- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] a__U101(tt,V1,V2) -> a__U102(a__isNatural(V1),V2) [2] a__U102(tt,V2) -> a__U103(a__isLNat(V2)) [3] a__U103(tt) -> tt [4] a__U11(tt,N,XS) -> a__snd(a__splitAt(mark(N),mark(XS))) [5] a__U111(tt,V1) -> a__U112(a__isLNat(V1)) [6] a__U112(tt) -> tt [7] a__U121(tt,V1) -> a__U122(a__isNatural(V1)) [8] a__U122(tt) -> tt [9] a__U131(tt,V1,V2) -> a__U132(a__isNatural(V1),V2) [10] a__U132(tt,V2) -> a__U133(a__isLNat(V2)) [11] a__U133(tt) -> tt [12] a__U141(tt,V1,V2) -> a__U142(a__isLNat(V1),V2) [13] a__U142(tt,V2) -> a__U143(a__isLNat(V2)) [14] a__U143(tt) -> tt [15] a__U151(tt,V1,V2) -> a__U152(a__isNatural(V1),V2) [16] a__U152(tt,V2) -> a__U153(a__isLNat(V2)) [17] a__U153(tt) -> tt [18] a__U161(tt,N) -> cons(mark(N),natsFrom(s(N))) [19] a__U171(tt,N,XS) -> a__head(a__afterNth(mark(N),mark(XS))) [20] a__U181(tt,Y) -> mark(Y) [21] a__U191(tt,XS) -> pair(nil,mark(XS)) [22] a__U201(tt,N,X,XS) -> a__U202(a__splitAt(mark(N),mark(XS)),X) [23] a__U202(pair(YS,ZS),X) -> pair(cons(mark(X),YS),mark(ZS)) [24] a__U21(tt,X) -> mark(X) [25] a__U211(tt,XS) -> mark(XS) [26] a__U221(tt,N,XS) -> a__fst(a__splitAt(mark(N),mark(XS))) [27] a__U31(tt,N) -> mark(N) [28] a__U41(tt,V1,V2) -> a__U42(a__isNatural(V1),V2) [29] a__U42(tt,V2) -> a__U43(a__isLNat(V2)) [30] a__U43(tt) -> tt [31] a__U51(tt,V1,V2) -> a__U52(a__isNatural(V1),V2) [32] a__U52(tt,V2) -> a__U53(a__isLNat(V2)) [33] a__U53(tt) -> tt [34] a__U61(tt,V1) -> a__U62(a__isPLNat(V1)) [35] a__U62(tt) -> tt [36] a__U71(tt,V1) -> a__U72(a__isNatural(V1)) [37] a__U72(tt) -> tt [38] a__U81(tt,V1) -> a__U82(a__isPLNat(V1)) [39] a__U82(tt) -> tt [40] a__U91(tt,V1) -> a__U92(a__isLNat(V1)) [41] a__U92(tt) -> tt [42] a__afterNth(N,XS) -> a__U11(a__and(a__and(a__isNatural(N),isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))),N,XS) [43] a__and(tt,X) -> mark(X) [44] a__fst(pair(X,Y)) -> a__U21(a__and(a__and(a__isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))), X) [45] a__head(cons(N,XS)) -> a__U31(a__and(a__and(a__isNatural(N),isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))),N) [46] a__isLNat(nil) -> tt [47] a__isLNat(afterNth(V1,V2)) -> a__U41(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2) [48] a__isLNat(cons(V1,V2)) -> a__U51(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2) [49] a__isLNat(fst(V1)) -> a__U61(a__isPLNatKind(V1),V1) [50] a__isLNat(natsFrom(V1)) -> a__U71(a__isNaturalKind(V1),V1) [51] a__isLNat(snd(V1)) -> a__U81(a__isPLNatKind(V1),V1) [52] a__isLNat(tail(V1)) -> a__U91(a__isLNatKind(V1),V1) [53] a__isLNat(take(V1,V2)) -> a__U101(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2) [54] a__isLNatKind(nil) -> tt [55] a__isLNatKind(afterNth(V1,V2)) -> a__and(a__isNaturalKind(V1),isLNatKind(V2)) [56] a__isLNatKind(cons(V1,V2)) -> a__and(a__isNaturalKind(V1),isLNatKind(V2)) [57] a__isLNatKind(fst(V1)) -> a__isPLNatKind(V1) [58] a__isLNatKind(natsFrom(V1)) -> a__isNaturalKind(V1) [59] a__isLNatKind(snd(V1)) -> a__isPLNatKind(V1) [60] a__isLNatKind(tail(V1)) -> a__isLNatKind(V1) [61] a__isLNatKind(take(V1,V2)) -> a__and(a__isNaturalKind(V1),isLNatKind(V2)) [62] a__isNatural(0) -> tt [63] a__isNatural(head(V1)) -> a__U111(a__isLNatKind(V1),V1) [64] a__isNatural(s(V1)) -> a__U121(a__isNaturalKind(V1),V1) [65] a__isNatural(sel(V1,V2)) -> a__U131(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2) [66] a__isNaturalKind(0) -> tt [67] a__isNaturalKind(head(V1)) -> a__isLNatKind(V1) [68] a__isNaturalKind(s(V1)) -> a__isNaturalKind(V1) [69] a__isNaturalKind(sel(V1,V2)) -> a__and(a__isNaturalKind(V1),isLNatKind(V2)) [70] a__isPLNat(pair(V1,V2)) -> a__U141(a__and(a__isLNatKind(V1),isLNatKind(V2)),V1,V2) [71] a__isPLNat(splitAt(V1,V2)) -> a__U151(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2) [72] a__isPLNatKind(pair(V1,V2)) -> a__and(a__isLNatKind(V1),isLNatKind(V2)) [73] a__isPLNatKind(splitAt(V1,V2)) -> a__and(a__isNaturalKind(V1),isLNatKind(V2)) [74] a__natsFrom(N) -> a__U161(a__and(a__isNatural(N),isNaturalKind(N)),N) [75] a__sel(N,XS) -> a__U171(a__and(a__and(a__isNatural(N),isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))),N,XS) [76] a__snd(pair(X,Y)) -> a__U181(a__and(a__and(a__isLNat(X),isLNatKind(X)), and(isLNat(Y),isLNatKind(Y))),Y) [77] a__splitAt(0,XS) -> a__U191(a__and(a__isLNat(XS),isLNatKind(XS)),XS) [78] a__splitAt(s(N),cons(X,XS)) -> a__U201(a__and(a__and(a__isNatural(N),isNaturalKind(N)), and(and(isNatural(X),isNaturalKind(X)), and(isLNat(XS),isLNatKind(XS)))),N,X,XS) [79] a__tail(cons(N,XS)) -> a__U211(a__and(a__and(a__isNatural(N),isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))),XS) [80] a__take(N,XS) -> a__U221(a__and(a__and(a__isNatural(N),isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))),N,XS) [81] mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) [82] mark(U102(X1,X2)) -> a__U102(mark(X1),X2) [83] mark(isNatural(X)) -> a__isNatural(X) [84] mark(U103(X)) -> a__U103(mark(X)) [85] mark(isLNat(X)) -> a__isLNat(X) [86] mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3) [87] mark(snd(X)) -> a__snd(mark(X)) [88] mark(splitAt(X1,X2)) -> a__splitAt(mark(X1),mark(X2)) [89] mark(U111(X1,X2)) -> a__U111(mark(X1),X2) [90] mark(U112(X)) -> a__U112(mark(X)) [91] mark(U121(X1,X2)) -> a__U121(mark(X1),X2) [92] mark(U122(X)) -> a__U122(mark(X)) [93] mark(U131(X1,X2,X3)) -> a__U131(mark(X1),X2,X3) [94] mark(U132(X1,X2)) -> a__U132(mark(X1),X2) [95] mark(U133(X)) -> a__U133(mark(X)) [96] mark(U141(X1,X2,X3)) -> a__U141(mark(X1),X2,X3) [97] mark(U142(X1,X2)) -> a__U142(mark(X1),X2) [98] mark(U143(X)) -> a__U143(mark(X)) [99] mark(U151(X1,X2,X3)) -> a__U151(mark(X1),X2,X3) [100] mark(U152(X1,X2)) -> a__U152(mark(X1),X2) [101] mark(U153(X)) -> a__U153(mark(X)) [102] mark(U161(X1,X2)) -> a__U161(mark(X1),X2) [103] mark(natsFrom(X)) -> a__natsFrom(mark(X)) [104] mark(U171(X1,X2,X3)) -> a__U171(mark(X1),X2,X3) [105] mark(head(X)) -> a__head(mark(X)) [106] mark(afterNth(X1,X2)) -> a__afterNth(mark(X1),mark(X2)) [107] mark(U181(X1,X2)) -> a__U181(mark(X1),X2) [108] mark(U191(X1,X2)) -> a__U191(mark(X1),X2) [109] mark(U201(X1,X2,X3,X4)) -> a__U201(mark(X1),X2,X3,X4) [110] mark(U202(X1,X2)) -> a__U202(mark(X1),X2) [111] mark(U21(X1,X2)) -> a__U21(mark(X1),X2) [112] mark(U211(X1,X2)) -> a__U211(mark(X1),X2) [113] mark(U221(X1,X2,X3)) -> a__U221(mark(X1),X2,X3) [114] mark(fst(X)) -> a__fst(mark(X)) [115] mark(U31(X1,X2)) -> a__U31(mark(X1),X2) [116] mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) [117] mark(U42(X1,X2)) -> a__U42(mark(X1),X2) [118] mark(U43(X)) -> a__U43(mark(X)) [119] mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) [120] mark(U52(X1,X2)) -> a__U52(mark(X1),X2) [121] mark(U53(X)) -> a__U53(mark(X)) [122] mark(U61(X1,X2)) -> a__U61(mark(X1),X2) [123] mark(U62(X)) -> a__U62(mark(X)) [124] mark(isPLNat(X)) -> a__isPLNat(X) [125] mark(U71(X1,X2)) -> a__U71(mark(X1),X2) [126] mark(U72(X)) -> a__U72(mark(X)) [127] mark(U81(X1,X2)) -> a__U81(mark(X1),X2) [128] mark(U82(X)) -> a__U82(mark(X)) [129] mark(U91(X1,X2)) -> a__U91(mark(X1),X2) [130] mark(U92(X)) -> a__U92(mark(X)) [131] mark(and(X1,X2)) -> a__and(mark(X1),X2) [132] mark(isNaturalKind(X)) -> a__isNaturalKind(X) [133] mark(isLNatKind(X)) -> a__isLNatKind(X) [134] mark(isPLNatKind(X)) -> a__isPLNatKind(X) [135] mark(tail(X)) -> a__tail(mark(X)) [136] mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) [137] mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2)) [138] mark(tt) -> tt [139] mark(cons(X1,X2)) -> cons(mark(X1),X2) [140] mark(s(X)) -> s(mark(X)) [141] mark(pair(X1,X2)) -> pair(mark(X1),mark(X2)) [142] mark(nil) -> nil [143] mark(0) -> 0 [144] a__U101(X1,X2,X3) -> U101(X1,X2,X3) [145] a__U102(X1,X2) -> U102(X1,X2) [146] a__isNatural(X) -> isNatural(X) [147] a__U103(X) -> U103(X) [148] a__isLNat(X) -> isLNat(X) [149] a__U11(X1,X2,X3) -> U11(X1,X2,X3) [150] a__snd(X) -> snd(X) [151] a__splitAt(X1,X2) -> splitAt(X1,X2) [152] a__U111(X1,X2) -> U111(X1,X2) [153] a__U112(X) -> U112(X) [154] a__U121(X1,X2) -> U121(X1,X2) [155] a__U122(X) -> U122(X) [156] a__U131(X1,X2,X3) -> U131(X1,X2,X3) [157] a__U132(X1,X2) -> U132(X1,X2) [158] a__U133(X) -> U133(X) [159] a__U141(X1,X2,X3) -> U141(X1,X2,X3) [160] a__U142(X1,X2) -> U142(X1,X2) [161] a__U143(X) -> U143(X) [162] a__U151(X1,X2,X3) -> U151(X1,X2,X3) [163] a__U152(X1,X2) -> U152(X1,X2) [164] a__U153(X) -> U153(X) [165] a__U161(X1,X2) -> U161(X1,X2) [166] a__natsFrom(X) -> natsFrom(X) [167] a__U171(X1,X2,X3) -> U171(X1,X2,X3) [168] a__head(X) -> head(X) [169] a__afterNth(X1,X2) -> afterNth(X1,X2) [170] a__U181(X1,X2) -> U181(X1,X2) [171] a__U191(X1,X2) -> U191(X1,X2) [172] a__U201(X1,X2,X3,X4) -> U201(X1,X2,X3,X4) [173] a__U202(X1,X2) -> U202(X1,X2) [174] a__U21(X1,X2) -> U21(X1,X2) [175] a__U211(X1,X2) -> U211(X1,X2) [176] a__U221(X1,X2,X3) -> U221(X1,X2,X3) [177] a__fst(X) -> fst(X) [178] a__U31(X1,X2) -> U31(X1,X2) [179] a__U41(X1,X2,X3) -> U41(X1,X2,X3) [180] a__U42(X1,X2) -> U42(X1,X2) [181] a__U43(X) -> U43(X) [182] a__U51(X1,X2,X3) -> U51(X1,X2,X3) [183] a__U52(X1,X2) -> U52(X1,X2) [184] a__U53(X) -> U53(X) [185] a__U61(X1,X2) -> U61(X1,X2) [186] a__U62(X) -> U62(X) [187] a__isPLNat(X) -> isPLNat(X) [188] a__U71(X1,X2) -> U71(X1,X2) [189] a__U72(X) -> U72(X) [190] a__U81(X1,X2) -> U81(X1,X2) [191] a__U82(X) -> U82(X) [192] a__U91(X1,X2) -> U91(X1,X2) [193] a__U92(X) -> U92(X) [194] a__and(X1,X2) -> and(X1,X2) [195] a__isNaturalKind(X) -> isNaturalKind(X) [196] a__isLNatKind(X) -> isLNatKind(X) [197] a__isPLNatKind(X) -> isPLNatKind(X) [198] a__tail(X) -> tail(X) [199] a__take(X1,X2) -> take(X1,X2) [200] a__sel(X1,X2) -> sel(X1,X2) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> 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--> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> 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mark(isLNatKind(X)) >= a__isLNatKind(X) ; mark(afterNth(X1,X2)) >= a__afterNth(mark(X1),mark(X2)) ; mark(fst(X)) >= a__fst(mark(X)) ; mark(snd(X)) >= a__snd(mark(X)) ; mark(tail(X)) >= a__tail(mark(X)) ; mark(take(X1,X2)) >= a__take(mark(X1),mark(X2)) ; mark(0) >= 0 ; mark(head(X)) >= a__head(mark(X)) ; mark(sel(X1,X2)) >= a__sel(mark(X1),mark(X2)) ; mark(splitAt(X1,X2)) >= a__splitAt(mark(X1),mark(X2)) ; mark(isNatural(X)) >= a__isNatural(X) ; mark(U101(X1,X2,X3)) >= a__U101(mark(X1),X2,X3) ; mark(U102(X1,X2)) >= a__U102(mark(X1),X2) ; mark(U103(X)) >= a__U103(mark(X)) ; mark(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) ; mark(U111(X1,X2)) >= a__U111(mark(X1),X2) ; mark(U112(X)) >= a__U112(mark(X)) ; mark(U121(X1,X2)) >= a__U121(mark(X1),X2) ; mark(U122(X)) >= a__U122(mark(X)) ; mark(U131(X1,X2,X3)) >= a__U131(mark(X1),X2,X3) ; mark(U132(X1,X2)) >= a__U132(mark(X1),X2) ; mark(U133(X)) >= a__U133(mark(X)) ; mark(U141(X1,X2,X3)) >= a__U141(mark(X1),X2,X3) ; mark(U142(X1,X2)) >= a__U142(mark(X1),X2) ; mark(U143(X)) >= a__U143(mark(X)) ; mark(U151(X1,X2,X3)) >= a__U151(mark(X1),X2,X3) ; mark(U152(X1,X2)) >= a__U152(mark(X1),X2) ; mark(U153(X)) >= a__U153(mark(X)) ; mark(U161(X1,X2)) >= a__U161(mark(X1),X2) ; mark(U171(X1,X2,X3)) >= a__U171(mark(X1),X2,X3) ; mark(U181(X1,X2)) >= a__U181(mark(X1),X2) ; mark(U191(X1,X2)) >= a__U191(mark(X1),X2) ; mark(U201(X1,X2,X3,X4)) >= a__U201(mark(X1),X2,X3,X4) ; mark(U202(X1,X2)) >= a__U202(mark(X1),X2) ; mark(U21(X1,X2)) >= a__U21(mark(X1),X2) ; mark(U211(X1,X2)) >= a__U211(mark(X1),X2) ; mark(U221(X1,X2,X3)) >= a__U221(mark(X1),X2,X3) ; mark(U31(X1,X2)) >= a__U31(mark(X1),X2) ; mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3) ; mark(U42(X1,X2)) >= a__U42(mark(X1),X2) ; mark(U43(X)) >= a__U43(mark(X)) ; mark(U51(X1,X2,X3)) >= a__U51(mark(X1),X2,X3) ; mark(U52(X1,X2)) >= a__U52(mark(X1),X2) ; mark(U53(X)) >= a__U53(mark(X)) ; mark(U61(X1,X2)) >= a__U61(mark(X1),X2) ; mark(U62(X)) >= a__U62(mark(X)) ; mark(isPLNat(X)) >= a__isPLNat(X) ; mark(U71(X1,X2)) >= a__U71(mark(X1),X2) ; mark(U72(X)) >= a__U72(mark(X)) ; mark(U81(X1,X2)) >= a__U81(mark(X1),X2) ; mark(U82(X)) >= a__U82(mark(X)) ; mark(U91(X1,X2)) >= a__U91(mark(X1),X2) ; mark(U92(X)) >= a__U92(mark(X)) ; mark(isPLNatKind(X)) >= a__isPLNatKind(X) ; a__U11(tt,N,XS) >= a__snd(a__splitAt(mark(N),mark(XS))) ; a__U11(X1,X2,X3) >= U11(X1,X2,X3) ; a__U112(tt) >= tt ; a__U112(X) >= U112(X) ; a__U111(tt,V1) >= a__U112(a__isLNat(V1)) ; a__U111(X1,X2) >= U111(X1,X2) ; a__U122(tt) >= tt ; a__U122(X) >= U122(X) ; a__U121(tt,V1) >= a__U122(a__isNatural(V1)) ; a__U121(X1,X2) >= U121(X1,X2) ; a__U132(tt,V2) >= a__U133(a__isLNat(V2)) ; a__U132(X1,X2) >= U132(X1,X2) ; a__U131(tt,V1,V2) >= a__U132(a__isNatural(V1),V2) ; a__U131(X1,X2,X3) >= U131(X1,X2,X3) ; a__U133(tt) >= tt ; a__U133(X) >= U133(X) ; a__U142(tt,V2) >= a__U143(a__isLNat(V2)) ; a__U142(X1,X2) >= U142(X1,X2) ; a__U141(tt,V1,V2) >= a__U142(a__isLNat(V1),V2) ; a__U141(X1,X2,X3) >= U141(X1,X2,X3) ; a__U143(tt) >= tt ; a__U143(X) >= U143(X) ; a__U152(tt,V2) >= a__U153(a__isLNat(V2)) ; a__U152(X1,X2) >= U152(X1,X2) ; a__U151(tt,V1,V2) >= a__U152(a__isNatural(V1),V2) ; a__U151(X1,X2,X3) >= U151(X1,X2,X3) ; a__U153(tt) >= tt ; a__U153(X) >= U153(X) ; a__U161(tt,N) >= cons(mark(N),natsFrom(s(N))) ; a__U161(X1,X2) >= U161(X1,X2) ; a__head(cons(N,XS)) >= a__U31(a__and(a__and(a__isNatural(N),isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))),N) ; a__head(X) >= head(X) ; a__afterNth(N,XS) >= a__U11(a__and(a__and(a__isNatural(N),isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))),N,XS) ; a__afterNth(X1,X2) >= afterNth(X1,X2) ; a__U171(tt,N,XS) >= a__head(a__afterNth(mark(N),mark(XS))) ; a__U171(X1,X2,X3) >= U171(X1,X2,X3) ; a__U181(tt,Y) >= mark(Y) ; a__U181(X1,X2) >= U181(X1,X2) ; a__U191(tt,XS) >= pair(nil,mark(XS)) ; a__U191(X1,X2) >= U191(X1,X2) ; a__U202(pair(YS,ZS),X) >= pair(cons(mark(X),YS),mark(ZS)) ; a__U202(X1,X2) >= U202(X1,X2) ; a__U201(tt,N,X,XS) >= a__U202(a__splitAt(mark(N),mark(XS)),X) ; a__U201(X1,X2,X3,X4) >= U201(X1,X2,X3,X4) ; a__U21(tt,X) >= mark(X) ; a__U21(X1,X2) >= U21(X1,X2) ; a__U211(tt,XS) >= mark(XS) ; a__U211(X1,X2) >= U211(X1,X2) ; a__fst(pair(X,Y)) >= a__U21(a__and(a__and(a__isLNat(X),isLNatKind(X)), and(isLNat(Y),isLNatKind(Y))),X) ; a__fst(X) >= fst(X) ; a__U221(tt,N,XS) >= a__fst(a__splitAt(mark(N),mark(XS))) ; a__U221(X1,X2,X3) >= U221(X1,X2,X3) ; a__U31(tt,N) >= mark(N) ; a__U31(X1,X2) >= U31(X1,X2) ; a__U42(tt,V2) >= a__U43(a__isLNat(V2)) ; a__U42(X1,X2) >= U42(X1,X2) ; a__U41(tt,V1,V2) >= a__U42(a__isNatural(V1),V2) ; a__U41(X1,X2,X3) >= U41(X1,X2,X3) ; a__U43(tt) >= tt ; a__U43(X) >= U43(X) ; a__U52(tt,V2) >= a__U53(a__isLNat(V2)) ; a__U52(X1,X2) >= U52(X1,X2) ; a__U51(tt,V1,V2) >= a__U52(a__isNatural(V1),V2) ; a__U51(X1,X2,X3) >= U51(X1,X2,X3) ; a__U53(tt) >= tt ; a__U53(X) >= U53(X) ; a__U62(tt) >= tt ; a__U62(X) >= U62(X) ; a__isPLNat(pair(V1,V2)) >= a__U141(a__and(a__isLNatKind(V1),isLNatKind(V2)), V1,V2) ; a__isPLNat(splitAt(V1,V2)) >= a__U151(a__and(a__isNaturalKind(V1), isLNatKind(V2)),V1,V2) ; a__isPLNat(X) >= isPLNat(X) ; a__U61(tt,V1) >= a__U62(a__isPLNat(V1)) ; a__U61(X1,X2) >= U61(X1,X2) ; a__U72(tt) >= tt ; a__U72(X) >= U72(X) ; a__U71(tt,V1) >= a__U72(a__isNatural(V1)) ; a__U71(X1,X2) >= U71(X1,X2) ; a__U82(tt) >= tt ; a__U82(X) >= U82(X) ; a__U81(tt,V1) >= a__U82(a__isPLNat(V1)) ; a__U81(X1,X2) >= U81(X1,X2) ; a__U92(tt) >= tt ; a__U92(X) >= U92(X) ; a__U91(tt,V1) >= a__U92(a__isLNat(V1)) ; a__U91(X1,X2) >= U91(X1,X2) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__isNaturalKind(s(V1)) >= a__isNaturalKind(V1) ; a__isNaturalKind(0) >= tt ; a__isNaturalKind(head(V1)) >= a__isLNatKind(V1) ; a__isNaturalKind(sel(V1,V2)) >= a__and(a__isNaturalKind(V1),isLNatKind(V2)) ; a__isNaturalKind(X) >= isNaturalKind(X) ; a__isPLNatKind(pair(V1,V2)) >= a__and(a__isLNatKind(V1),isLNatKind(V2)) ; a__isPLNatKind(splitAt(V1,V2)) >= a__and(a__isNaturalKind(V1),isLNatKind(V2)) ; a__isPLNatKind(X) >= isPLNatKind(X) ; a__isLNatKind(cons(V1,V2)) >= a__and(a__isNaturalKind(V1),isLNatKind(V2)) ; a__isLNatKind(natsFrom(V1)) >= a__isNaturalKind(V1) ; a__isLNatKind(nil) >= tt ; a__isLNatKind(afterNth(V1,V2)) >= a__and(a__isNaturalKind(V1),isLNatKind(V2)) ; a__isLNatKind(fst(V1)) >= a__isPLNatKind(V1) ; a__isLNatKind(snd(V1)) >= a__isPLNatKind(V1) ; a__isLNatKind(tail(V1)) >= a__isLNatKind(V1) ; a__isLNatKind(take(V1,V2)) >= a__and(a__isNaturalKind(V1),isLNatKind(V2)) ; a__isLNatKind(X) >= isLNatKind(X) ; a__natsFrom(N) >= a__U161(a__and(a__isNatural(N),isNaturalKind(N)),N) ; a__natsFrom(X) >= natsFrom(X) ; a__sel(N,XS) >= a__U171(a__and(a__and(a__isNatural(N),isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))),N,XS) ; a__sel(X1,X2) >= sel(X1,X2) ; a__tail(cons(N,XS)) >= a__U211(a__and(a__and(a__isNatural(N), isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))),XS) ; a__tail(X) >= tail(X) ; a__take(N,XS) >= a__U221(a__and(a__and(a__isNatural(N),isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))),N,XS) ; a__take(X1,X2) >= take(X1,X2) ; Marked_a__sel(N,XS) >= Marked_a__and(a__isNatural(N),isNaturalKind(N)) ; Marked_a__sel(N,XS) >= Marked_a__and(a__and(a__isNatural(N),isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))) ; Marked_a__sel(N,XS) >= Marked_a__U171(a__and(a__and(a__isNatural(N), isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))), N,XS) ; Marked_a__sel(N,XS) >= Marked_a__isNatural(N) ; Marked_a__take(N,XS) >= Marked_a__and(a__isNatural(N),isNaturalKind(N)) ; Marked_a__take(N,XS) >= Marked_a__and(a__and(a__isNatural(N), isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))) ; Marked_a__take(N,XS) >= Marked_a__U221(a__and(a__and(a__isNatural(N), isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))), N,XS) ; Marked_a__take(N,XS) >= Marked_a__isNatural(N) ; Marked_a__tail(cons(N,XS)) >= Marked_a__and(a__isNatural(N),isNaturalKind(N)) ; Marked_a__tail(cons(N,XS)) >= Marked_a__and(a__and(a__isNatural(N), isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))) ; Marked_a__tail(cons(N,XS)) >= Marked_a__U211(a__and(a__and(a__isNatural(N), isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))), XS) ; Marked_a__tail(cons(N,XS)) >= Marked_a__isNatural(N) ; Marked_a__isPLNatKind(pair(V1,V2)) >= Marked_a__isLNatKind(V1) ; Marked_a__isPLNatKind(pair(V1,V2)) >= Marked_a__and(a__isLNatKind(V1), isLNatKind(V2)) ; Marked_a__isPLNatKind(splitAt(V1,V2)) >= Marked_a__isNaturalKind(V1) ; Marked_a__isPLNatKind(splitAt(V1,V2)) >= Marked_a__and(a__isNaturalKind(V1), isLNatKind(V2)) ; Marked_a__isLNatKind(cons(V1,V2)) >= Marked_a__isNaturalKind(V1) ; Marked_a__isLNatKind(cons(V1,V2)) >= Marked_a__and(a__isNaturalKind(V1), isLNatKind(V2)) ; Marked_a__isLNatKind(natsFrom(V1)) >= Marked_a__isNaturalKind(V1) ; Marked_a__isLNatKind(afterNth(V1,V2)) >= Marked_a__isNaturalKind(V1) ; Marked_a__isLNatKind(afterNth(V1,V2)) >= Marked_a__and(a__isNaturalKind(V1), isLNatKind(V2)) ; Marked_a__isLNatKind(fst(V1)) >= Marked_a__isPLNatKind(V1) ; Marked_a__isLNatKind(snd(V1)) >= Marked_a__isPLNatKind(V1) ; Marked_a__isLNatKind(tail(V1)) >= Marked_a__isLNatKind(V1) ; Marked_a__isLNatKind(take(V1,V2)) >= Marked_a__isNaturalKind(V1) ; Marked_a__isLNatKind(take(V1,V2)) >= Marked_a__and(a__isNaturalKind(V1), isLNatKind(V2)) ; Marked_a__isNaturalKind(s(V1)) >= Marked_a__isNaturalKind(V1) ; Marked_a__isNaturalKind(head(V1)) >= Marked_a__isLNatKind(V1) ; Marked_a__isNaturalKind(sel(V1,V2)) >= Marked_a__isNaturalKind(V1) ; Marked_a__isNaturalKind(sel(V1,V2)) >= Marked_a__and(a__isNaturalKind(V1), isLNatKind(V2)) ; Marked_a__and(tt,X) >= Marked_mark(X) ; Marked_a__U91(tt,V1) >= Marked_a__isLNat(V1) ; Marked_a__U81(tt,V1) >= Marked_a__isPLNat(V1) ; Marked_a__U71(tt,V1) >= Marked_a__isNatural(V1) ; Marked_a__isPLNat(pair(V1,V2)) >= Marked_a__isLNatKind(V1) ; Marked_a__isPLNat(pair(V1,V2)) >= Marked_a__and(a__isLNatKind(V1), isLNatKind(V2)) ; Marked_a__isPLNat(pair(V1,V2)) >= Marked_a__U141(a__and(a__isLNatKind(V1), isLNatKind(V2)),V1, V2) ; Marked_a__isPLNat(splitAt(V1,V2)) >= Marked_a__isNaturalKind(V1) ; Marked_a__isPLNat(splitAt(V1,V2)) >= Marked_a__and(a__isNaturalKind(V1), isLNatKind(V2)) ; Marked_a__isPLNat(splitAt(V1,V2)) >= Marked_a__U151(a__and(a__isNaturalKind( V1), isLNatKind(V2)), V1,V2) ; Marked_a__U61(tt,V1) >= Marked_a__isPLNat(V1) ; Marked_a__U52(tt,V2) >= Marked_a__isLNat(V2) ; Marked_a__U51(tt,V1,V2) >= Marked_a__U52(a__isNatural(V1),V2) ; Marked_a__U51(tt,V1,V2) >= Marked_a__isNatural(V1) ; Marked_a__U42(tt,V2) >= Marked_a__isLNat(V2) ; Marked_a__U41(tt,V1,V2) >= Marked_a__U42(a__isNatural(V1),V2) ; Marked_a__U41(tt,V1,V2) >= Marked_a__isNatural(V1) ; Marked_a__U31(tt,N) >= Marked_mark(N) ; Marked_a__fst(pair(X,Y)) >= Marked_a__and(a__isLNat(X),isLNatKind(X)) ; Marked_a__fst(pair(X,Y)) >= Marked_a__and(a__and(a__isLNat(X),isLNatKind(X)), and(isLNat(Y),isLNatKind(Y))) ; Marked_a__fst(pair(X,Y)) >= Marked_a__U21(a__and(a__and(a__isLNat(X), isLNatKind(X)), and(isLNat(Y),isLNatKind(Y))), X) ; Marked_a__fst(pair(X,Y)) >= Marked_a__isLNat(X) ; Marked_a__U221(tt,N,XS) >= Marked_a__fst(a__splitAt(mark(N),mark(XS))) ; Marked_a__U221(tt,N,XS) >= Marked_a__splitAt(mark(N),mark(XS)) ; Marked_a__U221(tt,N,XS) >= Marked_mark(N) ; Marked_a__U221(tt,N,XS) >= Marked_mark(XS) ; Marked_a__U211(tt,XS) >= Marked_mark(XS) ; Marked_a__U21(tt,X) >= Marked_mark(X) ; Marked_a__U202(pair(YS,ZS),X) >= Marked_mark(X) ; Marked_a__U202(pair(YS,ZS),X) >= Marked_mark(ZS) ; Marked_a__U201(tt,N,X,XS) >= Marked_a__U202(a__splitAt(mark(N),mark(XS)),X) ; Marked_a__U201(tt,N,X,XS) >= Marked_a__splitAt(mark(N),mark(XS)) ; Marked_a__U201(tt,N,X,XS) >= Marked_mark(N) ; Marked_a__U201(tt,N,X,XS) >= Marked_mark(XS) ; Marked_a__U191(tt,XS) >= Marked_mark(XS) ; Marked_a__U181(tt,Y) >= Marked_mark(Y) ; Marked_a__afterNth(N,XS) >= Marked_a__and(a__isNatural(N),isNaturalKind(N)) ; Marked_a__afterNth(N,XS) >= Marked_a__and(a__and(a__isNatural(N), isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))) ; Marked_a__afterNth(N,XS) >= Marked_a__U11(a__and(a__and(a__isNatural(N), isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))), N,XS) ; Marked_a__afterNth(N,XS) >= Marked_a__isNatural(N) ; Marked_a__head(cons(N,XS)) >= Marked_a__and(a__isNatural(N),isNaturalKind(N)) ; Marked_a__head(cons(N,XS)) >= Marked_a__and(a__and(a__isNatural(N), isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))) ; Marked_a__head(cons(N,XS)) >= Marked_a__U31(a__and(a__and(a__isNatural(N), isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))), N) ; Marked_a__head(cons(N,XS)) >= Marked_a__isNatural(N) ; Marked_a__U171(tt,N,XS) >= Marked_a__afterNth(mark(N),mark(XS)) ; Marked_a__U171(tt,N,XS) >= Marked_a__head(a__afterNth(mark(N),mark(XS))) ; Marked_a__U171(tt,N,XS) >= Marked_mark(N) ; Marked_a__U171(tt,N,XS) >= Marked_mark(XS) ; Marked_a__natsFrom(N) >= Marked_a__and(a__isNatural(N),isNaturalKind(N)) ; Marked_a__natsFrom(N) >= Marked_a__U161(a__and(a__isNatural(N), isNaturalKind(N)),N) ; Marked_a__natsFrom(N) >= Marked_a__isNatural(N) ; Marked_a__U161(tt,N) >= Marked_mark(N) ; Marked_a__U152(tt,V2) >= Marked_a__isLNat(V2) ; Marked_a__U151(tt,V1,V2) >= Marked_a__U152(a__isNatural(V1),V2) ; Marked_a__U151(tt,V1,V2) >= Marked_a__isNatural(V1) ; Marked_a__U142(tt,V2) >= Marked_a__isLNat(V2) ; Marked_a__U141(tt,V1,V2) >= Marked_a__U142(a__isLNat(V1),V2) ; Marked_a__U141(tt,V1,V2) >= Marked_a__isLNat(V1) ; Marked_a__U132(tt,V2) >= Marked_a__isLNat(V2) ; Marked_a__U131(tt,V1,V2) >= Marked_a__U132(a__isNatural(V1),V2) ; Marked_a__U131(tt,V1,V2) >= Marked_a__isNatural(V1) ; Marked_a__U121(tt,V1) >= Marked_a__isNatural(V1) ; Marked_a__U111(tt,V1) >= Marked_a__isLNat(V1) ; Marked_a__splitAt(s(N),cons(X,XS)) >= Marked_a__and(a__isNatural(N), isNaturalKind(N)) ; Marked_a__splitAt(s(N),cons(X,XS)) >= Marked_a__and(a__and(a__isNatural(N), isNaturalKind(N)), and(and(isNatural(X),isNaturalKind(X)), and(isLNat(XS),isLNatKind(XS)))) ; Marked_a__splitAt(s(N),cons(X,XS)) >= Marked_a__U201(a__and(a__and( a__isNatural( N), isNaturalKind(N)), and(and(isNatural(X), isNaturalKind(X)), and(isLNat(XS), isLNatKind(XS)))), N,X,XS) ; Marked_a__splitAt(s(N),cons(X,XS)) >= Marked_a__isNatural(N) ; Marked_a__splitAt(0,XS) >= Marked_a__and(a__isLNat(XS),isLNatKind(XS)) ; Marked_a__splitAt(0,XS) >= Marked_a__U191(a__and(a__isLNat(XS), isLNatKind(XS)),XS) ; Marked_a__splitAt(0,XS) >= Marked_a__isLNat(XS) ; Marked_a__snd(pair(X,Y)) >= Marked_a__and(a__isLNat(X),isLNatKind(X)) ; Marked_a__snd(pair(X,Y)) >= Marked_a__and(a__and(a__isLNat(X),isLNatKind(X)), and(isLNat(Y),isLNatKind(Y))) ; Marked_a__snd(pair(X,Y)) >= Marked_a__U181(a__and(a__and(a__isLNat(X), isLNatKind(X)), and(isLNat(Y),isLNatKind(Y))), Y) ; Marked_a__snd(pair(X,Y)) >= Marked_a__isLNat(X) ; Marked_a__U11(tt,N,XS) >= Marked_a__splitAt(mark(N),mark(XS)) ; Marked_a__U11(tt,N,XS) >= Marked_a__snd(a__splitAt(mark(N),mark(XS))) ; Marked_a__U11(tt,N,XS) >= Marked_mark(N) ; Marked_a__U11(tt,N,XS) >= Marked_mark(XS) ; Marked_a__isLNat(cons(V1,V2)) >= Marked_a__isNaturalKind(V1) ; Marked_a__isLNat(cons(V1,V2)) >= Marked_a__and(a__isNaturalKind(V1), isLNatKind(V2)) ; Marked_a__isLNat(cons(V1,V2)) >= Marked_a__U51(a__and(a__isNaturalKind(V1), isLNatKind(V2)),V1, V2) ; Marked_a__isLNat(natsFrom(V1)) >= Marked_a__isNaturalKind(V1) ; Marked_a__isLNat(natsFrom(V1)) >= Marked_a__U71(a__isNaturalKind(V1),V1) ; Marked_a__isLNat(afterNth(V1,V2)) >= Marked_a__isNaturalKind(V1) ; Marked_a__isLNat(afterNth(V1,V2)) >= Marked_a__and(a__isNaturalKind(V1), isLNatKind(V2)) ; Marked_a__isLNat(afterNth(V1,V2)) >= Marked_a__U41(a__and(a__isNaturalKind( V1), isLNatKind(V2)), V1,V2) ; Marked_a__isLNat(fst(V1)) >= Marked_a__isPLNatKind(V1) ; Marked_a__isLNat(fst(V1)) >= Marked_a__U61(a__isPLNatKind(V1),V1) ; Marked_a__isLNat(snd(V1)) >= Marked_a__isPLNatKind(V1) ; Marked_a__isLNat(snd(V1)) >= Marked_a__U81(a__isPLNatKind(V1),V1) ; Marked_a__isLNat(tail(V1)) >= Marked_a__isLNatKind(V1) ; Marked_a__isLNat(tail(V1)) >= Marked_a__U91(a__isLNatKind(V1),V1) ; Marked_a__isLNat(take(V1,V2)) >= Marked_a__isNaturalKind(V1) ; Marked_a__isLNat(take(V1,V2)) >= Marked_a__and(a__isNaturalKind(V1), isLNatKind(V2)) ; Marked_a__isLNat(take(V1,V2)) >= Marked_a__U101(a__and(a__isNaturalKind(V1), isLNatKind(V2)),V1, V2) ; Marked_a__isNatural(s(V1)) >= Marked_a__isNaturalKind(V1) ; Marked_a__isNatural(s(V1)) >= Marked_a__U121(a__isNaturalKind(V1),V1) ; Marked_a__isNatural(head(V1)) >= Marked_a__isLNatKind(V1) ; Marked_a__isNatural(head(V1)) >= Marked_a__U111(a__isLNatKind(V1),V1) ; Marked_a__isNatural(sel(V1,V2)) >= Marked_a__isNaturalKind(V1) ; Marked_a__isNatural(sel(V1,V2)) >= Marked_a__and(a__isNaturalKind(V1), isLNatKind(V2)) ; Marked_a__isNatural(sel(V1,V2)) >= Marked_a__U131(a__and(a__isNaturalKind(V1), isLNatKind(V2)), V1,V2) ; Marked_a__U102(tt,V2) >= Marked_a__isLNat(V2) ; Marked_a__U101(tt,V1,V2) >= Marked_a__isNatural(V1) ; Marked_a__U101(tt,V1,V2) >= Marked_a__U102(a__isNatural(V1),V2) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(natsFrom(X)) >= Marked_a__natsFrom(mark(X)) ; Marked_mark(natsFrom(X)) >= Marked_mark(X) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(pair(X1,X2)) >= Marked_mark(X1) ; Marked_mark(pair(X1,X2)) >= Marked_mark(X2) ; Marked_mark(isNaturalKind(X)) >= Marked_a__isNaturalKind(X) ; Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(isLNat(X)) >= Marked_a__isLNat(X) ; Marked_mark(isLNatKind(X)) >= Marked_a__isLNatKind(X) ; Marked_mark(afterNth(X1,X2)) >= Marked_a__afterNth(mark(X1),mark(X2)) ; Marked_mark(afterNth(X1,X2)) >= Marked_mark(X1) ; Marked_mark(afterNth(X1,X2)) >= Marked_mark(X2) ; Marked_mark(fst(X)) >= Marked_a__fst(mark(X)) ; Marked_mark(fst(X)) >= Marked_mark(X) ; Marked_mark(snd(X)) >= Marked_a__snd(mark(X)) ; Marked_mark(snd(X)) >= Marked_mark(X) ; Marked_mark(tail(X)) >= Marked_a__tail(mark(X)) ; Marked_mark(tail(X)) >= Marked_mark(X) ; Marked_mark(take(X1,X2)) >= Marked_a__take(mark(X1),mark(X2)) ; Marked_mark(take(X1,X2)) >= Marked_mark(X1) ; Marked_mark(take(X1,X2)) >= Marked_mark(X2) ; Marked_mark(head(X)) >= Marked_a__head(mark(X)) ; Marked_mark(head(X)) >= Marked_mark(X) ; Marked_mark(sel(X1,X2)) >= Marked_a__sel(mark(X1),mark(X2)) ; Marked_mark(sel(X1,X2)) >= Marked_mark(X1) ; Marked_mark(sel(X1,X2)) >= Marked_mark(X2) ; Marked_mark(splitAt(X1,X2)) >= Marked_a__splitAt(mark(X1),mark(X2)) ; Marked_mark(splitAt(X1,X2)) >= Marked_mark(X1) ; Marked_mark(splitAt(X1,X2)) >= Marked_mark(X2) ; Marked_mark(isNatural(X)) >= Marked_a__isNatural(X) ; Marked_mark(U101(X1,X2,X3)) >= Marked_a__U101(mark(X1),X2,X3) ; Marked_mark(U101(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U102(X1,X2)) >= Marked_a__U102(mark(X1),X2) ; Marked_mark(U102(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U103(X)) >= Marked_mark(X) ; Marked_mark(U11(X1,X2,X3)) >= Marked_a__U11(mark(X1),X2,X3) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U111(X1,X2)) >= Marked_a__U111(mark(X1),X2) ; Marked_mark(U111(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U112(X)) >= Marked_mark(X) ; Marked_mark(U121(X1,X2)) >= Marked_a__U121(mark(X1),X2) ; Marked_mark(U121(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U122(X)) >= Marked_mark(X) ; Marked_mark(U131(X1,X2,X3)) >= Marked_a__U131(mark(X1),X2,X3) ; Marked_mark(U131(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U132(X1,X2)) >= Marked_a__U132(mark(X1),X2) ; Marked_mark(U132(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U133(X)) >= Marked_mark(X) ; Marked_mark(U141(X1,X2,X3)) >= Marked_a__U141(mark(X1),X2,X3) ; Marked_mark(U141(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U142(X1,X2)) >= Marked_a__U142(mark(X1),X2) ; Marked_mark(U142(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U143(X)) >= Marked_mark(X) ; Marked_mark(U151(X1,X2,X3)) >= Marked_a__U151(mark(X1),X2,X3) ; Marked_mark(U151(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U152(X1,X2)) >= Marked_a__U152(mark(X1),X2) ; Marked_mark(U152(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U153(X)) >= Marked_mark(X) ; Marked_mark(U161(X1,X2)) >= Marked_a__U161(mark(X1),X2) ; Marked_mark(U161(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U171(X1,X2,X3)) >= Marked_a__U171(mark(X1),X2,X3) ; Marked_mark(U171(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U181(X1,X2)) >= Marked_a__U181(mark(X1),X2) ; Marked_mark(U181(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U191(X1,X2)) >= Marked_a__U191(mark(X1),X2) ; Marked_mark(U191(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U201(X1,X2,X3,X4)) >= Marked_a__U201(mark(X1),X2,X3,X4) ; Marked_mark(U201(X1,X2,X3,X4)) >= Marked_mark(X1) ; Marked_mark(U202(X1,X2)) >= Marked_a__U202(mark(X1),X2) ; Marked_mark(U202(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U21(X1,X2)) >= Marked_a__U21(mark(X1),X2) ; Marked_mark(U21(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U211(X1,X2)) >= Marked_a__U211(mark(X1),X2) ; Marked_mark(U211(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U221(X1,X2,X3)) >= Marked_a__U221(mark(X1),X2,X3) ; Marked_mark(U221(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U31(X1,X2)) >= Marked_a__U31(mark(X1),X2) ; Marked_mark(U31(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U41(X1,X2,X3)) >= Marked_a__U41(mark(X1),X2,X3) ; Marked_mark(U41(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U42(X1,X2)) >= Marked_a__U42(mark(X1),X2) ; Marked_mark(U42(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U43(X)) >= Marked_mark(X) ; Marked_mark(U51(X1,X2,X3)) >= Marked_a__U51(mark(X1),X2,X3) ; Marked_mark(U51(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U52(X1,X2)) >= Marked_a__U52(mark(X1),X2) ; Marked_mark(U52(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U53(X)) >= Marked_mark(X) ; Marked_mark(U61(X1,X2)) >= Marked_a__U61(mark(X1),X2) ; Marked_mark(U61(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U62(X)) >= Marked_mark(X) ; Marked_mark(isPLNat(X)) >= Marked_a__isPLNat(X) ; Marked_mark(U71(X1,X2)) >= Marked_a__U71(mark(X1),X2) ; Marked_mark(U71(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U72(X)) >= Marked_mark(X) ; Marked_mark(U81(X1,X2)) >= Marked_a__U81(mark(X1),X2) ; Marked_mark(U81(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U82(X)) >= Marked_mark(X) ; Marked_mark(U91(X1,X2)) >= Marked_a__U91(mark(X1),X2) ; Marked_mark(U91(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U92(X)) >= Marked_mark(X) ; Marked_mark(isPLNatKind(X)) >= Marked_a__isPLNatKind(X) ; } + Disjunctions:{ { Marked_a__sel(N,XS) > Marked_a__and(a__isNatural(N),isNaturalKind(N)) ; } { Marked_a__sel(N,XS) > Marked_a__and(a__and(a__isNatural(N),isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))) ; } { Marked_a__sel(N,XS) > Marked_a__U171(a__and(a__and(a__isNatural(N), isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))), N,XS) ; } { Marked_a__sel(N,XS) > Marked_a__isNatural(N) ; } { Marked_a__take(N,XS) > Marked_a__and(a__isNatural(N),isNaturalKind(N)) ; } { Marked_a__take(N,XS) > Marked_a__and(a__and(a__isNatural(N),isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))) ; } { Marked_a__take(N,XS) > Marked_a__U221(a__and(a__and(a__isNatural(N), isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))), N,XS) ; } { Marked_a__take(N,XS) > Marked_a__isNatural(N) ; } { Marked_a__tail(cons(N,XS)) > Marked_a__and(a__isNatural(N),isNaturalKind(N)) ; } { Marked_a__tail(cons(N,XS)) > Marked_a__and(a__and(a__isNatural(N), isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))) ; } { Marked_a__tail(cons(N,XS)) > Marked_a__U211(a__and(a__and(a__isNatural(N), isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))), XS) ; } { Marked_a__tail(cons(N,XS)) > Marked_a__isNatural(N) ; } { Marked_a__isPLNatKind(pair(V1,V2)) > Marked_a__isLNatKind(V1) ; } { Marked_a__isPLNatKind(pair(V1,V2)) > Marked_a__and(a__isLNatKind(V1), isLNatKind(V2)) ; } { Marked_a__isPLNatKind(splitAt(V1,V2)) > Marked_a__isNaturalKind(V1) ; } { Marked_a__isPLNatKind(splitAt(V1,V2)) > Marked_a__and(a__isNaturalKind(V1), isLNatKind(V2)) ; } { Marked_a__isLNatKind(cons(V1,V2)) > Marked_a__isNaturalKind(V1) ; } { Marked_a__isLNatKind(cons(V1,V2)) > Marked_a__and(a__isNaturalKind(V1), isLNatKind(V2)) ; } { Marked_a__isLNatKind(natsFrom(V1)) > Marked_a__isNaturalKind(V1) ; } { Marked_a__isLNatKind(afterNth(V1,V2)) > Marked_a__isNaturalKind(V1) ; } { Marked_a__isLNatKind(afterNth(V1,V2)) > Marked_a__and(a__isNaturalKind(V1), isLNatKind(V2)) ; } { Marked_a__isLNatKind(fst(V1)) > Marked_a__isPLNatKind(V1) ; } { Marked_a__isLNatKind(snd(V1)) > Marked_a__isPLNatKind(V1) ; } { Marked_a__isLNatKind(tail(V1)) > Marked_a__isLNatKind(V1) ; } { Marked_a__isLNatKind(take(V1,V2)) > Marked_a__isNaturalKind(V1) ; } { Marked_a__isLNatKind(take(V1,V2)) > Marked_a__and(a__isNaturalKind(V1), isLNatKind(V2)) ; } { Marked_a__isNaturalKind(s(V1)) > Marked_a__isNaturalKind(V1) ; } { Marked_a__isNaturalKind(head(V1)) > Marked_a__isLNatKind(V1) ; } { Marked_a__isNaturalKind(sel(V1,V2)) > Marked_a__isNaturalKind(V1) ; } { Marked_a__isNaturalKind(sel(V1,V2)) > Marked_a__and(a__isNaturalKind(V1), isLNatKind(V2)) ; } { Marked_a__and(tt,X) > Marked_mark(X) ; } { Marked_a__U91(tt,V1) > Marked_a__isLNat(V1) ; } { Marked_a__U81(tt,V1) > Marked_a__isPLNat(V1) ; } { Marked_a__U71(tt,V1) > Marked_a__isNatural(V1) ; } { Marked_a__isPLNat(pair(V1,V2)) > Marked_a__isLNatKind(V1) ; } { Marked_a__isPLNat(pair(V1,V2)) > Marked_a__and(a__isLNatKind(V1), isLNatKind(V2)) ; } { Marked_a__isPLNat(pair(V1,V2)) > Marked_a__U141(a__and(a__isLNatKind(V1), isLNatKind(V2)),V1, V2) ; } { Marked_a__isPLNat(splitAt(V1,V2)) > Marked_a__isNaturalKind(V1) ; } { Marked_a__isPLNat(splitAt(V1,V2)) > Marked_a__and(a__isNaturalKind(V1), isLNatKind(V2)) ; } { Marked_a__isPLNat(splitAt(V1,V2)) > Marked_a__U151(a__and(a__isNaturalKind( V1), isLNatKind(V2)), V1,V2) ; } { Marked_a__U61(tt,V1) > Marked_a__isPLNat(V1) ; } { Marked_a__U52(tt,V2) > Marked_a__isLNat(V2) ; } { Marked_a__U51(tt,V1,V2) > Marked_a__U52(a__isNatural(V1),V2) ; } { Marked_a__U51(tt,V1,V2) > Marked_a__isNatural(V1) ; } { Marked_a__U42(tt,V2) > Marked_a__isLNat(V2) ; } { Marked_a__U41(tt,V1,V2) > Marked_a__U42(a__isNatural(V1),V2) ; } { Marked_a__U41(tt,V1,V2) > Marked_a__isNatural(V1) ; } { Marked_a__U31(tt,N) > Marked_mark(N) ; } { Marked_a__fst(pair(X,Y)) > Marked_a__and(a__isLNat(X),isLNatKind(X)) ; } { Marked_a__fst(pair(X,Y)) > Marked_a__and(a__and(a__isLNat(X),isLNatKind(X)), and(isLNat(Y),isLNatKind(Y))) ; } { Marked_a__fst(pair(X,Y)) > Marked_a__U21(a__and(a__and(a__isLNat(X), isLNatKind(X)), and(isLNat(Y),isLNatKind(Y))), X) ; } { Marked_a__fst(pair(X,Y)) > Marked_a__isLNat(X) ; } { Marked_a__U221(tt,N,XS) > Marked_a__fst(a__splitAt(mark(N),mark(XS))) ; } { Marked_a__U221(tt,N,XS) > Marked_a__splitAt(mark(N),mark(XS)) ; } { Marked_a__U221(tt,N,XS) > Marked_mark(N) ; } { Marked_a__U221(tt,N,XS) > Marked_mark(XS) ; } { Marked_a__U211(tt,XS) > Marked_mark(XS) ; } { Marked_a__U21(tt,X) > Marked_mark(X) ; } { Marked_a__U202(pair(YS,ZS),X) > Marked_mark(X) ; } { Marked_a__U202(pair(YS,ZS),X) > Marked_mark(ZS) ; } { Marked_a__U201(tt,N,X,XS) > Marked_a__U202(a__splitAt(mark(N),mark(XS)),X) ; } { Marked_a__U201(tt,N,X,XS) > Marked_a__splitAt(mark(N),mark(XS)) ; } { Marked_a__U201(tt,N,X,XS) > Marked_mark(N) ; } { Marked_a__U201(tt,N,X,XS) > Marked_mark(XS) ; } { Marked_a__U191(tt,XS) > Marked_mark(XS) ; } { Marked_a__U181(tt,Y) > Marked_mark(Y) ; } { Marked_a__afterNth(N,XS) > Marked_a__and(a__isNatural(N),isNaturalKind(N)) ; } { Marked_a__afterNth(N,XS) > Marked_a__and(a__and(a__isNatural(N), isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))) ; } { Marked_a__afterNth(N,XS) > Marked_a__U11(a__and(a__and(a__isNatural(N), isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))), N,XS) ; } { Marked_a__afterNth(N,XS) > Marked_a__isNatural(N) ; } { Marked_a__head(cons(N,XS)) > Marked_a__and(a__isNatural(N),isNaturalKind(N)) ; } { Marked_a__head(cons(N,XS)) > Marked_a__and(a__and(a__isNatural(N), isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))) ; } { Marked_a__head(cons(N,XS)) > Marked_a__U31(a__and(a__and(a__isNatural(N), isNaturalKind(N)), and(isLNat(XS),isLNatKind(XS))), N) ; } { Marked_a__head(cons(N,XS)) > Marked_a__isNatural(N) ; } { Marked_a__U171(tt,N,XS) > Marked_a__afterNth(mark(N),mark(XS)) ; } { Marked_a__U171(tt,N,XS) > Marked_a__head(a__afterNth(mark(N),mark(XS))) ; } { Marked_a__U171(tt,N,XS) > Marked_mark(N) ; } { Marked_a__U171(tt,N,XS) > Marked_mark(XS) ; } { Marked_a__natsFrom(N) > Marked_a__and(a__isNatural(N),isNaturalKind(N)) ; } { Marked_a__natsFrom(N) > Marked_a__U161(a__and(a__isNatural(N), isNaturalKind(N)),N) ; } { Marked_a__natsFrom(N) > Marked_a__isNatural(N) ; } { Marked_a__U161(tt,N) > Marked_mark(N) ; } { Marked_a__U152(tt,V2) > Marked_a__isLNat(V2) ; } { Marked_a__U151(tt,V1,V2) > Marked_a__U152(a__isNatural(V1),V2) ; } { Marked_a__U151(tt,V1,V2) > Marked_a__isNatural(V1) ; } { Marked_a__U142(tt,V2) > Marked_a__isLNat(V2) ; } { Marked_a__U141(tt,V1,V2) > Marked_a__U142(a__isLNat(V1),V2) ; } { Marked_a__U141(tt,V1,V2) > Marked_a__isLNat(V1) ; } { Marked_a__U132(tt,V2) > Marked_a__isLNat(V2) ; } { Marked_a__U131(tt,V1,V2) > Marked_a__U132(a__isNatural(V1),V2) ; } { Marked_a__U131(tt,V1,V2) > Marked_a__isNatural(V1) ; } { Marked_a__U121(tt,V1) > Marked_a__isNatural(V1) ; } { Marked_a__U111(tt,V1) > Marked_a__isLNat(V1) ; } { Marked_a__splitAt(s(N),cons(X,XS)) > Marked_a__and(a__isNatural(N), isNaturalKind(N)) ; } { Marked_a__splitAt(s(N),cons(X,XS)) > Marked_a__and(a__and(a__isNatural(N), isNaturalKind(N)), and(and(isNatural(X),isNaturalKind(X)), and(isLNat(XS),isLNatKind(XS)))) ; } { Marked_a__splitAt(s(N),cons(X,XS)) > Marked_a__U201(a__and(a__and(a__isNatural( N), isNaturalKind(N)), and(and(isNatural(X), isNaturalKind(X)), and(isLNat(XS), isLNatKind(XS)))), N,X,XS) ; } { Marked_a__splitAt(s(N),cons(X,XS)) > Marked_a__isNatural(N) ; } { Marked_a__splitAt(0,XS) > Marked_a__and(a__isLNat(XS),isLNatKind(XS)) ; } { Marked_a__splitAt(0,XS) > Marked_a__U191(a__and(a__isLNat(XS),isLNatKind(XS)), XS) ; } { Marked_a__splitAt(0,XS) > Marked_a__isLNat(XS) ; } { Marked_a__snd(pair(X,Y)) > Marked_a__and(a__isLNat(X),isLNatKind(X)) ; } { Marked_a__snd(pair(X,Y)) > Marked_a__and(a__and(a__isLNat(X),isLNatKind(X)), and(isLNat(Y),isLNatKind(Y))) ; } { Marked_a__snd(pair(X,Y)) > Marked_a__U181(a__and(a__and(a__isLNat(X), isLNatKind(X)), and(isLNat(Y),isLNatKind(Y))), Y) ; } { Marked_a__snd(pair(X,Y)) > Marked_a__isLNat(X) ; } { Marked_a__U11(tt,N,XS) > Marked_a__splitAt(mark(N),mark(XS)) ; } { Marked_a__U11(tt,N,XS) > Marked_a__snd(a__splitAt(mark(N),mark(XS))) ; } { Marked_a__U11(tt,N,XS) > Marked_mark(N) ; } { Marked_a__U11(tt,N,XS) > Marked_mark(XS) ; } { Marked_a__isLNat(cons(V1,V2)) > Marked_a__isNaturalKind(V1) ; } { Marked_a__isLNat(cons(V1,V2)) > Marked_a__and(a__isNaturalKind(V1), isLNatKind(V2)) ; } { Marked_a__isLNat(cons(V1,V2)) > Marked_a__U51(a__and(a__isNaturalKind(V1), isLNatKind(V2)),V1,V2) ; } { Marked_a__isLNat(natsFrom(V1)) > Marked_a__isNaturalKind(V1) ; } { Marked_a__isLNat(natsFrom(V1)) > Marked_a__U71(a__isNaturalKind(V1),V1) ; } { Marked_a__isLNat(afterNth(V1,V2)) > Marked_a__isNaturalKind(V1) ; } { Marked_a__isLNat(afterNth(V1,V2)) > Marked_a__and(a__isNaturalKind(V1), isLNatKind(V2)) ; } { Marked_a__isLNat(afterNth(V1,V2)) > Marked_a__U41(a__and(a__isNaturalKind(V1), isLNatKind(V2)), V1,V2) ; } { Marked_a__isLNat(fst(V1)) > Marked_a__isPLNatKind(V1) ; } { Marked_a__isLNat(fst(V1)) > Marked_a__U61(a__isPLNatKind(V1),V1) ; } { Marked_a__isLNat(snd(V1)) > Marked_a__isPLNatKind(V1) ; } { Marked_a__isLNat(snd(V1)) > Marked_a__U81(a__isPLNatKind(V1),V1) ; } { Marked_a__isLNat(tail(V1)) > Marked_a__isLNatKind(V1) ; } { Marked_a__isLNat(tail(V1)) > Marked_a__U91(a__isLNatKind(V1),V1) ; } { Marked_a__isLNat(take(V1,V2)) > Marked_a__isNaturalKind(V1) ; } { Marked_a__isLNat(take(V1,V2)) > Marked_a__and(a__isNaturalKind(V1), isLNatKind(V2)) ; } { Marked_a__isLNat(take(V1,V2)) > Marked_a__U101(a__and(a__isNaturalKind(V1), isLNatKind(V2)),V1, V2) ; } { Marked_a__isNatural(s(V1)) > Marked_a__isNaturalKind(V1) ; } { Marked_a__isNatural(s(V1)) > Marked_a__U121(a__isNaturalKind(V1),V1) ; } { Marked_a__isNatural(head(V1)) > Marked_a__isLNatKind(V1) ; } { Marked_a__isNatural(head(V1)) > Marked_a__U111(a__isLNatKind(V1),V1) ; } { Marked_a__isNatural(sel(V1,V2)) > Marked_a__isNaturalKind(V1) ; } { Marked_a__isNatural(sel(V1,V2)) > Marked_a__and(a__isNaturalKind(V1), isLNatKind(V2)) ; } { Marked_a__isNatural(sel(V1,V2)) > Marked_a__U131(a__and(a__isNaturalKind(V1), isLNatKind(V2)),V1, V2) ; } { Marked_a__U102(tt,V2) > Marked_a__isLNat(V2) ; } { Marked_a__U101(tt,V1,V2) > Marked_a__isNatural(V1) ; } { Marked_a__U101(tt,V1,V2) > Marked_a__U102(a__isNatural(V1),V2) ; } { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(natsFrom(X)) > Marked_a__natsFrom(mark(X)) ; } { Marked_mark(natsFrom(X)) > Marked_mark(X) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(pair(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(pair(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(isNaturalKind(X)) > Marked_a__isNaturalKind(X) ; } { Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(isLNat(X)) > Marked_a__isLNat(X) ; } { Marked_mark(isLNatKind(X)) > Marked_a__isLNatKind(X) ; } { Marked_mark(afterNth(X1,X2)) > Marked_a__afterNth(mark(X1),mark(X2)) ; } { Marked_mark(afterNth(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(afterNth(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(fst(X)) > Marked_a__fst(mark(X)) ; } { Marked_mark(fst(X)) > Marked_mark(X) ; } { Marked_mark(snd(X)) > Marked_a__snd(mark(X)) ; } { Marked_mark(snd(X)) > Marked_mark(X) ; } { Marked_mark(tail(X)) > Marked_a__tail(mark(X)) ; } { Marked_mark(tail(X)) > Marked_mark(X) ; } { Marked_mark(take(X1,X2)) > Marked_a__take(mark(X1),mark(X2)) ; } { Marked_mark(take(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(take(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(head(X)) > Marked_a__head(mark(X)) ; } { Marked_mark(head(X)) > Marked_mark(X) ; } { Marked_mark(sel(X1,X2)) > Marked_a__sel(mark(X1),mark(X2)) ; } { Marked_mark(sel(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(sel(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(splitAt(X1,X2)) > Marked_a__splitAt(mark(X1),mark(X2)) ; } { Marked_mark(splitAt(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(splitAt(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(isNatural(X)) > Marked_a__isNatural(X) ; } { Marked_mark(U101(X1,X2,X3)) > Marked_a__U101(mark(X1),X2,X3) ; } { Marked_mark(U101(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U102(X1,X2)) > Marked_a__U102(mark(X1),X2) ; } { Marked_mark(U102(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U103(X)) > Marked_mark(X) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_a__U11(mark(X1),X2,X3) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U111(X1,X2)) > Marked_a__U111(mark(X1),X2) ; } { Marked_mark(U111(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U112(X)) > Marked_mark(X) ; } { Marked_mark(U121(X1,X2)) > Marked_a__U121(mark(X1),X2) ; } { Marked_mark(U121(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U122(X)) > Marked_mark(X) ; } { Marked_mark(U131(X1,X2,X3)) > Marked_a__U131(mark(X1),X2,X3) ; } { Marked_mark(U131(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U132(X1,X2)) > Marked_a__U132(mark(X1),X2) ; } { Marked_mark(U132(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U133(X)) > Marked_mark(X) ; } { Marked_mark(U141(X1,X2,X3)) > Marked_a__U141(mark(X1),X2,X3) ; } { Marked_mark(U141(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U142(X1,X2)) > Marked_a__U142(mark(X1),X2) ; } { Marked_mark(U142(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U143(X)) > Marked_mark(X) ; } { Marked_mark(U151(X1,X2,X3)) > Marked_a__U151(mark(X1),X2,X3) ; } { Marked_mark(U151(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U152(X1,X2)) > Marked_a__U152(mark(X1),X2) ; } { Marked_mark(U152(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U153(X)) > Marked_mark(X) ; } { Marked_mark(U161(X1,X2)) > Marked_a__U161(mark(X1),X2) ; } { Marked_mark(U161(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U171(X1,X2,X3)) > Marked_a__U171(mark(X1),X2,X3) ; } { Marked_mark(U171(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U181(X1,X2)) > Marked_a__U181(mark(X1),X2) ; } { Marked_mark(U181(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U191(X1,X2)) > Marked_a__U191(mark(X1),X2) ; } { Marked_mark(U191(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U201(X1,X2,X3,X4)) > Marked_a__U201(mark(X1),X2,X3,X4) ; } { Marked_mark(U201(X1,X2,X3,X4)) > Marked_mark(X1) ; } { Marked_mark(U202(X1,X2)) > Marked_a__U202(mark(X1),X2) ; } { Marked_mark(U202(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U21(X1,X2)) > Marked_a__U21(mark(X1),X2) ; } { Marked_mark(U21(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U211(X1,X2)) > Marked_a__U211(mark(X1),X2) ; } { Marked_mark(U211(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U221(X1,X2,X3)) > Marked_a__U221(mark(X1),X2,X3) ; } { Marked_mark(U221(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U31(X1,X2)) > Marked_a__U31(mark(X1),X2) ; } { Marked_mark(U31(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U41(X1,X2,X3)) > Marked_a__U41(mark(X1),X2,X3) ; } { Marked_mark(U41(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U42(X1,X2)) > Marked_a__U42(mark(X1),X2) ; } { Marked_mark(U42(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U43(X)) > Marked_mark(X) ; } { Marked_mark(U51(X1,X2,X3)) > Marked_a__U51(mark(X1),X2,X3) ; } { Marked_mark(U51(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U52(X1,X2)) > Marked_a__U52(mark(X1),X2) ; } { Marked_mark(U52(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U53(X)) > Marked_mark(X) ; } { Marked_mark(U61(X1,X2)) > Marked_a__U61(mark(X1),X2) ; } { Marked_mark(U61(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U62(X)) > Marked_mark(X) ; } { Marked_mark(isPLNat(X)) > Marked_a__isPLNat(X) ; } { Marked_mark(U71(X1,X2)) > Marked_a__U71(mark(X1),X2) ; } { Marked_mark(U71(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U72(X)) > Marked_mark(X) ; } { Marked_mark(U81(X1,X2)) > Marked_a__U81(mark(X1),X2) ; } { Marked_mark(U81(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U82(X)) > Marked_mark(X) ; } { Marked_mark(U91(X1,X2)) > Marked_a__U91(mark(X1),X2) ; } { Marked_mark(U91(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U92(X)) > Marked_mark(X) ; } { Marked_mark(isPLNatKind(X)) > Marked_a__isPLNatKind(X) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. Entering rpo_solver === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === Time out for these parameters. === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization === STOPING TIMER virtual === Time out for these parameters. === TIMER virtual : 50.000000 === trying sub matrices of size: 1 Matrix interpretation constraints generated. Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. Termination constraints generated. Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 50.000000 === === STOPING TIMER real === Sat timeout reached === STOPING TIMER virtual === No solution found for these parameters. No solution found for these constraints. APPLY CRITERIA (ID_CRIT) NOT SOLVED No proof found Cime worked for 149.373755 seconds (real time) Cime Exit Status: 0