Y, mark(Z)) => U292(X, Y, Z) U292(active(X), Y, Z) => U292(X, Y, Z) U292(X, active(Y), Z) => U292(X, Y, Z) U292(X, Y, active(Z)) => U292(X, Y, Z) U293(mark(X), Y, Z) => U293(X, Y, Z) U293(X, mark(Y), Z) => U293(X, Y, Z) U293(X, Y, mark(Z)) => U293(X, Y, Z) U293(active(X), Y, Z) => U293(X, Y, Z) U293(X, active(Y), Z) => U293(X, Y, Z) U293(X, Y, active(Z)) => U293(X, Y, Z) U294(mark(X), Y, Z) => U294(X, Y, Z) U294(X, mark(Y), Z) => U294(X, Y, Z) U294(X, Y, mark(Z)) => U294(X, Y, Z) U294(active(X), Y, Z) => U294(X, Y, Z) U294(X, active(Y), Z) => U294(X, Y, Z) U294(X, Y, active(Z)) => U294(X, Y, Z) head(mark(X)) => head(X) head(active(X)) => head(X) afterNth(mark(X), Y) => afterNth(X, Y) afterNth(X, mark(Y)) => afterNth(X, Y) afterNth(active(X), Y) => afterNth(X, Y) afterNth(X, active(Y)) => afterNth(X, Y) U301(mark(X), Y, Z) => U301(X, Y, Z) U301(X, mark(Y), Z) => U301(X, Y, Z) U301(X, Y, mark(Z)) => U301(X, Y, Z) U301(active(X), Y, Z) => U301(X, Y, Z) U301(X, active(Y), Z) => U301(X, Y, Z) U301(X, Y, active(Z)) => U301(X, Y, Z) U302(mark(X), Y) => U302(X, Y) U302(X, mark(Y)) => U302(X, Y) U302(active(X), Y) => U302(X, Y) U302(X, active(Y)) => U302(X, Y) U303(mark(X), Y) => U303(X, Y) U303(X, mark(Y)) => U303(X, Y) U303(active(X), Y) => U303(X, Y) U303(X, active(Y)) => U303(X, Y) U304(mark(X), Y) => U304(X, Y) U304(X, mark(Y)) => U304(X, Y) U304(active(X), Y) => U304(X, Y) U304(X, active(Y)) => U304(X, Y) U31(mark(X), Y, Z) => U31(X, Y, Z) U31(X, mark(Y), Z) => U31(X, Y, Z) U31(X, Y, mark(Z)) => U31(X, Y, Z) U31(active(X), Y, Z) => U31(X, Y, Z) U31(X, active(Y), Z) => U31(X, Y, Z) U31(X, Y, active(Z)) => U31(X, Y, Z) U32(mark(X), Y, Z) => U32(X, Y, Z) U32(X, mark(Y), Z) => U32(X, Y, Z) U32(X, Y, mark(Z)) => U32(X, Y, Z) U32(active(X), Y, Z) => U32(X, Y, Z) U32(X, active(Y), Z) => U32(X, Y, Z) U32(X, Y, active(Z)) => U32(X, Y, Z) U311(mark(X), Y) => U311(X, Y) U311(X, mark(Y)) => U311(X, Y) U311(active(X), Y) => U311(X, Y) U311(X, active(Y)) => U311(X, Y) U312(mark(X), Y) => U312(X, Y) U312(X, mark(Y)) => U312(X, Y) U312(active(X), Y) => U312(X, Y) U312(X, active(Y)) => U312(X, Y) pair(mark(X), Y) => pair(X, Y) pair(X, mark(Y)) => pair(X, Y) pair(active(X), Y) => pair(X, Y) pair(X, active(Y)) => pair(X, Y) U33(mark(X), Y, Z) => U33(X, Y, Z) U33(X, mark(Y), Z) => U33(X, Y, Z) U33(X, Y, mark(Z)) => U33(X, Y, Z) U33(active(X), Y, Z) => U33(X, Y, Z) U33(X, active(Y), Z) => U33(X, Y, Z) U33(X, Y, active(Z)) => U33(X, Y, Z) U321(mark(X), Y, Z, U) => U321(X, Y, Z, U) U321(X, mark(Y), Z, U) => U321(X, Y, Z, U) U321(X, Y, mark(Z), U) => U321(X, Y, Z, U) U321(X, Y, Z, mark(U)) => U321(X, Y, Z, U) U321(active(X), Y, Z, U) => U321(X, Y, Z, U) U321(X, active(Y), Z, U) => U321(X, Y, Z, U) U321(X, Y, active(Z), U) => U321(X, Y, Z, U) U321(X, Y, Z, active(U)) => U321(X, Y, Z, U) U322(mark(X), Y, Z, U) => U322(X, Y, Z, U) U322(X, mark(Y), Z, U) => U322(X, Y, Z, U) U322(X, Y, mark(Z), U) => U322(X, Y, Z, U) U322(X, Y, Z, mark(U)) => U322(X, Y, Z, U) U322(active(X), Y, Z, U) => U322(X, Y, Z, U) U322(X, active(Y), Z, U) => U322(X, Y, Z, U) U322(X, Y, active(Z), U) => U322(X, Y, Z, U) U322(X, Y, Z, active(U)) => U322(X, Y, Z, U) U323(mark(X), Y, Z, U) => U323(X, Y, Z, U) U323(X, mark(Y), Z, U) => U323(X, Y, Z, U) U323(X, Y, mark(Z), U) => U323(X, Y, Z, U) U323(X, Y, Z, mark(U)) => U323(X, Y, Z, U) U323(active(X), Y, Z, U) => U323(X, Y, Z, U) U323(X, active(Y), Z, U) => U323(X, Y, Z, U) U323(X, Y, active(Z), U) => U323(X, Y, Z, U) U323(X, Y, Z, active(U)) => U323(X, Y, Z, U) U324(mark(X), Y, Z, U) => U324(X, Y, Z, U) U324(X, mark(Y), Z, U) => U324(X, Y, Z, U) U324(X, Y, mark(Z), U) => U324(X, Y, Z, U) U324(X, Y, Z, mark(U)) => U324(X, Y, Z, U) U324(active(X), Y, Z, U) => U324(X, Y, Z, U) U324(X, active(Y), Z, U) => U324(X, Y, Z, U) U324(X, Y, active(Z), U) => U324(X, Y, Z, U) U324(X, Y, Z, active(U)) => U324(X, Y, Z, U) U325(mark(X), Y, Z, U) => U325(X, Y, Z, U) U325(X, mark(Y), Z, U) => U325(X, Y, Z, U) U325(X, Y, mark(Z), U) => U325(X, Y, Z, U) U325(X, Y, Z, mark(U)) => U325(X, Y, Z, U) U325(active(X), Y, Z, U) => U325(X, Y, Z, U) U325(X, active(Y), Z, U) => U325(X, Y, Z, U) U325(X, Y, active(Z), U) => U325(X, Y, Z, U) U325(X, Y, Z, active(U)) => U325(X, Y, Z, U) U326(mark(X), Y, Z, U) => U326(X, Y, Z, U) U326(X, mark(Y), Z, U) => U326(X, Y, Z, U) U326(X, Y, mark(Z), U) => U326(X, Y, Z, U) U326(X, Y, Z, mark(U)) => U326(X, Y, Z, U) U326(active(X), Y, Z, U) => U326(X, Y, Z, U) U326(X, active(Y), Z, U) => U326(X, Y, Z, U) U326(X, Y, active(Z), U) => U326(X, Y, Z, U) U326(X, Y, Z, active(U)) => U326(X, Y, Z, U) U327(mark(X), Y) => U327(X, Y) U327(X, mark(Y)) => U327(X, Y) U327(active(X), Y) => U327(X, Y) U327(X, active(Y)) => U327(X, Y) U34(mark(X), Y) => U34(X, Y) U34(X, mark(Y)) => U34(X, Y) U34(active(X), Y) => U34(X, Y) U34(X, active(Y)) => U34(X, Y) U331(mark(X), Y, Z) => U331(X, Y, Z) U331(X, mark(Y), Z) => U331(X, Y, Z) U331(X, Y, mark(Z)) => U331(X, Y, Z) U331(active(X), Y, Z) => U331(X, Y, Z) U331(X, active(Y), Z) => U331(X, Y, Z) U331(X, Y, active(Z)) => U331(X, Y, Z) U332(mark(X), Y) => U332(X, Y) U332(X, mark(Y)) => U332(X, Y) U332(active(X), Y) => U332(X, Y) U332(X, active(Y)) => U332(X, Y) U333(mark(X), Y) => U333(X, Y) U333(X, mark(Y)) => U333(X, Y) U333(active(X), Y) => U333(X, Y) U333(X, active(Y)) => U333(X, Y) U334(mark(X), Y) => U334(X, Y) U334(X, mark(Y)) => U334(X, Y) U334(active(X), Y) => U334(X, Y) U334(X, active(Y)) => U334(X, Y) U341(mark(X), Y, Z) => U341(X, Y, Z) U341(X, mark(Y), Z) => U341(X, Y, Z) U341(X, Y, mark(Z)) => U341(X, Y, Z) U341(active(X), Y, Z) => U341(X, Y, Z) U341(X, active(Y), Z) => U341(X, Y, Z) U341(X, Y, active(Z)) => U341(X, Y, Z) U342(mark(X), Y, Z) => U342(X, Y, Z) U342(X, mark(Y), Z) => U342(X, Y, Z) U342(X, Y, mark(Z)) => U342(X, Y, Z) U342(active(X), Y, Z) => U342(X, Y, Z) U342(X, active(Y), Z) => U342(X, Y, Z) U342(X, Y, active(Z)) => U342(X, Y, Z) U343(mark(X), Y, Z) => U343(X, Y, Z) U343(X, mark(Y), Z) => U343(X, Y, Z) U343(X, Y, mark(Z)) => U343(X, Y, Z) U343(active(X), Y, Z) => U343(X, Y, Z) U343(X, active(Y), Z) => U343(X, Y, Z) U343(X, Y, active(Z)) => U343(X, Y, Z) U344(mark(X), Y, Z) => U344(X, Y, Z) U344(X, mark(Y), Z) => U344(X, Y, Z) U344(X, Y, mark(Z)) => U344(X, Y, Z) U344(active(X), Y, Z) => U344(X, Y, Z) U344(X, active(Y), Z) => U344(X, Y, Z) U344(X, Y, active(Z)) => U344(X, Y, Z) fst(mark(X)) => fst(X) fst(active(X)) => fst(X) U41(mark(X), Y, Z) => U41(X, Y, Z) U41(X, mark(Y), Z) => U41(X, Y, Z) U41(X, Y, mark(Z)) => U41(X, Y, Z) U41(active(X), Y, Z) => U41(X, Y, Z) U41(X, active(Y), Z) => U41(X, Y, Z) U41(X, Y, active(Z)) => U41(X, Y, Z) U42(mark(X), Y, Z) => U42(X, Y, Z) U42(X, mark(Y), Z) => U42(X, Y, Z) U42(X, Y, mark(Z)) => U42(X, Y, Z) U42(active(X), Y, Z) => U42(X, Y, Z) U42(X, active(Y), Z) => U42(X, Y, Z) U42(X, Y, active(Z)) => U42(X, Y, Z) U43(mark(X), Y, Z) => U43(X, Y, Z) U43(X, mark(Y), Z) => U43(X, Y, Z) U43(X, Y, mark(Z)) => U43(X, Y, Z) U43(active(X), Y, Z) => U43(X, Y, Z) U43(X, active(Y), Z) => U43(X, Y, Z) U43(X, Y, active(Z)) => U43(X, Y, Z) U44(mark(X), Y, Z) => U44(X, Y, Z) U44(X, mark(Y), Z) => U44(X, Y, Z) U44(X, Y, mark(Z)) => U44(X, Y, Z) U44(active(X), Y, Z) => U44(X, Y, Z) U44(X, active(Y), Z) => U44(X, Y, Z) U44(X, Y, active(Z)) => U44(X, Y, Z) U45(mark(X), Y) => U45(X, Y) U45(X, mark(Y)) => U45(X, Y) U45(active(X), Y) => U45(X, Y) U45(X, active(Y)) => U45(X, Y) U46(mark(X)) => U46(X) U46(active(X)) => U46(X) U51(mark(X), Y, Z) => U51(X, Y, Z) U51(X, mark(Y), Z) => U51(X, Y, Z) U51(X, Y, mark(Z)) => U51(X, Y, Z) U51(active(X), Y, Z) => U51(X, Y, Z) U51(X, active(Y), Z) => U51(X, Y, Z) U51(X, Y, active(Z)) => U51(X, Y, Z) U52(mark(X), Y, Z) => U52(X, Y, Z) U52(X, mark(Y), Z) => U52(X, Y, Z) U52(X, Y, mark(Z)) => U52(X, Y, Z) U52(active(X), Y, Z) => U52(X, Y, Z) U52(X, active(Y), Z) => U52(X, Y, Z) U52(X, Y, active(Z)) => U52(X, Y, Z) U53(mark(X), Y, Z) => U53(X, Y, Z) U53(X, mark(Y), Z) => U53(X, Y, Z) U53(X, Y, mark(Z)) => U53(X, Y, Z) U53(active(X), Y, Z) => U53(X, Y, Z) U53(X, active(Y), Z) => U53(X, Y, Z) U53(X, Y, active(Z)) => U53(X, Y, Z) U54(mark(X), Y, Z) => U54(X, Y, Z) U54(X, mark(Y), Z) => U54(X, Y, Z) U54(X, Y, mark(Z)) => U54(X, Y, Z) U54(active(X), Y, Z) => U54(X, Y, Z) U54(X, active(Y), Z) => U54(X, Y, Z) U54(X, Y, active(Z)) => U54(X, Y, Z) U55(mark(X), Y) => U55(X, Y) U55(X, mark(Y)) => U55(X, Y) U55(active(X), Y) => U55(X, Y) U55(X, active(Y)) => U55(X, Y) U56(mark(X)) => U56(X) U56(active(X)) => U56(X) U61(mark(X), Y) => U61(X, Y) U61(X, mark(Y)) => U61(X, Y) U61(active(X), Y) => U61(X, Y) U61(X, active(Y)) => U61(X, Y) U62(mark(X), Y) => U62(X, Y) U62(X, mark(Y)) => U62(X, Y) U62(active(X), Y) => U62(X, Y) U62(X, active(Y)) => U62(X, Y) isPLNatKind(mark(X)) => isPLNatKind(X) isPLNatKind(active(X)) => isPLNatKind(X) U63(mark(X)) => U63(X) U63(active(X)) => U63(X) isPLNat(mark(X)) => isPLNat(X) isPLNat(active(X)) => isPLNat(X) U71(mark(X), Y) => U71(X, Y) U71(X, mark(Y)) => U71(X, Y) U71(active(X), Y) => U71(X, Y) U71(X, active(Y)) => U71(X, Y) U72(mark(X), Y) => U72(X, Y) U72(X, mark(Y)) => U72(X, Y) U72(active(X), Y) => U72(X, Y) U72(X, active(Y)) => U72(X, Y) U73(mark(X)) => U73(X) U73(active(X)) => U73(X) U81(mark(X), Y) => U81(X, Y) U81(X, mark(Y)) => U81(X, Y) U81(active(X), Y) => U81(X, Y) U81(X, active(Y)) => U81(X, Y) U82(mark(X), Y) => U82(X, Y) U82(X, mark(Y)) => U82(X, Y) U82(active(X), Y) => U82(X, Y) U82(X, active(Y)) => U82(X, Y) U83(mark(X)) => U83(X) U83(active(X)) => U83(X) U91(mark(X), Y) => U91(X, Y) U91(X, mark(Y)) => U91(X, Y) U91(active(X), Y) => U91(X, Y) U91(X, active(Y)) => U91(X, Y) U92(mark(X), Y) => U92(X, Y) U92(X, mark(Y)) => U92(X, Y) U92(active(X), Y) => U92(X, Y) U92(X, active(Y)) => U92(X, Y) U93(mark(X)) => U93(X) U93(active(X)) => U93(X) tail(mark(X)) => tail(X) tail(active(X)) => tail(X) take(mark(X), Y) => take(X, Y) take(X, mark(Y)) => take(X, Y) take(active(X), Y) => take(X, Y) take(X, active(Y)) => take(X, Y) sel(mark(X), Y) => sel(X, Y) sel(X, mark(Y)) => sel(X, Y) sel(active(X), Y) => sel(X, Y) sel(X, active(Y)) => sel(X, Y)