- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] active(zeros) -> mark(cons(0,zeros)) [2] active(U11(tt,V1)) -> mark(U12(isNatList(V1))) [3] active(U12(tt)) -> mark(tt) [4] active(U21(tt,V1)) -> mark(U22(isNat(V1))) [5] active(U22(tt)) -> mark(tt) [6] active(U31(tt,V)) -> mark(U32(isNatList(V))) [7] active(U32(tt)) -> mark(tt) [8] active(U41(tt,V1,V2)) -> mark(U42(isNat(V1),V2)) [9] active(U42(tt,V2)) -> mark(U43(isNatIList(V2))) [10] active(U43(tt)) -> mark(tt) [11] active(U51(tt,V1,V2)) -> mark(U52(isNat(V1),V2)) [12] active(U52(tt,V2)) -> mark(U53(isNatList(V2))) [13] active(U53(tt)) -> mark(tt) [14] active(U61(tt,V1,V2)) -> mark(U62(isNat(V1),V2)) [15] active(U62(tt,V2)) -> mark(U63(isNatIList(V2))) [16] active(U63(tt)) -> mark(tt) [17] active(U71(tt,L)) -> mark(s(length(L))) [18] active(U81(tt)) -> mark(nil) [19] active(U91(tt,IL,M,N)) -> mark(cons(N,take(M,IL))) [20] active(and(tt,X)) -> mark(X) [21] active(isNat(0)) -> mark(tt) [22] active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) [23] active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) [24] active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) [25] active(isNatIList(zeros)) -> mark(tt) [26] active(isNatIList(cons(V1,V2))) -> mark(U41(and(isNatKind(V1),isNatIListKind(V2)),V1,V2)) [27] active(isNatIListKind(nil)) -> mark(tt) [28] active(isNatIListKind(zeros)) -> mark(tt) [29] active(isNatIListKind(cons(V1,V2))) -> mark(and(isNatKind(V1),isNatIListKind(V2))) [30] active(isNatIListKind(take(V1,V2))) -> mark(and(isNatKind(V1),isNatIListKind(V2))) [31] active(isNatKind(0)) -> mark(tt) [32] active(isNatKind(length(V1))) -> mark(isNatIListKind(V1)) [33] active(isNatKind(s(V1))) -> mark(isNatKind(V1)) [34] active(isNatList(nil)) -> mark(tt) [35] active(isNatList(cons(V1,V2))) -> mark(U51(and(isNatKind(V1),isNatIListKind(V2)),V1,V2)) [36] active(isNatList(take(V1,V2))) -> mark(U61(and(isNatKind(V1),isNatIListKind(V2)),V1,V2)) [37] active(length(nil)) -> mark(0) [38] active(length(cons(N,L))) -> mark(U71(and(and(isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))), L)) [39] active(take(0,IL)) -> mark(U81(and(isNatIList(IL),isNatIListKind(IL)))) [40] active(take(s(M),cons(N,IL))) -> mark(U91(and(and(isNatIList(IL),isNatIListKind(IL)), and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N)))), IL,M,N)) [41] mark(zeros) -> active(zeros) [42] mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) [43] mark(0) -> active(0) [44] mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) [45] mark(tt) -> active(tt) [46] mark(U12(X)) -> active(U12(mark(X))) [47] mark(isNatList(X)) -> active(isNatList(X)) [48] mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) [49] mark(U22(X)) -> active(U22(mark(X))) [50] mark(isNat(X)) -> active(isNat(X)) [51] mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) [52] mark(U32(X)) -> active(U32(mark(X))) [53] mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) [54] mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) [55] mark(U43(X)) -> active(U43(mark(X))) [56] mark(isNatIList(X)) -> active(isNatIList(X)) [57] mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) [58] mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) [59] mark(U53(X)) -> active(U53(mark(X))) [60] mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) [61] mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) [62] mark(U63(X)) -> active(U63(mark(X))) [63] mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) [64] mark(s(X)) -> active(s(mark(X))) [65] mark(length(X)) -> active(length(mark(X))) [66] mark(U81(X)) -> active(U81(mark(X))) [67] mark(nil) -> active(nil) [68] mark(U91(X1,X2,X3,X4)) -> active(U91(mark(X1),X2,X3,X4)) [69] mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) [70] mark(and(X1,X2)) -> active(and(mark(X1),X2)) [71] mark(isNatIListKind(X)) -> active(isNatIListKind(X)) [72] mark(isNatKind(X)) -> active(isNatKind(X)) [73] cons(mark(X1),X2) -> cons(X1,X2) [74] cons(X1,mark(X2)) -> cons(X1,X2) [75] cons(active(X1),X2) -> cons(X1,X2) [76] cons(X1,active(X2)) -> cons(X1,X2) [77] U11(mark(X1),X2) -> U11(X1,X2) [78] U11(X1,mark(X2)) -> U11(X1,X2) [79] U11(active(X1),X2) -> U11(X1,X2) [80] U11(X1,active(X2)) -> U11(X1,X2) [81] U12(mark(X)) -> U12(X) [82] U12(active(X)) -> U12(X) [83] isNatList(mark(X)) -> isNatList(X) [84] isNatList(active(X)) -> isNatList(X) [85] U21(mark(X1),X2) -> U21(X1,X2) [86] U21(X1,mark(X2)) -> U21(X1,X2) [87] U21(active(X1),X2) -> U21(X1,X2) [88] U21(X1,active(X2)) -> U21(X1,X2) [89] U22(mark(X)) -> U22(X) [90] U22(active(X)) -> U22(X) [91] isNat(mark(X)) -> isNat(X) [92] isNat(active(X)) -> isNat(X) [93] U31(mark(X1),X2) -> U31(X1,X2) [94] U31(X1,mark(X2)) -> U31(X1,X2) [95] U31(active(X1),X2) -> U31(X1,X2) [96] U31(X1,active(X2)) -> U31(X1,X2) [97] U32(mark(X)) -> U32(X) [98] U32(active(X)) -> U32(X) [99] U41(mark(X1),X2,X3) -> U41(X1,X2,X3) [100] U41(X1,mark(X2),X3) -> U41(X1,X2,X3) [101] U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) [102] U41(active(X1),X2,X3) -> U41(X1,X2,X3) [103] U41(X1,active(X2),X3) -> U41(X1,X2,X3) [104] U41(X1,X2,active(X3)) -> U41(X1,X2,X3) [105] U42(mark(X1),X2) -> U42(X1,X2) [106] U42(X1,mark(X2)) -> U42(X1,X2) [107] U42(active(X1),X2) -> U42(X1,X2) [108] U42(X1,active(X2)) -> U42(X1,X2) [109] U43(mark(X)) -> U43(X) [110] U43(active(X)) -> U43(X) [111] isNatIList(mark(X)) -> isNatIList(X) [112] isNatIList(active(X)) -> isNatIList(X) [113] U51(mark(X1),X2,X3) -> U51(X1,X2,X3) [114] U51(X1,mark(X2),X3) -> U51(X1,X2,X3) [115] U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) [116] U51(active(X1),X2,X3) -> U51(X1,X2,X3) [117] U51(X1,active(X2),X3) -> U51(X1,X2,X3) [118] U51(X1,X2,active(X3)) -> U51(X1,X2,X3) [119] U52(mark(X1),X2) -> U52(X1,X2) [120] U52(X1,mark(X2)) -> U52(X1,X2) [121] U52(active(X1),X2) -> U52(X1,X2) [122] U52(X1,active(X2)) -> U52(X1,X2) [123] U53(mark(X)) -> U53(X) [124] U53(active(X)) -> U53(X) [125] U61(mark(X1),X2,X3) -> U61(X1,X2,X3) [126] U61(X1,mark(X2),X3) -> U61(X1,X2,X3) [127] U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) [128] U61(active(X1),X2,X3) -> U61(X1,X2,X3) [129] U61(X1,active(X2),X3) -> U61(X1,X2,X3) [130] U61(X1,X2,active(X3)) -> U61(X1,X2,X3) [131] U62(mark(X1),X2) -> U62(X1,X2) [132] U62(X1,mark(X2)) -> U62(X1,X2) [133] U62(active(X1),X2) -> U62(X1,X2) [134] U62(X1,active(X2)) -> U62(X1,X2) [135] U63(mark(X)) -> U63(X) [136] U63(active(X)) -> U63(X) [137] U71(mark(X1),X2) -> U71(X1,X2) [138] U71(X1,mark(X2)) -> U71(X1,X2) [139] U71(active(X1),X2) -> U71(X1,X2) [140] U71(X1,active(X2)) -> U71(X1,X2) [141] s(mark(X)) -> s(X) [142] s(active(X)) -> s(X) [143] length(mark(X)) -> length(X) [144] length(active(X)) -> length(X) [145] U81(mark(X)) -> U81(X) [146] U81(active(X)) -> U81(X) [147] U91(mark(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) [148] U91(X1,mark(X2),X3,X4) -> U91(X1,X2,X3,X4) [149] U91(X1,X2,mark(X3),X4) -> U91(X1,X2,X3,X4) [150] U91(X1,X2,X3,mark(X4)) -> U91(X1,X2,X3,X4) [151] U91(active(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) [152] U91(X1,active(X2),X3,X4) -> U91(X1,X2,X3,X4) [153] U91(X1,X2,active(X3),X4) -> U91(X1,X2,X3,X4) [154] U91(X1,X2,X3,active(X4)) -> U91(X1,X2,X3,X4) [155] take(mark(X1),X2) -> take(X1,X2) [156] take(X1,mark(X2)) -> take(X1,X2) [157] take(active(X1),X2) -> take(X1,X2) [158] take(X1,active(X2)) -> take(X1,X2) [159] and(mark(X1),X2) -> and(X1,X2) [160] and(X1,mark(X2)) -> and(X1,X2) [161] and(active(X1),X2) -> and(X1,X2) [162] and(X1,active(X2)) -> and(X1,X2) [163] isNatIListKind(mark(X)) -> isNatIListKind(X) [164] isNatIListKind(active(X)) -> isNatIListKind(X) [165] isNatKind(mark(X)) -> isNatKind(X) [166] isNatKind(active(X)) -> isNatKind(X) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 29 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) ; mark(0) >= active(0) ; mark(zeros) >= active(zeros) ; mark(U12(X)) >= active(U12(mark(X))) ; mark(isNatList(X)) >= active(isNatList(X)) ; mark(U11(X1,X2)) >= active(U11(mark(X1),X2)) ; mark(tt) >= active(tt) ; mark(U22(X)) >= active(U22(mark(X))) ; mark(isNat(X)) >= active(isNat(X)) ; mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) ; mark(U32(X)) >= active(U32(mark(X))) ; mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) ; mark(U42(X1,X2)) >= active(U42(mark(X1),X2)) ; mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) ; mark(U43(X)) >= active(U43(mark(X))) ; mark(isNatIList(X)) >= active(isNatIList(X)) ; mark(U52(X1,X2)) >= active(U52(mark(X1),X2)) ; mark(U51(X1,X2,X3)) >= active(U51(mark(X1),X2,X3)) ; mark(U53(X)) >= active(U53(mark(X))) ; mark(U62(X1,X2)) >= active(U62(mark(X1),X2)) ; mark(U61(X1,X2,X3)) >= active(U61(mark(X1),X2,X3)) ; mark(U63(X)) >= active(U63(mark(X))) ; mark(s(X)) >= active(s(mark(X))) ; mark(length(X)) >= active(length(mark(X))) ; mark(U71(X1,X2)) >= active(U71(mark(X1),X2)) ; mark(nil) >= active(nil) ; mark(U81(X)) >= active(U81(mark(X))) ; mark(take(X1,X2)) >= active(take(mark(X1),mark(X2))) ; mark(U91(X1,X2,X3,X4)) >= active(U91(mark(X1),X2,X3,X4)) ; mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(isNatIListKind(X)) >= active(isNatIListKind(X)) ; mark(isNatKind(X)) >= active(isNatKind(X)) ; cons(mark(X1),X2) >= cons(X1,X2) ; cons(active(X1),X2) >= cons(X1,X2) ; cons(X1,mark(X2)) >= cons(X1,X2) ; cons(X1,active(X2)) >= cons(X1,X2) ; active(zeros) >= mark(cons(0,zeros)) ; active(U12(tt)) >= mark(tt) ; active(isNatList(cons(V1,V2))) >= mark(U51(and(isNatKind(V1), isNatIListKind(V2)),V1, V2)) ; active(isNatList(nil)) >= mark(tt) ; active(isNatList(take(V1,V2))) >= mark(U61(and(isNatKind(V1), isNatIListKind(V2)),V1, V2)) ; active(U11(tt,V1)) >= mark(U12(isNatList(V1))) ; active(U22(tt)) >= mark(tt) ; active(isNat(0)) >= mark(tt) ; active(isNat(s(V1))) >= mark(U21(isNatKind(V1),V1)) ; active(isNat(length(V1))) >= mark(U11(isNatIListKind(V1),V1)) ; active(U21(tt,V1)) >= mark(U22(isNat(V1))) ; active(U32(tt)) >= mark(tt) ; active(U31(tt,V)) >= mark(U32(isNatList(V))) ; active(U42(tt,V2)) >= mark(U43(isNatIList(V2))) ; active(U41(tt,V1,V2)) >= mark(U42(isNat(V1),V2)) ; active(U43(tt)) >= mark(tt) ; active(isNatIList(cons(V1,V2))) >= mark(U41(and(isNatKind(V1), isNatIListKind(V2)),V1, V2)) ; active(isNatIList(zeros)) >= mark(tt) ; active(isNatIList(V)) >= mark(U31(isNatIListKind(V),V)) ; active(U52(tt,V2)) >= mark(U53(isNatList(V2))) ; active(U51(tt,V1,V2)) >= mark(U52(isNat(V1),V2)) ; active(U53(tt)) >= mark(tt) ; active(U62(tt,V2)) >= mark(U63(isNatIList(V2))) ; active(U61(tt,V1,V2)) >= mark(U62(isNat(V1),V2)) ; active(U63(tt)) >= mark(tt) ; active(length(cons(N,L))) >= mark(U71(and(and(isNatList(L),isNatIListKind(L)), and(isNat(N),isNatKind(N))), L)) ; active(length(nil)) >= mark(0) ; active(U71(tt,L)) >= mark(s(length(L))) ; active(U81(tt)) >= mark(nil) ; active(take(0,IL)) >= mark(U81(and(isNatIList(IL),isNatIListKind(IL)))) ; active(take(s(M),cons(N,IL))) >= mark(U91(and(and(isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N)))), IL,M,N)) ; active(U91(tt,IL,M,N)) >= mark(cons(N,take(M,IL))) ; active(and(tt,X)) >= mark(X) ; active(isNatIListKind(cons(V1,V2))) >= mark(and(isNatKind(V1), isNatIListKind(V2))) ; active(isNatIListKind(zeros)) >= mark(tt) ; active(isNatIListKind(nil)) >= mark(tt) ; active(isNatIListKind(take(V1,V2))) >= mark(and(isNatKind(V1), isNatIListKind(V2))) ; active(isNatKind(0)) >= mark(tt) ; active(isNatKind(s(V1))) >= mark(isNatKind(V1)) ; active(isNatKind(length(V1))) >= mark(isNatIListKind(V1)) ; U12(mark(X)) >= U12(X) ; U12(active(X)) >= U12(X) ; isNatList(mark(X)) >= isNatList(X) ; isNatList(active(X)) >= isNatList(X) ; U11(mark(X1),X2) >= U11(X1,X2) ; U11(active(X1),X2) >= U11(X1,X2) ; U11(X1,mark(X2)) >= U11(X1,X2) ; U11(X1,active(X2)) >= U11(X1,X2) ; U22(mark(X)) >= U22(X) ; U22(active(X)) >= U22(X) ; isNat(mark(X)) >= isNat(X) ; isNat(active(X)) >= isNat(X) ; U21(mark(X1),X2) >= U21(X1,X2) ; U21(active(X1),X2) >= U21(X1,X2) ; U21(X1,mark(X2)) >= U21(X1,X2) ; U21(X1,active(X2)) >= U21(X1,X2) ; U32(mark(X)) >= U32(X) ; U32(active(X)) >= U32(X) ; U31(mark(X1),X2) >= U31(X1,X2) ; U31(active(X1),X2) >= U31(X1,X2) ; U31(X1,mark(X2)) >= U31(X1,X2) ; U31(X1,active(X2)) >= U31(X1,X2) ; U42(mark(X1),X2) >= U42(X1,X2) ; U42(active(X1),X2) >= U42(X1,X2) ; U42(X1,mark(X2)) >= U42(X1,X2) ; U42(X1,active(X2)) >= U42(X1,X2) ; U41(mark(X1),X2,X3) >= U41(X1,X2,X3) ; U41(active(X1),X2,X3) >= U41(X1,X2,X3) ; U41(X1,mark(X2),X3) >= U41(X1,X2,X3) ; U41(X1,active(X2),X3) >= U41(X1,X2,X3) ; U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) ; U41(X1,X2,active(X3)) >= U41(X1,X2,X3) ; U43(mark(X)) >= U43(X) ; U43(active(X)) >= U43(X) ; isNatIList(mark(X)) >= isNatIList(X) ; isNatIList(active(X)) >= isNatIList(X) ; U52(mark(X1),X2) >= U52(X1,X2) ; U52(active(X1),X2) >= U52(X1,X2) ; U52(X1,mark(X2)) >= U52(X1,X2) ; U52(X1,active(X2)) >= U52(X1,X2) ; U51(mark(X1),X2,X3) >= U51(X1,X2,X3) ; U51(active(X1),X2,X3) >= U51(X1,X2,X3) ; U51(X1,mark(X2),X3) >= U51(X1,X2,X3) ; U51(X1,active(X2),X3) >= U51(X1,X2,X3) ; U51(X1,X2,mark(X3)) >= U51(X1,X2,X3) ; U51(X1,X2,active(X3)) >= U51(X1,X2,X3) ; U53(mark(X)) >= U53(X) ; U53(active(X)) >= U53(X) ; U62(mark(X1),X2) >= U62(X1,X2) ; U62(active(X1),X2) >= U62(X1,X2) ; U62(X1,mark(X2)) >= U62(X1,X2) ; U62(X1,active(X2)) >= U62(X1,X2) ; U61(mark(X1),X2,X3) >= U61(X1,X2,X3) ; U61(active(X1),X2,X3) >= U61(X1,X2,X3) ; U61(X1,mark(X2),X3) >= U61(X1,X2,X3) ; U61(X1,active(X2),X3) >= U61(X1,X2,X3) ; U61(X1,X2,mark(X3)) >= U61(X1,X2,X3) ; U61(X1,X2,active(X3)) >= U61(X1,X2,X3) ; U63(mark(X)) >= U63(X) ; U63(active(X)) >= U63(X) ; s(mark(X)) >= s(X) ; s(active(X)) >= s(X) ; length(mark(X)) >= length(X) ; length(active(X)) >= length(X) ; U71(mark(X1),X2) >= U71(X1,X2) ; U71(active(X1),X2) >= U71(X1,X2) ; U71(X1,mark(X2)) >= U71(X1,X2) ; U71(X1,active(X2)) >= U71(X1,X2) ; U81(mark(X)) >= U81(X) ; U81(active(X)) >= U81(X) ; take(mark(X1),X2) >= take(X1,X2) ; take(active(X1),X2) >= take(X1,X2) ; take(X1,mark(X2)) >= take(X1,X2) ; take(X1,active(X2)) >= take(X1,X2) ; U91(mark(X1),X2,X3,X4) >= U91(X1,X2,X3,X4) ; U91(active(X1),X2,X3,X4) >= U91(X1,X2,X3,X4) ; U91(X1,mark(X2),X3,X4) >= U91(X1,X2,X3,X4) ; U91(X1,active(X2),X3,X4) >= U91(X1,X2,X3,X4) ; U91(X1,X2,mark(X3),X4) >= U91(X1,X2,X3,X4) ; U91(X1,X2,active(X3),X4) >= U91(X1,X2,X3,X4) ; U91(X1,X2,X3,mark(X4)) >= U91(X1,X2,X3,X4) ; U91(X1,X2,X3,active(X4)) >= U91(X1,X2,X3,X4) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; isNatIListKind(mark(X)) >= isNatIListKind(X) ; isNatIListKind(active(X)) >= isNatIListKind(X) ; isNatKind(mark(X)) >= isNatKind(X) ; isNatKind(active(X)) >= isNatKind(X) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(cons(X1,X2)) >= Marked_active(cons(mark(X1),X2)) ; Marked_mark(zeros) >= Marked_active(zeros) ; Marked_mark(U12(X)) >= Marked_mark(X) ; Marked_mark(U12(X)) >= Marked_active(U12(mark(X))) ; Marked_mark(isNatList(X)) >= Marked_active(isNatList(X)) ; Marked_mark(U11(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2)) >= Marked_active(U11(mark(X1),X2)) ; Marked_mark(U22(X)) >= Marked_mark(X) ; Marked_mark(U22(X)) >= Marked_active(U22(mark(X))) ; Marked_mark(isNat(X)) >= Marked_active(isNat(X)) ; Marked_mark(U21(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U21(X1,X2)) >= Marked_active(U21(mark(X1),X2)) ; Marked_mark(U32(X)) >= Marked_mark(X) ; Marked_mark(U32(X)) >= Marked_active(U32(mark(X))) ; Marked_mark(U31(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) ; Marked_mark(U42(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U42(X1,X2)) >= Marked_active(U42(mark(X1),X2)) ; Marked_mark(U41(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U41(X1,X2,X3)) >= Marked_active(U41(mark(X1),X2,X3)) ; Marked_mark(U43(X)) >= Marked_mark(X) ; Marked_mark(U43(X)) >= Marked_active(U43(mark(X))) ; Marked_mark(isNatIList(X)) >= Marked_active(isNatIList(X)) ; Marked_mark(U52(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U52(X1,X2)) >= Marked_active(U52(mark(X1),X2)) ; Marked_mark(U51(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U51(X1,X2,X3)) >= Marked_active(U51(mark(X1),X2,X3)) ; Marked_mark(U53(X)) >= Marked_mark(X) ; Marked_mark(U53(X)) >= Marked_active(U53(mark(X))) ; Marked_mark(U62(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U62(X1,X2)) >= Marked_active(U62(mark(X1),X2)) ; Marked_mark(U61(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U61(X1,X2,X3)) >= Marked_active(U61(mark(X1),X2,X3)) ; Marked_mark(U63(X)) >= Marked_mark(X) ; Marked_mark(U63(X)) >= Marked_active(U63(mark(X))) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(s(X)) >= Marked_active(s(mark(X))) ; Marked_mark(length(X)) >= Marked_mark(X) ; Marked_mark(length(X)) >= Marked_active(length(mark(X))) ; Marked_mark(U71(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U71(X1,X2)) >= Marked_active(U71(mark(X1),X2)) ; Marked_mark(U81(X)) >= Marked_mark(X) ; Marked_mark(U81(X)) >= Marked_active(U81(mark(X))) ; Marked_mark(take(X1,X2)) >= Marked_mark(X1) ; Marked_mark(take(X1,X2)) >= Marked_mark(X2) ; Marked_mark(take(X1,X2)) >= Marked_active(take(mark(X1),mark(X2))) ; Marked_mark(U91(X1,X2,X3,X4)) >= Marked_mark(X1) ; Marked_mark(U91(X1,X2,X3,X4)) >= Marked_active(U91(mark(X1),X2,X3,X4)) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(isNatIListKind(X)) >= Marked_active(isNatIListKind(X)) ; Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) ; Marked_active(zeros) >= Marked_mark(cons(0,zeros)) ; Marked_active(isNatList(cons(V1,V2))) >= Marked_mark(U51(and(isNatKind(V1), isNatIListKind(V2)), V1,V2)) ; Marked_active(isNatList(take(V1,V2))) >= Marked_mark(U61(and(isNatKind(V1), isNatIListKind(V2)), V1,V2)) ; Marked_active(U11(tt,V1)) >= Marked_mark(U12(isNatList(V1))) ; Marked_active(isNat(s(V1))) >= Marked_mark(U21(isNatKind(V1),V1)) ; Marked_active(isNat(length(V1))) >= Marked_mark(U11(isNatIListKind(V1),V1)) ; Marked_active(U21(tt,V1)) >= Marked_mark(U22(isNat(V1))) ; Marked_active(U31(tt,V)) >= Marked_mark(U32(isNatList(V))) ; Marked_active(U42(tt,V2)) >= Marked_mark(U43(isNatIList(V2))) ; Marked_active(U41(tt,V1,V2)) >= Marked_mark(U42(isNat(V1),V2)) ; Marked_active(isNatIList(cons(V1,V2))) >= Marked_mark(U41(and(isNatKind(V1), isNatIListKind(V2)), V1,V2)) ; Marked_active(isNatIList(V)) >= Marked_mark(U31(isNatIListKind(V),V)) ; Marked_active(U52(tt,V2)) >= Marked_mark(U53(isNatList(V2))) ; Marked_active(U51(tt,V1,V2)) >= Marked_mark(U52(isNat(V1),V2)) ; Marked_active(U62(tt,V2)) >= Marked_mark(U63(isNatIList(V2))) ; Marked_active(U61(tt,V1,V2)) >= Marked_mark(U62(isNat(V1),V2)) ; Marked_active(length(cons(N,L))) >= Marked_mark(U71(and(and(isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L)) ; Marked_active(U71(tt,L)) >= Marked_mark(s(length(L))) ; Marked_active(take(0,IL)) >= Marked_mark(U81(and(isNatIList(IL), isNatIListKind(IL)))) ; Marked_active(take(s(M),cons(N,IL))) >= Marked_mark(U91(and(and(isNatIList( IL), isNatIListKind( IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), IL,M,N)) ; Marked_active(U91(tt,IL,M,N)) >= Marked_mark(cons(N,take(M,IL))) ; Marked_active(and(tt,X)) >= Marked_mark(X) ; Marked_active(isNatIListKind(cons(V1,V2))) >= Marked_mark(and(isNatKind(V1), isNatIListKind(V2))) ; Marked_active(isNatIListKind(take(V1,V2))) >= Marked_mark(and(isNatKind(V1), isNatIListKind(V2))) ; Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) ; Marked_active(isNatKind(length(V1))) >= Marked_mark(isNatIListKind(V1)) ; } + Disjunctions:{ { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(cons(X1,X2)) > Marked_active(cons(mark(X1),X2)) ; } { Marked_mark(zeros) > Marked_active(zeros) ; } { Marked_mark(U12(X)) > Marked_mark(X) ; } { Marked_mark(U12(X)) > Marked_active(U12(mark(X))) ; } { Marked_mark(isNatList(X)) > Marked_active(isNatList(X)) ; } { Marked_mark(U11(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2)) > Marked_active(U11(mark(X1),X2)) ; } { Marked_mark(U22(X)) > Marked_mark(X) ; } { Marked_mark(U22(X)) > Marked_active(U22(mark(X))) ; } { Marked_mark(isNat(X)) > Marked_active(isNat(X)) ; } { Marked_mark(U21(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U21(X1,X2)) > Marked_active(U21(mark(X1),X2)) ; } { Marked_mark(U32(X)) > Marked_mark(X) ; } { Marked_mark(U32(X)) > Marked_active(U32(mark(X))) ; } { Marked_mark(U31(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U31(X1,X2)) > Marked_active(U31(mark(X1),X2)) ; } { Marked_mark(U42(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U42(X1,X2)) > Marked_active(U42(mark(X1),X2)) ; } { Marked_mark(U41(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U41(X1,X2,X3)) > Marked_active(U41(mark(X1),X2,X3)) ; } { Marked_mark(U43(X)) > Marked_mark(X) ; } { Marked_mark(U43(X)) > Marked_active(U43(mark(X))) ; } { Marked_mark(isNatIList(X)) > Marked_active(isNatIList(X)) ; } { Marked_mark(U52(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U52(X1,X2)) > Marked_active(U52(mark(X1),X2)) ; } { Marked_mark(U51(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U51(X1,X2,X3)) > Marked_active(U51(mark(X1),X2,X3)) ; } { Marked_mark(U53(X)) > Marked_mark(X) ; } { Marked_mark(U53(X)) > Marked_active(U53(mark(X))) ; } { Marked_mark(U62(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U62(X1,X2)) > Marked_active(U62(mark(X1),X2)) ; } { Marked_mark(U61(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U61(X1,X2,X3)) > Marked_active(U61(mark(X1),X2,X3)) ; } { Marked_mark(U63(X)) > Marked_mark(X) ; } { Marked_mark(U63(X)) > Marked_active(U63(mark(X))) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(s(X)) > Marked_active(s(mark(X))) ; } { Marked_mark(length(X)) > Marked_mark(X) ; } { Marked_mark(length(X)) > Marked_active(length(mark(X))) ; } { Marked_mark(U71(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U71(X1,X2)) > Marked_active(U71(mark(X1),X2)) ; } { Marked_mark(U81(X)) > Marked_mark(X) ; } { Marked_mark(U81(X)) > Marked_active(U81(mark(X))) ; } { Marked_mark(take(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(take(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(take(X1,X2)) > Marked_active(take(mark(X1),mark(X2))) ; } { Marked_mark(U91(X1,X2,X3,X4)) > Marked_mark(X1) ; } { Marked_mark(U91(X1,X2,X3,X4)) > Marked_active(U91(mark(X1),X2,X3,X4)) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(isNatIListKind(X)) > Marked_active(isNatIListKind(X)) ; } { Marked_mark(isNatKind(X)) > Marked_active(isNatKind(X)) ; } { Marked_active(zeros) > Marked_mark(cons(0,zeros)) ; } { Marked_active(isNatList(cons(V1,V2))) > Marked_mark(U51(and(isNatKind(V1), isNatIListKind(V2)), V1,V2)) ; } { Marked_active(isNatList(take(V1,V2))) > Marked_mark(U61(and(isNatKind(V1), isNatIListKind(V2)), V1,V2)) ; } { Marked_active(U11(tt,V1)) > Marked_mark(U12(isNatList(V1))) ; } { Marked_active(isNat(s(V1))) > Marked_mark(U21(isNatKind(V1),V1)) ; } { Marked_active(isNat(length(V1))) > Marked_mark(U11(isNatIListKind(V1),V1)) ; } { Marked_active(U21(tt,V1)) > Marked_mark(U22(isNat(V1))) ; } { Marked_active(U31(tt,V)) > Marked_mark(U32(isNatList(V))) ; } { Marked_active(U42(tt,V2)) > Marked_mark(U43(isNatIList(V2))) ; } { Marked_active(U41(tt,V1,V2)) > Marked_mark(U42(isNat(V1),V2)) ; } { Marked_active(isNatIList(cons(V1,V2))) > Marked_mark(U41(and(isNatKind(V1), isNatIListKind(V2)), V1,V2)) ; } { Marked_active(isNatIList(V)) > Marked_mark(U31(isNatIListKind(V),V)) ; } { Marked_active(U52(tt,V2)) > Marked_mark(U53(isNatList(V2))) ; } { Marked_active(U51(tt,V1,V2)) > Marked_mark(U52(isNat(V1),V2)) ; } { Marked_active(U62(tt,V2)) > Marked_mark(U63(isNatIList(V2))) ; } { Marked_active(U61(tt,V1,V2)) > Marked_mark(U62(isNat(V1),V2)) ; } { Marked_active(length(cons(N,L))) > Marked_mark(U71(and(and(isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L)) ; } { Marked_active(U71(tt,L)) > Marked_mark(s(length(L))) ; } { Marked_active(take(0,IL)) > Marked_mark(U81(and(isNatIList(IL), isNatIListKind(IL)))) ; } { Marked_active(take(s(M),cons(N,IL))) > Marked_mark(U91(and(and(isNatIList(IL), isNatIListKind( IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), IL,M,N)) ; } { Marked_active(U91(tt,IL,M,N)) > Marked_mark(cons(N,take(M,IL))) ; } { Marked_active(and(tt,X)) > Marked_mark(X) ; } { Marked_active(isNatIListKind(cons(V1,V2))) > Marked_mark(and(isNatKind(V1), isNatIListKind(V2))) ; } { Marked_active(isNatIListKind(take(V1,V2))) > Marked_mark(and(isNatKind(V1), isNatIListKind(V2))) ; } { Marked_active(isNatKind(s(V1))) > Marked_mark(isNatKind(V1)) ; } { Marked_active(isNatKind(length(V1))) > Marked_mark(isNatIListKind(V1)) ; } } === 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 Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(zeros) >= active(zeros) constraint: mark(U12(X)) >= active(U12(mark(X))) constraint: mark(isNatList(X)) >= active(isNatList(X)) constraint: mark(U11(X1,X2)) >= active(U11(mark(X1),X2)) constraint: mark(tt) >= active(tt) constraint: mark(U22(X)) >= active(U22(mark(X))) constraint: mark(isNat(X)) >= active(isNat(X)) constraint: mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) constraint: mark(U32(X)) >= active(U32(mark(X))) constraint: mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) constraint: mark(U42(X1,X2)) >= active(U42(mark(X1),X2)) constraint: mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) constraint: mark(U43(X)) >= active(U43(mark(X))) constraint: mark(isNatIList(X)) >= active(isNatIList(X)) constraint: mark(U52(X1,X2)) >= active(U52(mark(X1),X2)) constraint: mark(U51(X1,X2,X3)) >= active(U51(mark(X1),X2,X3)) constraint: mark(U53(X)) >= active(U53(mark(X))) constraint: mark(U62(X1,X2)) >= active(U62(mark(X1),X2)) constraint: mark(U61(X1,X2,X3)) >= active(U61(mark(X1),X2,X3)) constraint: mark(U63(X)) >= active(U63(mark(X))) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(length(X)) >= active(length(mark(X))) constraint: mark(U71(X1,X2)) >= active(U71(mark(X1),X2)) constraint: mark(nil) >= active(nil) constraint: mark(U81(X)) >= active(U81(mark(X))) constraint: mark(take(X1,X2)) >= active(take(mark(X1),mark(X2))) constraint: mark(U91(X1,X2,X3,X4)) >= active(U91(mark(X1),X2,X3,X4)) constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(isNatIListKind(X)) >= active(isNatIListKind(X)) constraint: mark(isNatKind(X)) >= active(isNatKind(X)) constraint: cons(mark(X1),X2) >= cons(X1,X2) constraint: cons(active(X1),X2) >= cons(X1,X2) constraint: cons(X1,mark(X2)) >= cons(X1,X2) constraint: cons(X1,active(X2)) >= cons(X1,X2) constraint: active(zeros) >= mark(cons(0,zeros)) constraint: active(U12(tt)) >= mark(tt) constraint: active(isNatList(cons(V1,V2))) >= mark(U51(and(isNatKind(V1), isNatIListKind(V2)), V1,V2)) constraint: active(isNatList(nil)) >= mark(tt) constraint: active(isNatList(take(V1,V2))) >= mark(U61(and(isNatKind(V1), isNatIListKind(V2)), V1,V2)) constraint: active(U11(tt,V1)) >= mark(U12(isNatList(V1))) constraint: active(U22(tt)) >= mark(tt) constraint: active(isNat(0)) >= mark(tt) constraint: active(isNat(s(V1))) >= mark(U21(isNatKind(V1),V1)) constraint: active(isNat(length(V1))) >= mark(U11(isNatIListKind(V1),V1)) constraint: active(U21(tt,V1)) >= mark(U22(isNat(V1))) constraint: active(U32(tt)) >= mark(tt) constraint: active(U31(tt,V)) >= mark(U32(isNatList(V))) constraint: active(U42(tt,V2)) >= mark(U43(isNatIList(V2))) constraint: active(U41(tt,V1,V2)) >= mark(U42(isNat(V1),V2)) constraint: active(U43(tt)) >= mark(tt) constraint: active(isNatIList(cons(V1,V2))) >= mark(U41(and(isNatKind(V1), isNatIListKind(V2)), V1,V2)) constraint: active(isNatIList(zeros)) >= mark(tt) constraint: active(isNatIList(V)) >= mark(U31(isNatIListKind(V),V)) constraint: active(U52(tt,V2)) >= mark(U53(isNatList(V2))) constraint: active(U51(tt,V1,V2)) >= mark(U52(isNat(V1),V2)) constraint: active(U53(tt)) >= mark(tt) constraint: active(U62(tt,V2)) >= mark(U63(isNatIList(V2))) constraint: active(U61(tt,V1,V2)) >= mark(U62(isNat(V1),V2)) constraint: active(U63(tt)) >= mark(tt) constraint: active(length(cons(N,L))) >= mark(U71(and(and(isNatList(L), isNatIListKind(L)), and(isNat(N),isNatKind(N))), L)) constraint: active(length(nil)) >= mark(0) constraint: active(U71(tt,L)) >= mark(s(length(L))) constraint: active(U81(tt)) >= mark(nil) constraint: active(take(0,IL)) >= mark(U81(and(isNatIList(IL), isNatIListKind(IL)))) constraint: active(take(s(M),cons(N,IL))) >= mark(U91(and(and(isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), IL,M,N)) constraint: active(U91(tt,IL,M,N)) >= mark(cons(N,take(M,IL))) constraint: active(and(tt,X)) >= mark(X) constraint: active(isNatIListKind(cons(V1,V2))) >= mark(and(isNatKind(V1), isNatIListKind(V2))) constraint: active(isNatIListKind(zeros)) >= mark(tt) constraint: active(isNatIListKind(nil)) >= mark(tt) constraint: active(isNatIListKind(take(V1,V2))) >= mark(and(isNatKind(V1), isNatIListKind(V2))) constraint: active(isNatKind(0)) >= mark(tt) constraint: active(isNatKind(s(V1))) >= mark(isNatKind(V1)) constraint: active(isNatKind(length(V1))) >= mark(isNatIListKind(V1)) constraint: U12(mark(X)) >= U12(X) constraint: U12(active(X)) >= U12(X) constraint: isNatList(mark(X)) >= isNatList(X) constraint: isNatList(active(X)) >= isNatList(X) constraint: U11(mark(X1),X2) >= U11(X1,X2) constraint: U11(active(X1),X2) >= U11(X1,X2) constraint: U11(X1,mark(X2)) >= U11(X1,X2) constraint: U11(X1,active(X2)) >= U11(X1,X2) constraint: U22(mark(X)) >= U22(X) constraint: U22(active(X)) >= U22(X) constraint: isNat(mark(X)) >= isNat(X) constraint: isNat(active(X)) >= isNat(X) constraint: U21(mark(X1),X2) >= U21(X1,X2) constraint: U21(active(X1),X2) >= U21(X1,X2) constraint: U21(X1,mark(X2)) >= U21(X1,X2) constraint: U21(X1,active(X2)) >= U21(X1,X2) constraint: U32(mark(X)) >= U32(X) constraint: U32(active(X)) >= U32(X) constraint: U31(mark(X1),X2) >= U31(X1,X2) constraint: U31(active(X1),X2) >= U31(X1,X2) constraint: U31(X1,mark(X2)) >= U31(X1,X2) constraint: U31(X1,active(X2)) >= U31(X1,X2) constraint: U42(mark(X1),X2) >= U42(X1,X2) constraint: U42(active(X1),X2) >= U42(X1,X2) constraint: U42(X1,mark(X2)) >= U42(X1,X2) constraint: U42(X1,active(X2)) >= U42(X1,X2) constraint: U41(mark(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(active(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(X1,mark(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,active(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) constraint: U41(X1,X2,active(X3)) >= U41(X1,X2,X3) constraint: U43(mark(X)) >= U43(X) constraint: U43(active(X)) >= U43(X) constraint: isNatIList(mark(X)) >= isNatIList(X) constraint: isNatIList(active(X)) >= isNatIList(X) constraint: U52(mark(X1),X2) >= U52(X1,X2) constraint: U52(active(X1),X2) >= U52(X1,X2) constraint: U52(X1,mark(X2)) >= U52(X1,X2) constraint: U52(X1,active(X2)) >= U52(X1,X2) constraint: U51(mark(X1),X2,X3) >= U51(X1,X2,X3) constraint: U51(active(X1),X2,X3) >= U51(X1,X2,X3) constraint: U51(X1,mark(X2),X3) >= U51(X1,X2,X3) constraint: U51(X1,active(X2),X3) >= U51(X1,X2,X3) constraint: U51(X1,X2,mark(X3)) >= U51(X1,X2,X3) constraint: U51(X1,X2,active(X3)) >= U51(X1,X2,X3) constraint: U53(mark(X)) >= U53(X) constraint: U53(active(X)) >= U53(X) constraint: U62(mark(X1),X2) >= U62(X1,X2) constraint: U62(active(X1),X2) >= U62(X1,X2) constraint: U62(X1,mark(X2)) >= U62(X1,X2) constraint: U62(X1,active(X2)) >= U62(X1,X2) constraint: U61(mark(X1),X2,X3) >= U61(X1,X2,X3) constraint: U61(active(X1),X2,X3) >= U61(X1,X2,X3) constraint: U61(X1,mark(X2),X3) >= U61(X1,X2,X3) constraint: U61(X1,active(X2),X3) >= U61(X1,X2,X3) constraint: U61(X1,X2,mark(X3)) >= U61(X1,X2,X3) constraint: U61(X1,X2,active(X3)) >= U61(X1,X2,X3) constraint: U63(mark(X)) >= U63(X) constraint: U63(active(X)) >= U63(X) constraint: s(mark(X)) >= s(X) constraint: s(active(X)) >= s(X) constraint: length(mark(X)) >= length(X) constraint: length(active(X)) >= length(X) constraint: U71(mark(X1),X2) >= U71(X1,X2) constraint: U71(active(X1),X2) >= U71(X1,X2) constraint: U71(X1,mark(X2)) >= U71(X1,X2) constraint: U71(X1,active(X2)) >= U71(X1,X2) constraint: U81(mark(X)) >= U81(X) constraint: U81(active(X)) >= U81(X) constraint: take(mark(X1),X2) >= take(X1,X2) constraint: take(active(X1),X2) >= take(X1,X2) constraint: take(X1,mark(X2)) >= take(X1,X2) constraint: take(X1,active(X2)) >= take(X1,X2) constraint: U91(mark(X1),X2,X3,X4) >= U91(X1,X2,X3,X4) constraint: U91(active(X1),X2,X3,X4) >= U91(X1,X2,X3,X4) constraint: U91(X1,mark(X2),X3,X4) >= U91(X1,X2,X3,X4) constraint: U91(X1,active(X2),X3,X4) >= U91(X1,X2,X3,X4) constraint: U91(X1,X2,mark(X3),X4) >= U91(X1,X2,X3,X4) constraint: U91(X1,X2,active(X3),X4) >= U91(X1,X2,X3,X4) constraint: U91(X1,X2,X3,mark(X4)) >= U91(X1,X2,X3,X4) constraint: U91(X1,X2,X3,active(X4)) >= U91(X1,X2,X3,X4) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: isNatIListKind(mark(X)) >= isNatIListKind(X) constraint: isNatIListKind(active(X)) >= isNatIListKind(X) constraint: isNatKind(mark(X)) >= isNatKind(X) constraint: isNatKind(active(X)) >= isNatKind(X) constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(cons(X1,X2)) >= Marked_active(cons(mark(X1),X2)) constraint: Marked_mark(zeros) >= Marked_active(zeros) constraint: Marked_mark(U12(X)) >= Marked_mark(X) constraint: Marked_mark(U12(X)) >= Marked_active(U12(mark(X))) constraint: Marked_mark(isNatList(X)) >= Marked_active(isNatList(X)) constraint: Marked_mark(U11(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2)) >= Marked_active(U11(mark(X1),X2)) constraint: Marked_mark(U22(X)) >= Marked_mark(X) constraint: Marked_mark(U22(X)) >= Marked_active(U22(mark(X))) constraint: Marked_mark(isNat(X)) >= Marked_active(isNat(X)) constraint: Marked_mark(U21(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U21(X1,X2)) >= Marked_active(U21(mark(X1),X2)) constraint: Marked_mark(U32(X)) >= Marked_mark(X) constraint: Marked_mark(U32(X)) >= Marked_active(U32(mark(X))) constraint: Marked_mark(U31(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) constraint: Marked_mark(U42(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U42(X1,X2)) >= Marked_active(U42(mark(X1),X2)) constraint: Marked_mark(U41(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U41(X1,X2,X3)) >= Marked_active(U41(mark(X1),X2,X3)) constraint: Marked_mark(U43(X)) >= Marked_mark(X) constraint: Marked_mark(U43(X)) >= Marked_active(U43(mark(X))) constraint: Marked_mark(isNatIList(X)) >= Marked_active(isNatIList(X)) constraint: Marked_mark(U52(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U52(X1,X2)) >= Marked_active(U52(mark(X1),X2)) constraint: Marked_mark(U51(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U51(X1,X2,X3)) >= Marked_active(U51(mark(X1),X2,X3)) constraint: Marked_mark(U53(X)) >= Marked_mark(X) constraint: Marked_mark(U53(X)) >= Marked_active(U53(mark(X))) constraint: Marked_mark(U62(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U62(X1,X2)) >= Marked_active(U62(mark(X1),X2)) constraint: Marked_mark(U61(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U61(X1,X2,X3)) >= Marked_active(U61(mark(X1),X2,X3)) constraint: Marked_mark(U63(X)) >= Marked_mark(X) constraint: Marked_mark(U63(X)) >= Marked_active(U63(mark(X))) constraint: Marked_mark(s(X)) >= Marked_mark(X) constraint: Marked_mark(s(X)) >= Marked_active(s(mark(X))) constraint: Marked_mark(length(X)) >= Marked_mark(X) constraint: Marked_mark(length(X)) >= Marked_active(length(mark(X))) constraint: Marked_mark(U71(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U71(X1,X2)) >= Marked_active(U71(mark(X1),X2)) constraint: Marked_mark(U81(X)) >= Marked_mark(X) constraint: Marked_mark(U81(X)) >= Marked_active(U81(mark(X))) constraint: Marked_mark(take(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(take(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(take(X1,X2)) >= Marked_active(take(mark(X1),mark(X2))) constraint: Marked_mark(U91(X1,X2,X3,X4)) >= Marked_mark(X1) constraint: Marked_mark(U91(X1,X2,X3,X4)) >= Marked_active(U91(mark(X1), X2,X3,X4)) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(isNatIListKind(X)) >= Marked_active(isNatIListKind(X)) constraint: Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) constraint: Marked_active(zeros) >= Marked_mark(cons(0,zeros)) constraint: Marked_active(isNatList(cons(V1,V2))) >= Marked_mark(U51( and( isNatKind( V1), isNatIListKind( V2)), V1, V2)) constraint: Marked_active(isNatList(take(V1,V2))) >= Marked_mark(U61( and( isNatKind( V1), isNatIListKind( V2)), V1, V2)) constraint: Marked_active(U11(tt,V1)) >= Marked_mark(U12(isNatList(V1))) constraint: Marked_active(isNat(s(V1))) >= Marked_mark(U21(isNatKind(V1),V1)) constraint: Marked_active(isNat(length(V1))) >= Marked_mark(U11(isNatIListKind( V1), V1)) constraint: Marked_active(U21(tt,V1)) >= Marked_mark(U22(isNat(V1))) constraint: Marked_active(U31(tt,V)) >= Marked_mark(U32(isNatList(V))) constraint: Marked_active(U42(tt,V2)) >= Marked_mark(U43(isNatIList(V2))) constraint: Marked_active(U41(tt,V1,V2)) >= Marked_mark(U42(isNat(V1),V2)) constraint: Marked_active(isNatIList(cons(V1,V2))) >= Marked_mark(U41( and( isNatKind( V1), isNatIListKind( V2)), V1, V2)) constraint: Marked_active(isNatIList(V)) >= Marked_mark(U31(isNatIListKind(V), V)) constraint: Marked_active(U52(tt,V2)) >= Marked_mark(U53(isNatList(V2))) constraint: Marked_active(U51(tt,V1,V2)) >= Marked_mark(U52(isNat(V1),V2)) constraint: Marked_active(U62(tt,V2)) >= Marked_mark(U63(isNatIList(V2))) constraint: Marked_active(U61(tt,V1,V2)) >= Marked_mark(U62(isNat(V1),V2)) constraint: Marked_active(length(cons(N,L))) >= Marked_mark(U71(and(and( isNatList( L), isNatIListKind( L)), and( isNat(N), isNatKind(N))), L)) constraint: Marked_active(U71(tt,L)) >= Marked_mark(s(length(L))) constraint: Marked_active(take(0,IL)) >= Marked_mark(U81(and(isNatIList(IL), isNatIListKind(IL)))) constraint: Marked_active(take(s(M),cons(N,IL))) >= Marked_mark(U91(and( and( isNatIList( IL), isNatIListKind( IL)), and( and( isNat( M), isNatKind( M)), and( isNat( N), isNatKind( N)))), IL,M, N)) constraint: Marked_active(U91(tt,IL,M,N)) >= Marked_mark(cons(N,take(M,IL))) constraint: Marked_active(and(tt,X)) >= Marked_mark(X) constraint: Marked_active(isNatIListKind(cons(V1,V2))) >= Marked_mark( and(isNatKind(V1), isNatIListKind(V2))) constraint: Marked_active(isNatIListKind(take(V1,V2))) >= Marked_mark( and(isNatKind(V1), isNatIListKind(V2))) constraint: Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) constraint: Marked_active(isNatKind(length(V1))) >= Marked_mark(isNatIListKind( V1)) APPLY CRITERIA (Subterm criterion) ST: Marked_cons -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_U11 -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_U12 -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_isNatList -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_U21 -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_U22 -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_isNat -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_U31 -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_U32 -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_U41 -> 3 APPLY CRITERIA (Subterm criterion) ST: Marked_U42 -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_U43 -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_isNatIList -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_U51 -> 3 APPLY CRITERIA (Subterm criterion) ST: Marked_U52 -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_U53 -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_U61 -> 3 APPLY CRITERIA (Subterm criterion) ST: Marked_U62 -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_U63 -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_U71 -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_s -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_length -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_U81 -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_U91 -> 4 APPLY CRITERIA (Subterm criterion) ST: Marked_take -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_and -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_isNatIListKind -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_isNatKind -> 1 APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> 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