/export/starexec/sandbox2/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/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 ok : [o] --> o pair : [o * o] --> o proper : [o] --> o s : [o] --> o sel : [o * o] --> o snd : [o] --> o splitAt : [o * o] --> o tail : [o] --> o take : [o * o] --> o top : [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)) active(U101(X, Y, Z)) => U101(active(X), Y, Z) active(U102(X, Y, Z)) => U102(active(X), Y, Z) active(U103(X, Y, Z)) => U103(active(X), Y, Z) active(U104(X, Y, Z)) => U104(active(X), Y, Z) active(U105(X, Y)) => U105(active(X), Y) active(U106(X)) => U106(active(X)) active(U11(X, Y, Z)) => U11(active(X), Y, Z) active(U12(X, Y, Z)) => U12(active(X), Y, Z) active(U111(X, Y)) => U111(active(X), Y) active(U112(X)) => U112(active(X)) active(U13(X, Y, Z)) => U13(active(X), Y, Z) active(U121(X, Y)) => U121(active(X), Y) active(U122(X)) => U122(active(X)) active(U14(X, Y, Z)) => U14(active(X), Y, Z) active(U131(X)) => U131(active(X)) active(snd(X)) => snd(active(X)) active(splitAt(X, Y)) => splitAt(active(X), Y) active(splitAt(X, Y)) => splitAt(X, active(Y)) active(U141(X)) => U141(active(X)) active(U151(X)) => U151(active(X)) active(U161(X)) => U161(active(X)) active(U171(X, Y)) => U171(active(X), Y) active(U172(X)) => U172(active(X)) active(U181(X, Y)) => U181(active(X), Y) active(U182(X, Y)) => U182(active(X), Y) active(U183(X)) => U183(active(X)) active(U191(X, Y)) => U191(active(X), Y) active(U192(X, Y)) => U192(active(X), Y) active(U193(X)) => U193(active(X)) active(U201(X, Y, Z)) => U201(active(X), Y, Z) active(U202(X, Y, Z)) => U202(active(X), Y, Z) active(U203(X, Y, Z)) => U203(active(X), Y, Z) active(U204(X, Y, Z)) => U204(active(X), Y, Z) active(U205(X, Y)) => U205(active(X), Y) active(U206(X)) => U206(active(X)) active(U21(X, Y, Z)) => U21(active(X), Y, Z) active(U22(X, Y, Z)) => U22(active(X), Y, Z) active(U211(X)) => U211(active(X)) active(U23(X, Y, Z)) => U23(active(X), Y, Z) active(U221(X)) => U221(active(X)) active(U24(X, Y)) => U24(active(X), Y) active(U231(X, Y)) => U231(active(X), Y) active(U232(X)) => U232(active(X)) active(U241(X, Y, Z)) => U241(active(X), Y, Z) active(U242(X, Y, Z)) => U242(active(X), Y, Z) active(U243(X, Y, Z)) => U243(active(X), Y, Z) active(U244(X, Y, Z)) => U244(active(X), Y, Z) active(U245(X, Y)) => U245(active(X), Y) active(U246(X)) => U246(active(X)) active(U251(X, Y, Z)) => U251(active(X), Y, Z) active(U252(X, Y, Z)) => U252(active(X), Y, Z) active(U253(X, Y, Z)) => U253(active(X), Y, Z) active(U254(X, Y, Z)) => U254(active(X), Y, Z) active(U255(X, Y)) => U255(active(X), Y) active(U256(X)) => U256(active(X)) active(U261(X, Y)) => U261(active(X), Y) active(U262(X)) => U262(active(X)) active(U271(X, Y)) => U271(active(X), Y) active(U272(X)) => U272(active(X)) active(U281(X, Y)) => U281(active(X), Y) active(U282(X, Y)) => U282(active(X), Y) active(cons(X, Y)) => cons(active(X), Y) active(natsFrom(X)) => natsFrom(active(X)) active(s(X)) => s(active(X)) active(U291(X, Y, Z)) => U291(active(X), Y, Z) active(U292(X, Y, Z)) => U292(active(X), Y, Z) active(U293(X, Y, Z)) => U293(active(X), Y, Z) active(U294(X, Y, Z)) => U294(active(X), Y, Z) active(head(X)) => head(active(X)) active(afterNth(X, Y)) => afterNth(active(X), Y) active(afterNth(X, Y)) => afterNth(X, active(Y)) active(U301(X, Y, Z)) => U301(active(X), Y, Z) active(U302(X, Y)) => U302(active(X), Y) active(U303(X, Y)) => U303(active(X), Y) active(U304(X, Y)) => U304(active(X), Y) active(U31(X, Y, Z)) => U31(active(X), Y, Z) active(U32(X, Y, Z)) => U32(active(X), Y, Z) active(U311(X, Y)) => U311(active(X), Y) active(U312(X, Y)) => U312(active(X), Y) active(pair(X, Y)) => pair(active(X), Y) active(pair(X, Y)) => pair(X, active(Y)) active(U33(X, Y, Z)) => U33(active(X), Y, Z) active(U321(X, Y, Z, U)) => U321(active(X), Y, Z, U) active(U322(X, Y, Z, U)) => U322(active(X), Y, Z, U) active(U323(X, Y, Z, U)) => U323(active(X), Y, Z, U) active(U324(X, Y, Z, U)) => U324(active(X), Y, Z, U) active(U325(X, Y, Z, U)) => U325(active(X), Y, Z, U) active(U326(X, Y, Z, U)) => U326(active(X), Y, Z, U) active(U327(X, Y)) => U327(active(X), Y) active(U34(X, Y)) => U34(active(X), Y) active(U331(X, Y, Z)) => U331(active(X), Y, Z) active(U332(X, Y)) => U332(active(X), Y) active(U333(X, Y)) => U333(active(X), Y) active(U334(X, Y)) => U334(active(X), Y) active(U341(X, Y, Z)) => U341(active(X), Y, Z) active(U342(X, Y, Z)) => U342(active(X), Y, Z) active(U343(X, Y, Z)) => U343(active(X), Y, Z) active(U344(X, Y, Z)) => U344(active(X), Y, Z) active(fst(X)) => fst(active(X)) active(U41(X, Y, Z)) => U41(active(X), Y, Z) active(U42(X, Y, Z)) => U42(active(X), Y, Z) active(U43(X, Y, Z)) => U43(active(X), Y, Z) active(U44(X, Y, Z)) => U44(active(X), Y, Z) active(U45(X, Y)) => U45(active(X), Y) active(U46(X)) => U46(active(X)) active(U51(X, Y, Z)) => U51(active(X), Y, Z) active(U52(X, Y, Z)) => U52(active(X), Y, Z) active(U53(X, Y, Z)) => U53(active(X), Y, Z) active(U54(X, Y, Z)) => U54(active(X), Y, Z) active(U55(X, Y)) => U55(active(X), Y) active(U56(X)) => U56(active(X)) active(U61(X, Y)) => U61(active(X), Y) active(U62(X, Y)) => U62(active(X), Y) active(U63(X)) => U63(active(X)) active(U71(X, Y)) => U71(active(X), Y) active(U72(X, Y)) => U72(active(X), Y) active(U73(X)) => U73(active(X)) active(U81(X, Y)) => U81(active(X), Y) active(U82(X, Y)) => U82(active(X), Y) active(U83(X)) => U83(active(X)) active(U91(X, Y)) => U91(active(X), Y) active(U92(X, Y)) => U92(active(X), Y) active(U93(X)) => U93(active(X)) active(tail(X)) => tail(active(X)) active(take(X, Y)) => take(active(X), Y) active(take(X, Y)) => take(X, active(Y)) active(sel(X, Y)) => sel(active(X), Y) active(sel(X, Y)) => sel(X, active(Y)) U101(mark(X), Y, Z) => mark(U101(X, Y, Z)) U102(mark(X), Y, Z) => mark(U102(X, Y, Z)) U103(mark(X), Y, Z) => mark(U103(X, Y, Z)) U104(mark(X), Y, Z) => mark(U104(X, Y, Z)) U105(mark(X), Y) => mark(U105(X, Y)) U106(mark(X)) => mark(U106(X)) U11(mark(X), Y, Z) => mark(U11(X, Y, Z)) U12(mark(X), Y, Z) => mark(U12(X, Y, Z)) U111(mark(X), Y) => mark(U111(X, Y)) U112(mark(X)) => mark(U112(X)) U13(mark(X), Y, Z) => mark(U13(X, Y, Z)) U121(mark(X), Y) => mark(U121(X, Y)) U122(mark(X)) => mark(U122(X)) U14(mark(X), Y, Z) => mark(U14(X, Y, Z)) U131(mark(X)) => mark(U131(X)) snd(mark(X)) => mark(snd(X)) splitAt(mark(X), Y) => mark(splitAt(X, Y)) splitAt(X, mark(Y)) => mark(splitAt(X, Y)) U141(mark(X)) => mark(U141(X)) U151(mark(X)) => mark(U151(X)) U161(mark(X)) => mark(U161(X)) U171(mark(X), Y) => mark(U171(X, Y)) U172(mark(X)) => mark(U172(X)) U181(mark(X), Y) => mark(U181(X, Y)) U182(mark(X), Y) => mark(U182(X, Y)) U183(mark(X)) => mark(U183(X)) U191(mark(X), Y) => mark(U191(X, Y)) U192(mark(X), Y) => mark(U192(X, Y)) U193(mark(X)) => mark(U193(X)) U201(mark(X), Y, Z) => mark(U201(X, Y, Z)) U202(mark(X), Y, Z) => mark(U202(X, Y, Z)) U203(mark(X), Y, Z) => mark(U203(X, Y, Z)) U204(mark(X), Y, Z) => mark(U204(X, Y, Z)) U205(mark(X), Y) => mark(U205(X, Y)) U206(mark(X)) => mark(U206(X)) U21(mark(X), Y, Z) => mark(U21(X, Y, Z)) U22(mark(X), Y, Z) => mark(U22(X, Y, Z)) U211(mark(X)) => mark(U211(X)) U23(mark(X), Y, Z) => mark(U23(X, Y, Z)) U221(mark(X)) => mark(U221(X)) U24(mark(X), Y) => mark(U24(X, Y)) U231(mark(X), Y) => mark(U231(X, Y)) U232(mark(X)) => mark(U232(X)) U241(mark(X), Y, Z) => mark(U241(X, Y, Z)) U242(mark(X), Y, Z) => mark(U242(X, Y, Z)) U243(mark(X), Y, Z) => mark(U243(X, Y, Z)) U244(mark(X), Y, Z) => mark(U244(X, Y, Z)) U245(mark(X), Y) => mark(U245(X, Y)) U246(mark(X)) => mark(U246(X)) U251(mark(X), Y, Z) => mark(U251(X, Y, Z)) U252(mark(X), Y, Z) => mark(U252(X, Y, Z)) U253(mark(X), Y, Z) => mark(U253(X, Y, Z)) U254(mark(X), Y, Z) => mark(U254(X, Y, Z)) U255(mark(X), Y) => mark(U255(X, Y)) U256(mark(X)) => mark(U256(X)) U261(mark(X), Y) => mark(U261(X, Y)) U262(mark(X)) => mark(U262(X)) U271(mark(X), Y) => mark(U271(X, Y)) U272(mark(X)) => mark(U272(X)) U281(mark(X), Y) => mark(U281(X, Y)) U282(mark(X), Y) => mark(U282(X, Y)) cons(mark(X), Y) => mark(cons(X, Y)) natsFrom(mark(X)) => mark(natsFrom(X)) s(mark(X)) => mark(s(X)) U291(mark(X), Y, Z) => mark(U291(X, Y, Z)) U292(mark(X), Y, Z) => mark(U292(X, Y, Z)) U293(mark(X), Y, Z) => mark(U293(X, Y, Z)) U294(mark(X), Y, Z) => mark(U294(X, Y, Z)) head(mark(X)) => mark(head(X)) afterNth(mark(X), Y) => mark(afterNth(X, Y)) afterNth(X, mark(Y)) => mark(afterNth(X, Y)) U301(mark(X), Y, Z) => mark(U301(X, Y, Z)) U302(mark(X), Y) => mark(U302(X, Y)) U303(mark(X), Y) => mark(U303(X, Y)) U304(mark(X), Y) => mark(U304(X, Y)) U31(mark(X), Y, Z) => mark(U31(X, Y, Z)) U32(mark(X), Y, Z) => mark(U32(X, Y, Z)) U311(mark(X), Y) => mark(U311(X, Y)) U312(mark(X), Y) => mark(U312(X, Y)) pair(mark(X), Y) => mark(pair(X, Y)) pair(X, mark(Y)) => mark(pair(X, Y)) U33(mark(X), Y, Z) => mark(U33(X, Y, Z)) U321(mark(X), Y, Z, U) => mark(U321(X, Y, Z, U)) U322(mark(X), Y, Z, U) => mark(U322(X, Y, Z, U)) U323(mark(X), Y, Z, U) => mark(U323(X, Y, Z, U)) U324(mark(X), Y, Z, U) => mark(U324(X, Y, Z, U)) U325(mark(X), Y, Z, U) => mark(U325(X, Y, Z, U)) U326(mark(X), Y, Z, U) => mark(U326(X, Y, Z, U)) U327(mark(X), Y) => mark(U327(X, Y)) U34(mark(X), Y) => mark(U34(X, Y)) U331(mark(X), Y, Z) => mark(U331(X, Y, Z)) U332(mark(X), Y) => mark(U332(X, Y)) U333(mark(X), Y) => mark(U333(X, Y)) U334(mark(X), Y) => mark(U334(X, Y)) U341(mark(X), Y, Z) => mark(U341(X, Y, Z)) U342(mark(X), Y, Z) => mark(U342(X, Y, Z)) U343(mark(X), Y, Z) => mark(U343(X, Y, Z)) U344(mark(X), Y, Z) => mark(U344(X, Y, Z)) fst(mark(X)) => mark(fst(X)) U41(mark(X), Y, Z) => mark(U41(X, Y, Z)) U42(mark(X), Y, Z) => mark(U42(X, Y, Z)) U43(mark(X), Y, Z) => mark(U43(X, Y, Z)) U44(mark(X), Y, Z) => mark(U44(X, Y, Z)) U45(mark(X), Y) => mark(U45(X, Y)) U46(mark(X)) => mark(U46(X)) U51(mark(X), Y, Z) => mark(U51(X, Y, Z)) U52(mark(X), Y, Z) => mark(U52(X, Y, Z)) U53(mark(X), Y, Z) => mark(U53(X, Y, Z)) U54(mark(X), Y, Z) => mark(U54(X, Y, Z)) U55(mark(X), Y) => mark(U55(X, Y)) U56(mark(X)) => mark(U56(X)) U61(mark(X), Y) => mark(U61(X, Y)) U62(mark(X), Y) => mark(U62(X, Y)) U63(mark(X)) => mark(U63(X)) U71(mark(X), Y) => mark(U71(X, Y)) U72(mark(X), Y) => mark(U72(X, Y)) U73(mark(X)) => mark(U73(X)) U81(mark(X), Y) => mark(U81(X, Y)) U82(mark(X), Y) => mark(U82(X, Y)) U83(mark(X)) => mark(U83(X)) U91(mark(X), Y) => mark(U91(X, Y)) U92(mark(X), Y) => mark(U92(X, Y)) U93(mark(X)) => mark(U93(X)) tail(mark(X)) => mark(tail(X)) take(mark(X), Y) => mark(take(X, Y)) take(X, mark(Y)) => mark(take(X, Y)) sel(mark(X), Y) => mark(sel(X, Y)) sel(X, mark(Y)) => mark(sel(X, Y)) proper(U101(X, Y, Z)) => U101(proper(X), proper(Y), proper(Z)) proper(tt) => ok(tt) proper(U102(X, Y, Z)) => U102(proper(X), proper(Y), proper(Z)) proper(isNaturalKind(X)) => isNaturalKind(proper(X)) proper(U103(X, Y, Z)) => U103(proper(X), proper(Y), proper(Z)) proper(isLNatKind(X)) => isLNatKind(proper(X)) proper(U104(X, Y, Z)) => U104(proper(X), proper(Y), proper(Z)) proper(U105(X, Y)) => U105(proper(X), proper(Y)) proper(isNatural(X)) => isNatural(proper(X)) proper(U106(X)) => U106(proper(X)) proper(isLNat(X)) => isLNat(proper(X)) proper(U11(X, Y, Z)) => U11(proper(X), proper(Y), proper(Z)) proper(U12(X, Y, Z)) => U12(proper(X), proper(Y), proper(Z)) proper(U111(X, Y)) => U111(proper(X), proper(Y)) proper(U112(X)) => U112(proper(X)) proper(U13(X, Y, Z)) => U13(proper(X), proper(Y), proper(Z)) proper(U121(X, Y)) => U121(proper(X), proper(Y)) proper(U122(X)) => U122(proper(X)) proper(U14(X, Y, Z)) => U14(proper(X), proper(Y), proper(Z)) proper(U131(X)) => U131(proper(X)) proper(snd(X)) => snd(proper(X)) proper(splitAt(X, Y)) => splitAt(proper(X), proper(Y)) proper(U141(X)) => U141(proper(X)) proper(U151(X)) => U151(proper(X)) proper(U161(X)) => U161(proper(X)) proper(U171(X, Y)) => U171(proper(X), proper(Y)) proper(U172(X)) => U172(proper(X)) proper(U181(X, Y)) => U181(proper(X), proper(Y)) proper(U182(X, Y)) => U182(proper(X), proper(Y)) proper(U183(X)) => U183(proper(X)) proper(U191(X, Y)) => U191(proper(X), proper(Y)) proper(U192(X, Y)) => U192(proper(X), proper(Y)) proper(U193(X)) => U193(proper(X)) proper(U201(X, Y, Z)) => U201(proper(X), proper(Y), proper(Z)) proper(U202(X, Y, Z)) => U202(proper(X), proper(Y), proper(Z)) proper(U203(X, Y, Z)) => U203(proper(X), proper(Y), proper(Z)) proper(U204(X, Y, Z)) => U204(proper(X), proper(Y), proper(Z)) proper(U205(X, Y)) => U205(proper(X), proper(Y)) proper(U206(X)) => U206(proper(X)) proper(U21(X, Y, Z)) => U21(proper(X), proper(Y), proper(Z)) proper(U22(X, Y, Z)) => U22(proper(X), proper(Y), proper(Z)) proper(U211(X)) => U211(proper(X)) proper(U23(X, Y, Z)) => U23(proper(X), proper(Y), proper(Z)) proper(U221(X)) => U221(proper(X)) proper(U24(X, Y)) => U24(proper(X), proper(Y)) proper(U231(X, Y)) => U231(proper(X), proper(Y)) proper(U232(X)) => U232(proper(X)) proper(U241(X, Y, Z)) => U241(proper(X), proper(Y), proper(Z)) proper(U242(X, Y, Z)) => U242(proper(X), proper(Y), proper(Z)) proper(U243(X, Y, Z)) => U243(proper(X), proper(Y), proper(Z)) proper(U244(X, Y, Z)) => U244(proper(X), proper(Y), proper(Z)) proper(U245(X, Y)) => U245(proper(X), proper(Y)) proper(U246(X)) => U246(proper(X)) proper(U251(X, Y, Z)) => U251(proper(X), proper(Y), proper(Z)) proper(U252(X, Y, Z)) => U252(proper(X), proper(Y), proper(Z)) proper(U253(X, Y, Z)) => U253(proper(X), proper(Y), proper(Z)) proper(U254(X, Y, Z)) => U254(proper(X), proper(Y), proper(Z)) proper(U255(X, Y)) => U255(proper(X), proper(Y)) proper(U256(X)) => U256(proper(X)) proper(U261(X, Y)) => U261(proper(X), proper(Y)) proper(U262(X)) => U262(proper(X)) proper(U271(X, Y)) => U271(proper(X), proper(Y)) proper(U272(X)) => U272(proper(X)) proper(U281(X, Y)) => U281(proper(X), proper(Y)) proper(U282(X, Y)) => U282(proper(X), proper(Y)) proper(cons(X, Y)) => cons(proper(X), proper(Y)) proper(natsFrom(X)) => natsFrom(proper(X)) proper(s(X)) => s(proper(X)) proper(U291(X, Y, Z)) => U291(proper(X), proper(Y), proper(Z)) proper(U292(X, Y, Z)) => U292(proper(X), proper(Y), proper(Z)) proper(U293(X, Y, Z)) => U293(proper(X), proper(Y), proper(Z)) proper(U294(X, Y, Z)) => U294(proper(X), proper(Y), proper(Z)) proper(head(X)) => head(proper(X)) proper(afterNth(X, Y)) => afterNth(proper(X), proper(Y)) proper(U301(X, Y, Z)) => U301(proper(X), proper(Y), proper(Z)) proper(U302(X, Y)) => U302(proper(X), proper(Y)) proper(U303(X, Y)) => U303(proper(X), proper(Y)) proper(U304(X, Y)) => U304(proper(X), proper(Y)) proper(U31(X, Y, Z)) => U31(proper(X), proper(Y), proper(Z)) proper(U32(X, Y, Z)) => U32(proper(X), proper(Y), proper(Z)) proper(U311(X, Y)) => U311(proper(X), proper(Y)) proper(U312(X, Y)) => U312(proper(X), proper(Y)) proper(pair(X, Y)) => pair(proper(X), proper(Y)) proper(nil) => ok(nil) proper(U33(X, Y, Z)) => U33(proper(X), proper(Y), proper(Z)) proper(U321(X, Y, Z, U)) => U321(proper(X), proper(Y), proper(Z), proper(U)) proper(U322(X, Y, Z, U)) => U322(proper(X), proper(Y), proper(Z), proper(U)) proper(U323(X, Y, Z, U)) => U323(proper(X), proper(Y), proper(Z), proper(U)) proper(U324(X, Y, Z, U)) => U324(proper(X), proper(Y), proper(Z), proper(U)) proper(U325(X, Y, Z, U)) => U325(proper(X), proper(Y), proper(Z), proper(U)) proper(U326(X, Y, Z, U)) => U326(proper(X), proper(Y), proper(Z), proper(U)) proper(U327(X, Y)) => U327(proper(X), proper(Y)) proper(U34(X, Y)) => U34(proper(X), proper(Y)) proper(U331(X, Y, Z)) => U331(proper(X), proper(Y), proper(Z)) proper(U332(X, Y)) => U332(proper(X), proper(Y)) proper(U333(X, Y)) => U333(proper(X), proper(Y)) proper(U334(X, Y)) => U334(proper(X), proper(Y)) proper(U341(X, Y, Z)) => U341(proper(X), proper(Y), proper(Z)) proper(U342(X, Y, Z)) => U342(proper(X), proper(Y), proper(Z)) proper(U343(X, Y, Z)) => U343(proper(X), proper(Y), proper(Z)) proper(U344(X, Y, Z)) => U344(proper(X), proper(Y), proper(Z)) proper(fst(X)) => fst(proper(X)) proper(U41(X, Y, Z)) => U41(proper(X), proper(Y), proper(Z)) proper(U42(X, Y, Z)) => U42(proper(X), proper(Y), proper(Z)) proper(U43(X, Y, Z)) => U43(proper(X), proper(Y), proper(Z)) proper(U44(X, Y, Z)) => U44(proper(X), proper(Y), proper(Z)) proper(U45(X, Y)) => U45(proper(X), proper(Y)) proper(U46(X)) => U46(proper(X)) proper(U51(X, Y, Z)) => U51(proper(X), proper(Y), proper(Z)) proper(U52(X, Y, Z)) => U52(proper(X), proper(Y), proper(Z)) proper(U53(X, Y, Z)) => U53(proper(X), proper(Y), proper(Z)) proper(U54(X, Y, Z)) => U54(proper(X), proper(Y), proper(Z)) proper(U55(X, Y)) => U55(proper(X), proper(Y)) proper(U56(X)) => U56(proper(X)) proper(U61(X, Y)) => U61(proper(X), proper(Y)) proper(U62(X, Y)) => U62(proper(X), proper(Y)) proper(isPLNatKind(X)) => isPLNatKind(proper(X)) proper(U63(X)) => U63(proper(X)) proper(isPLNat(X)) => isPLNat(proper(X)) proper(U71(X, Y)) => U71(proper(X), proper(Y)) proper(U72(X, Y)) => U72(proper(X), proper(Y)) proper(U73(X)) => U73(proper(X)) proper(U81(X, Y)) => U81(proper(X), proper(Y)) proper(U82(X, Y)) => U82(proper(X), proper(Y)) proper(U83(X)) => U83(proper(X)) proper(U91(X, Y)) => U91(proper(X), proper(Y)) proper(U92(X, Y)) => U92(proper(X), proper(Y)) proper(U93(X)) => U93(proper(X)) proper(tail(X)) => tail(proper(X)) proper(take(X, Y)) => take(proper(X), proper(Y)) proper(0) => ok(0) proper(sel(X, Y)) => sel(proper(X), proper(Y)) U101(ok(X), ok(Y), ok(Z)) => ok(U101(X, Y, Z)) U102(ok(X), ok(Y), ok(Z)) => ok(U102(X, Y, Z)) isNaturalKind(ok(X)) => ok(isNaturalKind(X)) U103(ok(X), ok(Y), ok(Z)) => ok(U103(X, Y, Z)) isLNatKind(ok(X)) => ok(isLNatKind(X)) U104(ok(X), ok(Y), ok(Z)) => ok(U104(X, Y, Z)) U105(ok(X), ok(Y)) => ok(U105(X, Y)) isNatural(ok(X)) => ok(isNatural(X)) U106(ok(X)) => ok(U106(X)) isLNat(ok(X)) => ok(isLNat(X)) U11(ok(X), ok(Y), ok(Z)) => ok(U11(X, Y, Z)) U12(ok(X), ok(Y), ok(Z)) => ok(U12(X, Y, Z)) U111(ok(X), ok(Y)) => ok(U111(X, Y)) U112(ok(X)) => ok(U112(X)) U13(ok(X), ok(Y), ok(Z)) => ok(U13(X, Y, Z)) U121(ok(X), ok(Y)) => ok(U121(X, Y)) U122(ok(X)) => ok(U122(X)) U14(ok(X), ok(Y), ok(Z)) => ok(U14(X, Y, Z)) U131(ok(X)) => ok(U131(X)) snd(ok(X)) => ok(snd(X)) splitAt(ok(X), ok(Y)) => ok(splitAt(X, Y)) U141(ok(X)) => ok(U141(X)) U151(ok(X)) => ok(U151(X)) U161(ok(X)) => ok(U161(X)) U171(ok(X), ok(Y)) => ok(U171(X, Y)) U172(ok(X)) => ok(U172(X)) U181(ok(X), ok(Y)) => ok(U181(X, Y)) U182(ok(X), ok(Y)) => ok(U182(X, Y)) U183(ok(X)) => ok(U183(X)) U191(ok(X), ok(Y)) => ok(U191(X, Y)) U192(ok(X), ok(Y)) => ok(U192(X, Y)) U193(ok(X)) => ok(U193(X)) U201(ok(X), ok(Y), ok(Z)) => ok(U201(X, Y, Z)) U202(ok(X), ok(Y), ok(Z)) => ok(U202(X, Y, Z)) U203(ok(X), ok(Y), ok(Z)) => ok(U203(X, Y, Z)) U204(ok(X), ok(Y), ok(Z)) => ok(U204(X, Y, Z)) U205(ok(X), ok(Y)) => ok(U205(X, Y)) U206(ok(X)) => ok(U206(X)) U21(ok(X), ok(Y), ok(Z)) => ok(U21(X, Y, Z)) U22(ok(X), ok(Y), ok(Z)) => ok(U22(X, Y, Z)) U211(ok(X)) => ok(U211(X)) U23(ok(X), ok(Y), ok(Z)) => ok(U23(X, Y, Z)) U221(ok(X)) => ok(U221(X)) U24(ok(X), ok(Y)) => ok(U24(X, Y)) U231(ok(X), ok(Y)) => ok(U231(X, Y)) U232(ok(X)) => ok(U232(X)) U241(ok(X), ok(Y), ok(Z)) => ok(U241(X, Y, Z)) U242(ok(X), ok(Y), ok(Z)) => ok(U242(X, Y, Z)) U243(ok(X), ok(Y), ok(Z)) => ok(U243(X, Y, Z)) U244(ok(X), ok(Y), ok(Z)) => ok(U244(X, Y, Z)) U245(ok(X), ok(Y)) => ok(U245(X, Y)) U246(ok(X)) => ok(U246(X)) U251(ok(X), ok(Y), ok(Z)) => ok(U251(X, Y, Z)) U252(ok(X), ok(Y), ok(Z)) => ok(U252(X, Y, Z)) U253(ok(X), ok(Y), ok(Z)) => ok(U253(X, Y, Z)) U254(ok(X), ok(Y), ok(Z)) => ok(U254(X, Y, Z)) U255(ok(X), ok(Y)) => ok(U255(X, Y)) U256(ok(X)) => ok(U256(X)) U261(ok(X), ok(Y)) => ok(U261(X, Y)) U262(ok(X)) => ok(U262(X)) U271(ok(X), ok(Y)) => ok(U271(X, Y)) U272(ok(X)) => ok(U272(X)) U281(ok(X), ok(Y)) => ok(U281(X, Y)) U282(ok(X), ok(Y)) => ok(U282(X, Y)) cons(ok(X), ok(Y)) => ok(cons(X, Y)) natsFrom(ok(X)) => ok(natsFrom(X)) s(ok(X)) => ok(s(X)) U291(ok(X), ok(Y), ok(Z)) => ok(U291(X, Y, Z)) U292(ok(X), ok(Y), ok(Z)) => ok(U292(X, Y, Z)) U293(ok(X), ok(Y), ok(Z)) => ok(U293(X, Y, Z)) U294(ok(X), ok(Y), ok(Z)) => ok(U294(X, Y, Z)) head(ok(X)) => ok(head(X)) afterNth(ok(X), ok(Y)) => ok(afterNth(X, Y)) U301(ok(X), ok(Y), ok(Z)) => ok(U301(X, Y, Z)) U302(ok(X), ok(Y)) => ok(U302(X, Y)) U303(ok(X), ok(Y)) => ok(U303(X, Y)) U304(ok(X), ok(Y)) => ok(U304(X, Y)) U31(ok(X), ok(Y), ok(Z)) => ok(U31(X, Y, Z)) U32(ok(X), ok(Y), ok(Z)) => ok(U32(X, Y, Z)) U311(ok(X), ok(Y)) => ok(U311(X, Y)) U312(ok(X), ok(Y)) => ok(U312(X, Y)) pair(ok(X), ok(Y)) => ok(pair(X, Y)) U33(ok(X), ok(Y), ok(Z)) => ok(U33(X, Y, Z)) U321(ok(X), ok(Y), ok(Z), ok(U)) => ok(U321(X, Y, Z, U)) U322(ok(X), ok(Y), ok(Z), ok(U)) => ok(U322(X, Y, Z, U)) U323(ok(X), ok(Y), ok(Z), ok(U)) => ok(U323(X, Y, Z, U)) U324(ok(X), ok(Y), ok(Z), ok(U)) => ok(U324(X, Y, Z, U)) U325(ok(X), ok(Y), ok(Z), ok(U)) => ok(U325(X, Y, Z, U)) U326(ok(X), ok(Y), ok(Z), ok(U)) => ok(U326(X, Y, Z, U)) U327(ok(X), ok(Y)) => ok(U327(X, Y)) U34(ok(X), ok(Y)) => ok(U34(X, Y)) U331(ok(X), ok(Y), ok(Z)) => ok(U331(X, Y, Z)) U332(ok(X), ok(Y)) => ok(U332(X, Y)) U333(ok(X), ok(Y)) => ok(U333(X, Y)) U334(ok(X), ok(Y)) => ok(U334(X, Y)) U341(ok(X), ok(Y), ok(Z)) => ok(U341(X, Y, Z)) U342(ok(X), ok(Y), ok(Z)) => ok(U342(X, Y, Z)) U343(ok(X), ok(Y), ok(Z)) => ok(U343(X, Y, Z)) U344(ok(X), ok(Y), ok(Z)) => ok(U344(X, Y, Z)) fst(ok(X)) => ok(fst(X)) U41(ok(X), ok(Y), ok(Z)) => ok(U41(X, Y, Z)) U42(ok(X), ok(Y), ok(Z)) => ok(U42(X, Y, Z)) U43(ok(X), ok(Y), ok(Z)) => ok(U43(X, Y, Z)) U44(ok(X), ok(Y), ok(Z)) => ok(U44(X, Y, Z)) U45(ok(X), ok(Y)) => ok(U45(X, Y)) U46(ok(X)) => ok(U46(X)) U51(ok(X), ok(Y), ok(Z)) => ok(U51(X, Y, Z)) U52(ok(X), ok(Y), ok(Z)) => ok(U52(X, Y, Z)) U53(ok(X), ok(Y), ok(Z)) => ok(U53(X, Y, Z)) U54(ok(X), ok(Y), ok(Z)) => ok(U54(X, Y, Z)) U55(ok(X), ok(Y)) => ok(U55(X, Y)) U56(ok(X)) => ok(U56(X)) U61(ok(X), ok(Y)) => ok(U61(X, Y)) U62(ok(X), ok(Y)) => ok(U62(X, Y)) isPLNatKind(ok(X)) => ok(isPLNatKind(X)) U63(ok(X)) => ok(U63(X)) isPLNat(ok(X)) => ok(isPLNat(X)) U71(ok(X), ok(Y)) => ok(U71(X, Y)) U72(ok(X), ok(Y)) => ok(U72(X, Y)) U73(ok(X)) => ok(U73(X)) U81(ok(X), ok(Y)) => ok(U81(X, Y)) U82(ok(X), ok(Y)) => ok(U82(X, Y)) U83(ok(X)) => ok(U83(X)) U91(ok(X), ok(Y)) => ok(U91(X, Y)) U92(ok(X), ok(Y)) => ok(U92(X, Y)) U93(ok(X)) => ok(U93(X)) tail(ok(X)) => ok(tail(X)) take(ok(X), ok(Y)) => ok(take(X, Y)) sel(ok(X), ok(Y)) => ok(sel(X, Y)) top(mark(X)) => top(proper(X)) top(ok(X)) => top(active(X))