- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] a__zeros -> cons(0,zeros) [2] a__U11(tt,V1) -> a__U12(a__isNatList(V1)) [3] a__U12(tt) -> tt [4] a__U21(tt,V1) -> a__U22(a__isNat(V1)) [5] a__U22(tt) -> tt [6] a__U31(tt,V) -> a__U32(a__isNatList(V)) [7] a__U32(tt) -> tt [8] a__U41(tt,V1,V2) -> a__U42(a__isNat(V1),V2) [9] a__U42(tt,V2) -> a__U43(a__isNatIList(V2)) [10] a__U43(tt) -> tt [11] a__U51(tt,V1,V2) -> a__U52(a__isNat(V1),V2) [12] a__U52(tt,V2) -> a__U53(a__isNatList(V2)) [13] a__U53(tt) -> tt [14] a__U61(tt,V1,V2) -> a__U62(a__isNat(V1),V2) [15] a__U62(tt,V2) -> a__U63(a__isNatIList(V2)) [16] a__U63(tt) -> tt [17] a__U71(tt,L) -> s(a__length(mark(L))) [18] a__U81(tt) -> nil [19] a__U91(tt,IL,M,N) -> cons(mark(N),take(M,IL)) [20] a__and(tt,X) -> mark(X) [21] a__isNat(0) -> tt [22] a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) [23] a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) [24] a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) [25] a__isNatIList(zeros) -> tt [26] a__isNatIList(cons(V1,V2)) -> a__U41(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) [27] a__isNatIListKind(nil) -> tt [28] a__isNatIListKind(zeros) -> tt [29] a__isNatIListKind(cons(V1,V2)) -> a__and(a__isNatKind(V1),isNatIListKind(V2)) [30] a__isNatIListKind(take(V1,V2)) -> a__and(a__isNatKind(V1),isNatIListKind(V2)) [31] a__isNatKind(0) -> tt [32] a__isNatKind(length(V1)) -> a__isNatIListKind(V1) [33] a__isNatKind(s(V1)) -> a__isNatKind(V1) [34] a__isNatList(nil) -> tt [35] a__isNatList(cons(V1,V2)) -> a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) [36] a__isNatList(take(V1,V2)) -> a__U61(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) [37] a__length(nil) -> 0 [38] a__length(cons(N,L)) -> a__U71(a__and(a__and(a__isNatList(L),isNatIListKind(L)), and(isNat(N),isNatKind(N))),L) [39] a__take(0,IL) -> a__U81(a__and(a__isNatIList(IL),isNatIListKind(IL))) [40] a__take(s(M),cons(N,IL)) -> a__U91(a__and(a__and(a__isNatIList(IL),isNatIListKind(IL)), and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N)))), IL,M,N) [41] mark(zeros) -> a__zeros [42] mark(U11(X1,X2)) -> a__U11(mark(X1),X2) [43] mark(U12(X)) -> a__U12(mark(X)) [44] mark(isNatList(X)) -> a__isNatList(X) [45] mark(U21(X1,X2)) -> a__U21(mark(X1),X2) [46] mark(U22(X)) -> a__U22(mark(X)) [47] mark(isNat(X)) -> a__isNat(X) [48] mark(U31(X1,X2)) -> a__U31(mark(X1),X2) [49] mark(U32(X)) -> a__U32(mark(X)) [50] mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) [51] mark(U42(X1,X2)) -> a__U42(mark(X1),X2) [52] mark(U43(X)) -> a__U43(mark(X)) [53] mark(isNatIList(X)) -> a__isNatIList(X) [54] mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) [55] mark(U52(X1,X2)) -> a__U52(mark(X1),X2) [56] mark(U53(X)) -> a__U53(mark(X)) [57] mark(U61(X1,X2,X3)) -> a__U61(mark(X1),X2,X3) [58] mark(U62(X1,X2)) -> a__U62(mark(X1),X2) [59] mark(U63(X)) -> a__U63(mark(X)) [60] mark(U71(X1,X2)) -> a__U71(mark(X1),X2) [61] mark(length(X)) -> a__length(mark(X)) [62] mark(U81(X)) -> a__U81(mark(X)) [63] mark(U91(X1,X2,X3,X4)) -> a__U91(mark(X1),X2,X3,X4) [64] mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) [65] mark(and(X1,X2)) -> a__and(mark(X1),X2) [66] mark(isNatIListKind(X)) -> a__isNatIListKind(X) [67] mark(isNatKind(X)) -> a__isNatKind(X) [68] mark(cons(X1,X2)) -> cons(mark(X1),X2) [69] mark(0) -> 0 [70] mark(tt) -> tt [71] mark(s(X)) -> s(mark(X)) [72] mark(nil) -> nil [73] a__zeros -> zeros [74] a__U11(X1,X2) -> U11(X1,X2) [75] a__U12(X) -> U12(X) [76] a__isNatList(X) -> isNatList(X) [77] a__U21(X1,X2) -> U21(X1,X2) [78] a__U22(X) -> U22(X) [79] a__isNat(X) -> isNat(X) [80] a__U31(X1,X2) -> U31(X1,X2) [81] a__U32(X) -> U32(X) [82] a__U41(X1,X2,X3) -> U41(X1,X2,X3) [83] a__U42(X1,X2) -> U42(X1,X2) [84] a__U43(X) -> U43(X) [85] a__isNatIList(X) -> isNatIList(X) [86] a__U51(X1,X2,X3) -> U51(X1,X2,X3) [87] a__U52(X1,X2) -> U52(X1,X2) [88] a__U53(X) -> U53(X) [89] a__U61(X1,X2,X3) -> U61(X1,X2,X3) [90] a__U62(X1,X2) -> U62(X1,X2) [91] a__U63(X) -> U63(X) [92] a__U71(X1,X2) -> U71(X1,X2) [93] a__length(X) -> length(X) [94] a__U81(X) -> U81(X) [95] a__U91(X1,X2,X3,X4) -> U91(X1,X2,X3,X4) [96] a__take(X1,X2) -> take(X1,X2) [97] a__and(X1,X2) -> and(X1,X2) [98] a__isNatIListKind(X) -> isNatIListKind(X) [99] a__isNatKind(X) -> isNatKind(X) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__zeros >= cons(0,zeros) ; a__zeros >= zeros ; a__U12(tt) >= tt ; a__U12(X) >= U12(X) ; a__isNatList(cons(V1,V2)) >= a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)),V1,V2) ; a__isNatList(nil) >= tt ; a__isNatList(take(V1,V2)) >= a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)),V1,V2) ; a__isNatList(X) >= isNatList(X) ; a__U11(tt,V1) >= a__U12(a__isNatList(V1)) ; a__U11(X1,X2) >= U11(X1,X2) ; a__U22(tt) >= tt ; a__U22(X) >= U22(X) ; a__isNat(0) >= tt ; a__isNat(s(V1)) >= a__U21(a__isNatKind(V1),V1) ; a__isNat(length(V1)) >= a__U11(a__isNatIListKind(V1),V1) ; a__isNat(X) >= isNat(X) ; a__U21(tt,V1) >= a__U22(a__isNat(V1)) ; a__U21(X1,X2) >= U21(X1,X2) ; a__U32(tt) >= tt ; a__U32(X) >= U32(X) ; a__U31(tt,V) >= a__U32(a__isNatList(V)) ; a__U31(X1,X2) >= U31(X1,X2) ; a__U42(tt,V2) >= a__U43(a__isNatIList(V2)) ; a__U42(X1,X2) >= U42(X1,X2) ; a__U41(tt,V1,V2) >= a__U42(a__isNat(V1),V2) ; a__U41(X1,X2,X3) >= U41(X1,X2,X3) ; a__U43(tt) >= tt ; a__U43(X) >= U43(X) ; a__isNatIList(cons(V1,V2)) >= a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)),V1,V2) ; a__isNatIList(zeros) >= tt ; a__isNatIList(V) >= a__U31(a__isNatIListKind(V),V) ; a__isNatIList(X) >= isNatIList(X) ; a__U52(tt,V2) >= a__U53(a__isNatList(V2)) ; a__U52(X1,X2) >= U52(X1,X2) ; a__U51(tt,V1,V2) >= a__U52(a__isNat(V1),V2) ; a__U51(X1,X2,X3) >= U51(X1,X2,X3) ; a__U53(tt) >= tt ; a__U53(X) >= U53(X) ; a__U62(tt,V2) >= a__U63(a__isNatIList(V2)) ; a__U62(X1,X2) >= U62(X1,X2) ; a__U61(tt,V1,V2) >= a__U62(a__isNat(V1),V2) ; a__U61(X1,X2,X3) >= U61(X1,X2,X3) ; a__U63(tt) >= tt ; a__U63(X) >= U63(X) ; a__length(cons(N,L)) >= a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N),isNatKind(N))),L) ; a__length(nil) >= 0 ; a__length(X) >= length(X) ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(0) >= 0 ; mark(zeros) >= a__zeros ; mark(tt) >= tt ; mark(s(X)) >= s(mark(X)) ; mark(nil) >= nil ; mark(take(X1,X2)) >= a__take(mark(X1),mark(X2)) ; mark(length(X)) >= a__length(mark(X)) ; mark(isNatIListKind(X)) >= a__isNatIListKind(X) ; mark(and(X1,X2)) >= a__and(mark(X1),X2) ; mark(isNat(X)) >= a__isNat(X) ; mark(isNatKind(X)) >= a__isNatKind(X) ; mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ; mark(U12(X)) >= a__U12(mark(X)) ; mark(isNatList(X)) >= a__isNatList(X) ; mark(U21(X1,X2)) >= a__U21(mark(X1),X2) ; mark(U22(X)) >= a__U22(mark(X)) ; mark(U31(X1,X2)) >= a__U31(mark(X1),X2) ; mark(U32(X)) >= a__U32(mark(X)) ; 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(isNatIList(X)) >= a__isNatIList(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,X3)) >= a__U61(mark(X1),X2,X3) ; mark(U62(X1,X2)) >= a__U62(mark(X1),X2) ; mark(U63(X)) >= a__U63(mark(X)) ; mark(U71(X1,X2)) >= a__U71(mark(X1),X2) ; mark(U81(X)) >= a__U81(mark(X)) ; mark(U91(X1,X2,X3,X4)) >= a__U91(mark(X1),X2,X3,X4) ; a__U71(tt,L) >= s(a__length(mark(L))) ; a__U71(X1,X2) >= U71(X1,X2) ; a__U81(tt) >= nil ; a__U81(X) >= U81(X) ; a__U91(tt,IL,M,N) >= cons(mark(N),take(M,IL)) ; a__U91(X1,X2,X3,X4) >= U91(X1,X2,X3,X4) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__isNatIListKind(cons(V1,V2)) >= a__and(a__isNatKind(V1),isNatIListKind(V2)) ; a__isNatIListKind(zeros) >= tt ; a__isNatIListKind(nil) >= tt ; a__isNatIListKind(take(V1,V2)) >= a__and(a__isNatKind(V1),isNatIListKind(V2)) ; a__isNatIListKind(X) >= isNatIListKind(X) ; a__isNatKind(0) >= tt ; a__isNatKind(s(V1)) >= a__isNatKind(V1) ; a__isNatKind(length(V1)) >= a__isNatIListKind(V1) ; a__isNatKind(X) >= isNatKind(X) ; a__take(0,IL) >= a__U81(a__and(a__isNatIList(IL),isNatIListKind(IL))) ; a__take(s(M),cons(N,IL)) >= a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N)))),IL, M,N) ; a__take(X1,X2) >= take(X1,X2) ; Marked_a__isNatKind(s(V1)) >= Marked_a__isNatKind(V1) ; Marked_a__isNatKind(length(V1)) >= Marked_a__isNatIListKind(V1) ; Marked_a__isNatIListKind(cons(V1,V2)) >= Marked_a__isNatKind(V1) ; Marked_a__isNatIListKind(cons(V1,V2)) >= Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; Marked_a__isNatIListKind(take(V1,V2)) >= Marked_a__isNatKind(V1) ; Marked_a__isNatIListKind(take(V1,V2)) >= Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; Marked_a__and(tt,X) >= Marked_mark(X) ; Marked_a__take(0,IL) >= Marked_a__and(a__isNatIList(IL),isNatIListKind(IL)) ; Marked_a__take(0,IL) >= Marked_a__isNatIList(IL) ; Marked_a__take(s(M),cons(N,IL)) >= Marked_a__and(a__isNatIList(IL), isNatIListKind(IL)) ; Marked_a__take(s(M),cons(N,IL)) >= Marked_a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N)))) ; Marked_a__take(s(M),cons(N,IL)) >= Marked_a__U91(a__and(a__and(a__isNatIList( IL), isNatIListKind(IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N),isNatKind(N)))) ,IL,M,N) ; Marked_a__take(s(M),cons(N,IL)) >= Marked_a__isNatIList(IL) ; Marked_a__U91(tt,IL,M,N) >= Marked_mark(N) ; Marked_a__length(cons(N,L)) >= Marked_a__and(a__isNatList(L), isNatIListKind(L)) ; Marked_a__length(cons(N,L)) >= Marked_a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N),isNatKind(N))) ; Marked_a__length(cons(N,L)) >= Marked_a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N),isNatKind(N))), L) ; Marked_a__length(cons(N,L)) >= Marked_a__isNatList(L) ; Marked_a__U71(tt,L) >= Marked_a__length(mark(L)) ; Marked_a__U71(tt,L) >= Marked_mark(L) ; Marked_a__U62(tt,V2) >= Marked_a__isNatIList(V2) ; Marked_a__U61(tt,V1,V2) >= Marked_a__U62(a__isNat(V1),V2) ; Marked_a__U61(tt,V1,V2) >= Marked_a__isNat(V1) ; Marked_a__U52(tt,V2) >= Marked_a__isNatList(V2) ; Marked_a__U51(tt,V1,V2) >= Marked_a__U52(a__isNat(V1),V2) ; Marked_a__U51(tt,V1,V2) >= Marked_a__isNat(V1) ; Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__isNatKind(V1) ; Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1,V2) ; Marked_a__isNatIList(V) >= Marked_a__isNatIListKind(V) ; Marked_a__isNatIList(V) >= Marked_a__U31(a__isNatIListKind(V),V) ; Marked_a__U42(tt,V2) >= Marked_a__isNatIList(V2) ; Marked_a__U41(tt,V1,V2) >= Marked_a__U42(a__isNat(V1),V2) ; Marked_a__U41(tt,V1,V2) >= Marked_a__isNat(V1) ; Marked_a__U31(tt,V) >= Marked_a__isNatList(V) ; Marked_a__isNat(s(V1)) >= Marked_a__isNatKind(V1) ; Marked_a__isNat(s(V1)) >= Marked_a__U21(a__isNatKind(V1),V1) ; Marked_a__isNat(length(V1)) >= Marked_a__isNatIListKind(V1) ; Marked_a__isNat(length(V1)) >= Marked_a__U11(a__isNatIListKind(V1),V1) ; Marked_a__U21(tt,V1) >= Marked_a__isNat(V1) ; Marked_a__isNatList(cons(V1,V2)) >= Marked_a__isNatKind(V1) ; Marked_a__isNatList(cons(V1,V2)) >= Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; Marked_a__isNatList(cons(V1,V2)) >= Marked_a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1,V2) ; Marked_a__isNatList(take(V1,V2)) >= Marked_a__isNatKind(V1) ; Marked_a__isNatList(take(V1,V2)) >= Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; Marked_a__isNatList(take(V1,V2)) >= Marked_a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1,V2) ; Marked_a__U11(tt,V1) >= Marked_a__isNatList(V1) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(s(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(length(X)) >= Marked_a__length(mark(X)) ; Marked_mark(length(X)) >= Marked_mark(X) ; Marked_mark(isNatIListKind(X)) >= Marked_a__isNatIListKind(X) ; Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(isNat(X)) >= Marked_a__isNat(X) ; Marked_mark(isNatKind(X)) >= Marked_a__isNatKind(X) ; Marked_mark(U11(X1,X2)) >= Marked_a__U11(mark(X1),X2) ; Marked_mark(U11(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U12(X)) >= Marked_mark(X) ; Marked_mark(isNatList(X)) >= Marked_a__isNatList(X) ; Marked_mark(U21(X1,X2)) >= Marked_a__U21(mark(X1),X2) ; Marked_mark(U21(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U22(X)) >= Marked_mark(X) ; Marked_mark(U31(X1,X2)) >= Marked_a__U31(mark(X1),X2) ; Marked_mark(U31(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U32(X)) >= Marked_mark(X) ; 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(isNatIList(X)) >= Marked_a__isNatIList(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,X3)) >= Marked_a__U61(mark(X1),X2,X3) ; Marked_mark(U61(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U62(X1,X2)) >= Marked_a__U62(mark(X1),X2) ; Marked_mark(U62(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U63(X)) >= Marked_mark(X) ; Marked_mark(U71(X1,X2)) >= Marked_a__U71(mark(X1),X2) ; Marked_mark(U71(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U81(X)) >= Marked_mark(X) ; Marked_mark(U91(X1,X2,X3,X4)) >= Marked_a__U91(mark(X1),X2,X3,X4) ; Marked_mark(U91(X1,X2,X3,X4)) >= Marked_mark(X1) ; } + Disjunctions:{ { Marked_a__isNatKind(s(V1)) > Marked_a__isNatKind(V1) ; } { Marked_a__isNatKind(length(V1)) > Marked_a__isNatIListKind(V1) ; } { Marked_a__isNatIListKind(cons(V1,V2)) > Marked_a__isNatKind(V1) ; } { Marked_a__isNatIListKind(cons(V1,V2)) > Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; } { Marked_a__isNatIListKind(take(V1,V2)) > Marked_a__isNatKind(V1) ; } { Marked_a__isNatIListKind(take(V1,V2)) > Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; } { Marked_a__and(tt,X) > Marked_mark(X) ; } { Marked_a__take(0,IL) > Marked_a__and(a__isNatIList(IL),isNatIListKind(IL)) ; } { Marked_a__take(0,IL) > Marked_a__isNatIList(IL) ; } { Marked_a__take(s(M),cons(N,IL)) > Marked_a__and(a__isNatIList(IL), isNatIListKind(IL)) ; } { Marked_a__take(s(M),cons(N,IL)) > Marked_a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N)))) ; } { Marked_a__take(s(M),cons(N,IL)) > Marked_a__U91(a__and(a__and(a__isNatIList( IL), isNatIListKind(IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N),isNatKind(N)))), IL,M,N) ; } { Marked_a__take(s(M),cons(N,IL)) > Marked_a__isNatIList(IL) ; } { Marked_a__U91(tt,IL,M,N) > Marked_mark(N) ; } { Marked_a__length(cons(N,L)) > Marked_a__and(a__isNatList(L), isNatIListKind(L)) ; } { Marked_a__length(cons(N,L)) > Marked_a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N),isNatKind(N))) ; } { Marked_a__length(cons(N,L)) > Marked_a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N),isNatKind(N))), L) ; } { Marked_a__length(cons(N,L)) > Marked_a__isNatList(L) ; } { Marked_a__U71(tt,L) > Marked_a__length(mark(L)) ; } { Marked_a__U71(tt,L) > Marked_mark(L) ; } { Marked_a__U62(tt,V2) > Marked_a__isNatIList(V2) ; } { Marked_a__U61(tt,V1,V2) > Marked_a__U62(a__isNat(V1),V2) ; } { Marked_a__U61(tt,V1,V2) > Marked_a__isNat(V1) ; } { Marked_a__U52(tt,V2) > Marked_a__isNatList(V2) ; } { Marked_a__U51(tt,V1,V2) > Marked_a__U52(a__isNat(V1),V2) ; } { Marked_a__U51(tt,V1,V2) > Marked_a__isNat(V1) ; } { Marked_a__isNatIList(cons(V1,V2)) > Marked_a__isNatKind(V1) ; } { Marked_a__isNatIList(cons(V1,V2)) > Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; } { Marked_a__isNatIList(cons(V1,V2)) > Marked_a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1,V2) ; } { Marked_a__isNatIList(V) > Marked_a__isNatIListKind(V) ; } { Marked_a__isNatIList(V) > Marked_a__U31(a__isNatIListKind(V),V) ; } { Marked_a__U42(tt,V2) > Marked_a__isNatIList(V2) ; } { Marked_a__U41(tt,V1,V2) > Marked_a__U42(a__isNat(V1),V2) ; } { Marked_a__U41(tt,V1,V2) > Marked_a__isNat(V1) ; } { Marked_a__U31(tt,V) > Marked_a__isNatList(V) ; } { Marked_a__isNat(s(V1)) > Marked_a__isNatKind(V1) ; } { Marked_a__isNat(s(V1)) > Marked_a__U21(a__isNatKind(V1),V1) ; } { Marked_a__isNat(length(V1)) > Marked_a__isNatIListKind(V1) ; } { Marked_a__isNat(length(V1)) > Marked_a__U11(a__isNatIListKind(V1),V1) ; } { Marked_a__U21(tt,V1) > Marked_a__isNat(V1) ; } { Marked_a__isNatList(cons(V1,V2)) > Marked_a__isNatKind(V1) ; } { Marked_a__isNatList(cons(V1,V2)) > Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; } { Marked_a__isNatList(cons(V1,V2)) > Marked_a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1,V2) ; } { Marked_a__isNatList(take(V1,V2)) > Marked_a__isNatKind(V1) ; } { Marked_a__isNatList(take(V1,V2)) > Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; } { Marked_a__isNatList(take(V1,V2)) > Marked_a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1,V2) ; } { Marked_a__U11(tt,V1) > Marked_a__isNatList(V1) ; } { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(s(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(length(X)) > Marked_a__length(mark(X)) ; } { Marked_mark(length(X)) > Marked_mark(X) ; } { Marked_mark(isNatIListKind(X)) > Marked_a__isNatIListKind(X) ; } { Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(isNat(X)) > Marked_a__isNat(X) ; } { Marked_mark(isNatKind(X)) > Marked_a__isNatKind(X) ; } { Marked_mark(U11(X1,X2)) > Marked_a__U11(mark(X1),X2) ; } { Marked_mark(U11(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U12(X)) > Marked_mark(X) ; } { Marked_mark(isNatList(X)) > Marked_a__isNatList(X) ; } { Marked_mark(U21(X1,X2)) > Marked_a__U21(mark(X1),X2) ; } { Marked_mark(U21(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U22(X)) > Marked_mark(X) ; } { Marked_mark(U31(X1,X2)) > Marked_a__U31(mark(X1),X2) ; } { Marked_mark(U31(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U32(X)) > Marked_mark(X) ; } { 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(isNatIList(X)) > Marked_a__isNatIList(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,X3)) > Marked_a__U61(mark(X1),X2,X3) ; } { Marked_mark(U61(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U62(X1,X2)) > Marked_a__U62(mark(X1),X2) ; } { Marked_mark(U62(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U63(X)) > Marked_mark(X) ; } { Marked_mark(U71(X1,X2)) > Marked_a__U71(mark(X1),X2) ; } { Marked_mark(U71(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U81(X)) > Marked_mark(X) ; } { Marked_mark(U91(X1,X2,X3,X4)) > Marked_a__U91(mark(X1),X2,X3,X4) ; } { Marked_mark(U91(X1,X2,X3,X4)) > Marked_mark(X1) ; } } === 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: a__zeros >= cons(0,zeros) constraint: a__zeros >= zeros constraint: a__U12(tt) >= tt constraint: a__U12(X) >= U12(X) constraint: a__isNatList(cons(V1,V2)) >= a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1,V2) constraint: a__isNatList(nil) >= tt constraint: a__isNatList(take(V1,V2)) >= a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1,V2) constraint: a__isNatList(X) >= isNatList(X) constraint: a__U11(tt,V1) >= a__U12(a__isNatList(V1)) constraint: a__U11(X1,X2) >= U11(X1,X2) constraint: a__U22(tt) >= tt constraint: a__U22(X) >= U22(X) constraint: a__isNat(0) >= tt constraint: a__isNat(s(V1)) >= a__U21(a__isNatKind(V1),V1) constraint: a__isNat(length(V1)) >= a__U11(a__isNatIListKind(V1),V1) constraint: a__isNat(X) >= isNat(X) constraint: a__U21(tt,V1) >= a__U22(a__isNat(V1)) constraint: a__U21(X1,X2) >= U21(X1,X2) constraint: a__U32(tt) >= tt constraint: a__U32(X) >= U32(X) constraint: a__U31(tt,V) >= a__U32(a__isNatList(V)) constraint: a__U31(X1,X2) >= U31(X1,X2) constraint: a__U42(tt,V2) >= a__U43(a__isNatIList(V2)) constraint: a__U42(X1,X2) >= U42(X1,X2) constraint: a__U41(tt,V1,V2) >= a__U42(a__isNat(V1),V2) constraint: a__U41(X1,X2,X3) >= U41(X1,X2,X3) constraint: a__U43(tt) >= tt constraint: a__U43(X) >= U43(X) constraint: a__isNatIList(cons(V1,V2)) >= a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1,V2) constraint: a__isNatIList(zeros) >= tt constraint: a__isNatIList(V) >= a__U31(a__isNatIListKind(V),V) constraint: a__isNatIList(X) >= isNatIList(X) constraint: a__U52(tt,V2) >= a__U53(a__isNatList(V2)) constraint: a__U52(X1,X2) >= U52(X1,X2) constraint: a__U51(tt,V1,V2) >= a__U52(a__isNat(V1),V2) constraint: a__U51(X1,X2,X3) >= U51(X1,X2,X3) constraint: a__U53(tt) >= tt constraint: a__U53(X) >= U53(X) constraint: a__U62(tt,V2) >= a__U63(a__isNatIList(V2)) constraint: a__U62(X1,X2) >= U62(X1,X2) constraint: a__U61(tt,V1,V2) >= a__U62(a__isNat(V1),V2) constraint: a__U61(X1,X2,X3) >= U61(X1,X2,X3) constraint: a__U63(tt) >= tt constraint: a__U63(X) >= U63(X) constraint: a__length(cons(N,L)) >= a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N),isNatKind(N))), L) constraint: a__length(nil) >= 0 constraint: a__length(X) >= length(X) constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2) constraint: mark(0) >= 0 constraint: mark(zeros) >= a__zeros constraint: mark(tt) >= tt constraint: mark(s(X)) >= s(mark(X)) constraint: mark(nil) >= nil constraint: mark(take(X1,X2)) >= a__take(mark(X1),mark(X2)) constraint: mark(length(X)) >= a__length(mark(X)) constraint: mark(isNatIListKind(X)) >= a__isNatIListKind(X) constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2) constraint: mark(isNat(X)) >= a__isNat(X) constraint: mark(isNatKind(X)) >= a__isNatKind(X) constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2) constraint: mark(U12(X)) >= a__U12(mark(X)) constraint: mark(isNatList(X)) >= a__isNatList(X) constraint: mark(U21(X1,X2)) >= a__U21(mark(X1),X2) constraint: mark(U22(X)) >= a__U22(mark(X)) constraint: mark(U31(X1,X2)) >= a__U31(mark(X1),X2) constraint: mark(U32(X)) >= a__U32(mark(X)) constraint: mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3) constraint: mark(U42(X1,X2)) >= a__U42(mark(X1),X2) constraint: mark(U43(X)) >= a__U43(mark(X)) constraint: mark(isNatIList(X)) >= a__isNatIList(X) constraint: mark(U51(X1,X2,X3)) >= a__U51(mark(X1),X2,X3) constraint: mark(U52(X1,X2)) >= a__U52(mark(X1),X2) constraint: mark(U53(X)) >= a__U53(mark(X)) constraint: mark(U61(X1,X2,X3)) >= a__U61(mark(X1),X2,X3) constraint: mark(U62(X1,X2)) >= a__U62(mark(X1),X2) constraint: mark(U63(X)) >= a__U63(mark(X)) constraint: mark(U71(X1,X2)) >= a__U71(mark(X1),X2) constraint: mark(U81(X)) >= a__U81(mark(X)) constraint: mark(U91(X1,X2,X3,X4)) >= a__U91(mark(X1),X2,X3,X4) constraint: a__U71(tt,L) >= s(a__length(mark(L))) constraint: a__U71(X1,X2) >= U71(X1,X2) constraint: a__U81(tt) >= nil constraint: a__U81(X) >= U81(X) constraint: a__U91(tt,IL,M,N) >= cons(mark(N),take(M,IL)) constraint: a__U91(X1,X2,X3,X4) >= U91(X1,X2,X3,X4) constraint: a__and(tt,X) >= mark(X) constraint: a__and(X1,X2) >= and(X1,X2) constraint: a__isNatIListKind(cons(V1,V2)) >= a__and(a__isNatKind(V1), isNatIListKind(V2)) constraint: a__isNatIListKind(zeros) >= tt constraint: a__isNatIListKind(nil) >= tt constraint: a__isNatIListKind(take(V1,V2)) >= a__and(a__isNatKind(V1), isNatIListKind(V2)) constraint: a__isNatIListKind(X) >= isNatIListKind(X) constraint: a__isNatKind(0) >= tt constraint: a__isNatKind(s(V1)) >= a__isNatKind(V1) constraint: a__isNatKind(length(V1)) >= a__isNatIListKind(V1) constraint: a__isNatKind(X) >= isNatKind(X) constraint: a__take(0,IL) >= a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL))) constraint: a__take(s(M),cons(N,IL)) >= a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N)))), IL,M,N) constraint: a__take(X1,X2) >= take(X1,X2) constraint: Marked_a__isNatKind(s(V1)) >= Marked_a__isNatKind(V1) constraint: Marked_a__isNatKind(length(V1)) >= Marked_a__isNatIListKind(V1) constraint: Marked_a__isNatIListKind(cons(V1,V2)) >= Marked_a__isNatKind(V1) constraint: Marked_a__isNatIListKind(cons(V1,V2)) >= Marked_a__and(a__isNatKind( V1), isNatIListKind(V2)) constraint: Marked_a__isNatIListKind(take(V1,V2)) >= Marked_a__isNatKind(V1) constraint: Marked_a__isNatIListKind(take(V1,V2)) >= Marked_a__and(a__isNatKind( V1), isNatIListKind(V2)) constraint: Marked_a__and(tt,X) >= Marked_mark(X) constraint: Marked_a__take(0,IL) >= Marked_a__and(a__isNatIList(IL), isNatIListKind(IL)) constraint: Marked_a__take(0,IL) >= Marked_a__isNatIList(IL) constraint: Marked_a__take(s(M),cons(N,IL)) >= Marked_a__and(a__isNatIList(IL), isNatIListKind(IL)) constraint: Marked_a__take(s(M),cons(N,IL)) >= Marked_a__and(a__and(a__isNatIList( IL), isNatIListKind( IL)), and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N)))) constraint: Marked_a__take(s(M),cons(N,IL)) >= Marked_a__U91(a__and(a__and( a__isNatIList( IL), isNatIListKind( IL)), and(and( isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), IL,M,N) constraint: Marked_a__take(s(M),cons(N,IL)) >= Marked_a__isNatIList(IL) constraint: Marked_a__U91(tt,IL,M,N) >= Marked_mark(N) constraint: Marked_a__length(cons(N,L)) >= Marked_a__and(a__isNatList(L), isNatIListKind(L)) constraint: Marked_a__length(cons(N,L)) >= Marked_a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N),isNatKind(N))) constraint: Marked_a__length(cons(N,L)) >= Marked_a__U71(a__and(a__and( a__isNatList( L), isNatIListKind( L)), and(isNat(N), isNatKind(N))), L) constraint: Marked_a__length(cons(N,L)) >= Marked_a__isNatList(L) constraint: Marked_a__U71(tt,L) >= Marked_a__length(mark(L)) constraint: Marked_a__U71(tt,L) >= Marked_mark(L) constraint: Marked_a__U62(tt,V2) >= Marked_a__isNatIList(V2) constraint: Marked_a__U61(tt,V1,V2) >= Marked_a__U62(a__isNat(V1),V2) constraint: Marked_a__U61(tt,V1,V2) >= Marked_a__isNat(V1) constraint: Marked_a__U52(tt,V2) >= Marked_a__isNatList(V2) constraint: Marked_a__U51(tt,V1,V2) >= Marked_a__U52(a__isNat(V1),V2) constraint: Marked_a__U51(tt,V1,V2) >= Marked_a__isNat(V1) constraint: Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__isNatKind(V1) constraint: Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) constraint: Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__U41(a__and( a__isNatKind( V1), isNatIListKind( V2)), V1,V2) constraint: Marked_a__isNatIList(V) >= Marked_a__isNatIListKind(V) constraint: Marked_a__isNatIList(V) >= Marked_a__U31(a__isNatIListKind(V),V) constraint: Marked_a__U42(tt,V2) >= Marked_a__isNatIList(V2) constraint: Marked_a__U41(tt,V1,V2) >= Marked_a__U42(a__isNat(V1),V2) constraint: Marked_a__U41(tt,V1,V2) >= Marked_a__isNat(V1) constraint: Marked_a__U31(tt,V) >= Marked_a__isNatList(V) constraint: Marked_a__isNat(s(V1)) >= Marked_a__isNatKind(V1) constraint: Marked_a__isNat(s(V1)) >= Marked_a__U21(a__isNatKind(V1),V1) constraint: Marked_a__isNat(length(V1)) >= Marked_a__isNatIListKind(V1) constraint: Marked_a__isNat(length(V1)) >= Marked_a__U11(a__isNatIListKind(V1), V1) constraint: Marked_a__U21(tt,V1) >= Marked_a__isNat(V1) constraint: Marked_a__isNatList(cons(V1,V2)) >= Marked_a__isNatKind(V1) constraint: Marked_a__isNatList(cons(V1,V2)) >= Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) constraint: Marked_a__isNatList(cons(V1,V2)) >= Marked_a__U51(a__and( a__isNatKind( V1), isNatIListKind( V2)), V1,V2) constraint: Marked_a__isNatList(take(V1,V2)) >= Marked_a__isNatKind(V1) constraint: Marked_a__isNatList(take(V1,V2)) >= Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) constraint: Marked_a__isNatList(take(V1,V2)) >= Marked_a__U61(a__and( a__isNatKind( V1), isNatIListKind( V2)), V1,V2) constraint: Marked_a__U11(tt,V1) >= Marked_a__isNatList(V1) constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(s(X)) >= Marked_mark(X) constraint: Marked_mark(take(X1,X2)) >= Marked_a__take(mark(X1),mark(X2)) constraint: Marked_mark(take(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(take(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(length(X)) >= Marked_a__length(mark(X)) constraint: Marked_mark(length(X)) >= Marked_mark(X) constraint: Marked_mark(isNatIListKind(X)) >= Marked_a__isNatIListKind(X) constraint: Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(isNat(X)) >= Marked_a__isNat(X) constraint: Marked_mark(isNatKind(X)) >= Marked_a__isNatKind(X) constraint: Marked_mark(U11(X1,X2)) >= Marked_a__U11(mark(X1),X2) constraint: Marked_mark(U11(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U12(X)) >= Marked_mark(X) constraint: Marked_mark(isNatList(X)) >= Marked_a__isNatList(X) constraint: Marked_mark(U21(X1,X2)) >= Marked_a__U21(mark(X1),X2) constraint: Marked_mark(U21(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U22(X)) >= Marked_mark(X) constraint: Marked_mark(U31(X1,X2)) >= Marked_a__U31(mark(X1),X2) constraint: Marked_mark(U31(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U32(X)) >= Marked_mark(X) constraint: Marked_mark(U41(X1,X2,X3)) >= Marked_a__U41(mark(X1),X2,X3) constraint: Marked_mark(U41(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U42(X1,X2)) >= Marked_a__U42(mark(X1),X2) constraint: Marked_mark(U42(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U43(X)) >= Marked_mark(X) constraint: Marked_mark(isNatIList(X)) >= Marked_a__isNatIList(X) constraint: Marked_mark(U51(X1,X2,X3)) >= Marked_a__U51(mark(X1),X2,X3) constraint: Marked_mark(U51(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U52(X1,X2)) >= Marked_a__U52(mark(X1),X2) constraint: Marked_mark(U52(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U53(X)) >= Marked_mark(X) constraint: Marked_mark(U61(X1,X2,X3)) >= Marked_a__U61(mark(X1),X2,X3) constraint: Marked_mark(U61(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U62(X1,X2)) >= Marked_a__U62(mark(X1),X2) constraint: Marked_mark(U62(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U63(X)) >= Marked_mark(X) constraint: Marked_mark(U71(X1,X2)) >= Marked_a__U71(mark(X1),X2) constraint: Marked_mark(U71(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U81(X)) >= Marked_mark(X) constraint: Marked_mark(U91(X1,X2,X3,X4)) >= Marked_a__U91(mark(X1),X2,X3,X4) constraint: Marked_mark(U91(X1,X2,X3,X4)) >= Marked_mark(X1) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__zeros >= cons(0,zeros) ; a__zeros >= zeros ; a__U12(tt) >= tt ; a__U12(X) >= U12(X) ; a__isNatList(cons(V1,V2)) >= a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)),V1,V2) ; a__isNatList(nil) >= tt ; a__isNatList(take(V1,V2)) >= a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)),V1,V2) ; a__isNatList(X) >= isNatList(X) ; a__U11(tt,V1) >= a__U12(a__isNatList(V1)) ; a__U11(X1,X2) >= U11(X1,X2) ; a__U22(tt) >= tt ; a__U22(X) >= U22(X) ; a__isNat(0) >= tt ; a__isNat(s(V1)) >= a__U21(a__isNatKind(V1),V1) ; a__isNat(length(V1)) >= a__U11(a__isNatIListKind(V1),V1) ; a__isNat(X) >= isNat(X) ; a__U21(tt,V1) >= a__U22(a__isNat(V1)) ; a__U21(X1,X2) >= U21(X1,X2) ; a__U32(tt) >= tt ; a__U32(X) >= U32(X) ; a__U31(tt,V) >= a__U32(a__isNatList(V)) ; a__U31(X1,X2) >= U31(X1,X2) ; a__U42(tt,V2) >= a__U43(a__isNatIList(V2)) ; a__U42(X1,X2) >= U42(X1,X2) ; a__U41(tt,V1,V2) >= a__U42(a__isNat(V1),V2) ; a__U41(X1,X2,X3) >= U41(X1,X2,X3) ; a__U43(tt) >= tt ; a__U43(X) >= U43(X) ; a__isNatIList(cons(V1,V2)) >= a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)),V1,V2) ; a__isNatIList(zeros) >= tt ; a__isNatIList(V) >= a__U31(a__isNatIListKind(V),V) ; a__isNatIList(X) >= isNatIList(X) ; a__U52(tt,V2) >= a__U53(a__isNatList(V2)) ; a__U52(X1,X2) >= U52(X1,X2) ; a__U51(tt,V1,V2) >= a__U52(a__isNat(V1),V2) ; a__U51(X1,X2,X3) >= U51(X1,X2,X3) ; a__U53(tt) >= tt ; a__U53(X) >= U53(X) ; a__U62(tt,V2) >= a__U63(a__isNatIList(V2)) ; a__U62(X1,X2) >= U62(X1,X2) ; a__U61(tt,V1,V2) >= a__U62(a__isNat(V1),V2) ; a__U61(X1,X2,X3) >= U61(X1,X2,X3) ; a__U63(tt) >= tt ; a__U63(X) >= U63(X) ; a__length(cons(N,L)) >= a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N),isNatKind(N))),L) ; a__length(nil) >= 0 ; a__length(X) >= length(X) ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(0) >= 0 ; mark(zeros) >= a__zeros ; mark(tt) >= tt ; mark(s(X)) >= s(mark(X)) ; mark(nil) >= nil ; mark(take(X1,X2)) >= a__take(mark(X1),mark(X2)) ; mark(length(X)) >= a__length(mark(X)) ; mark(isNatIListKind(X)) >= a__isNatIListKind(X) ; mark(and(X1,X2)) >= a__and(mark(X1),X2) ; mark(isNat(X)) >= a__isNat(X) ; mark(isNatKind(X)) >= a__isNatKind(X) ; mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ; mark(U12(X)) >= a__U12(mark(X)) ; mark(isNatList(X)) >= a__isNatList(X) ; mark(U21(X1,X2)) >= a__U21(mark(X1),X2) ; mark(U22(X)) >= a__U22(mark(X)) ; mark(U31(X1,X2)) >= a__U31(mark(X1),X2) ; mark(U32(X)) >= a__U32(mark(X)) ; 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(isNatIList(X)) >= a__isNatIList(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,X3)) >= a__U61(mark(X1),X2,X3) ; mark(U62(X1,X2)) >= a__U62(mark(X1),X2) ; mark(U63(X)) >= a__U63(mark(X)) ; mark(U71(X1,X2)) >= a__U71(mark(X1),X2) ; mark(U81(X)) >= a__U81(mark(X)) ; mark(U91(X1,X2,X3,X4)) >= a__U91(mark(X1),X2,X3,X4) ; a__U71(tt,L) >= s(a__length(mark(L))) ; a__U71(X1,X2) >= U71(X1,X2) ; a__U81(tt) >= nil ; a__U81(X) >= U81(X) ; a__U91(tt,IL,M,N) >= cons(mark(N),take(M,IL)) ; a__U91(X1,X2,X3,X4) >= U91(X1,X2,X3,X4) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__isNatIListKind(cons(V1,V2)) >= a__and(a__isNatKind(V1),isNatIListKind(V2)) ; a__isNatIListKind(zeros) >= tt ; a__isNatIListKind(nil) >= tt ; a__isNatIListKind(take(V1,V2)) >= a__and(a__isNatKind(V1),isNatIListKind(V2)) ; a__isNatIListKind(X) >= isNatIListKind(X) ; a__isNatKind(0) >= tt ; a__isNatKind(s(V1)) >= a__isNatKind(V1) ; a__isNatKind(length(V1)) >= a__isNatIListKind(V1) ; a__isNatKind(X) >= isNatKind(X) ; a__take(0,IL) >= a__U81(a__and(a__isNatIList(IL),isNatIListKind(IL))) ; a__take(s(M),cons(N,IL)) >= a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N)))),IL, M,N) ; a__take(X1,X2) >= take(X1,X2) ; Marked_a__isNatKind(s(V1)) >= Marked_a__isNatKind(V1) ; Marked_a__isNatKind(length(V1)) >= Marked_a__isNatIListKind(V1) ; Marked_a__isNatIListKind(cons(V1,V2)) >= Marked_a__isNatKind(V1) ; Marked_a__isNatIListKind(cons(V1,V2)) >= Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; Marked_a__isNatIListKind(take(V1,V2)) >= Marked_a__isNatKind(V1) ; Marked_a__isNatIListKind(take(V1,V2)) >= Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; Marked_a__and(tt,X) >= Marked_mark(X) ; Marked_a__length(cons(N,L)) >= Marked_a__and(a__isNatList(L), isNatIListKind(L)) ; Marked_a__length(cons(N,L)) >= Marked_a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N),isNatKind(N))) ; Marked_a__length(cons(N,L)) >= Marked_a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N),isNatKind(N))), L) ; Marked_a__length(cons(N,L)) >= Marked_a__isNatList(L) ; Marked_a__U71(tt,L) >= Marked_a__length(mark(L)) ; Marked_a__U71(tt,L) >= Marked_mark(L) ; Marked_a__U62(tt,V2) >= Marked_a__isNatIList(V2) ; Marked_a__U61(tt,V1,V2) >= Marked_a__U62(a__isNat(V1),V2) ; Marked_a__U61(tt,V1,V2) >= Marked_a__isNat(V1) ; Marked_a__U52(tt,V2) >= Marked_a__isNatList(V2) ; Marked_a__U51(tt,V1,V2) >= Marked_a__U52(a__isNat(V1),V2) ; Marked_a__U51(tt,V1,V2) >= Marked_a__isNat(V1) ; Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__isNatKind(V1) ; Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1,V2) ; Marked_a__isNatIList(V) >= Marked_a__isNatIListKind(V) ; Marked_a__isNatIList(V) >= Marked_a__U31(a__isNatIListKind(V),V) ; Marked_a__U42(tt,V2) >= Marked_a__isNatIList(V2) ; Marked_a__U41(tt,V1,V2) >= Marked_a__U42(a__isNat(V1),V2) ; Marked_a__U41(tt,V1,V2) >= Marked_a__isNat(V1) ; Marked_a__U31(tt,V) >= Marked_a__isNatList(V) ; Marked_a__isNat(s(V1)) >= Marked_a__isNatKind(V1) ; Marked_a__isNat(s(V1)) >= Marked_a__U21(a__isNatKind(V1),V1) ; Marked_a__isNat(length(V1)) >= Marked_a__isNatIListKind(V1) ; Marked_a__isNat(length(V1)) >= Marked_a__U11(a__isNatIListKind(V1),V1) ; Marked_a__U21(tt,V1) >= Marked_a__isNat(V1) ; Marked_a__isNatList(cons(V1,V2)) >= Marked_a__isNatKind(V1) ; Marked_a__isNatList(cons(V1,V2)) >= Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; Marked_a__isNatList(cons(V1,V2)) >= Marked_a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1,V2) ; Marked_a__isNatList(take(V1,V2)) >= Marked_a__isNatKind(V1) ; Marked_a__isNatList(take(V1,V2)) >= Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; Marked_a__isNatList(take(V1,V2)) >= Marked_a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1,V2) ; Marked_a__U11(tt,V1) >= Marked_a__isNatList(V1) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(length(X)) >= Marked_a__length(mark(X)) ; Marked_mark(length(X)) >= Marked_mark(X) ; Marked_mark(isNatIListKind(X)) >= Marked_a__isNatIListKind(X) ; Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(isNat(X)) >= Marked_a__isNat(X) ; Marked_mark(isNatKind(X)) >= Marked_a__isNatKind(X) ; Marked_mark(U11(X1,X2)) >= Marked_a__U11(mark(X1),X2) ; Marked_mark(U11(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U12(X)) >= Marked_mark(X) ; Marked_mark(isNatList(X)) >= Marked_a__isNatList(X) ; Marked_mark(U21(X1,X2)) >= Marked_a__U21(mark(X1),X2) ; Marked_mark(U21(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U22(X)) >= Marked_mark(X) ; Marked_mark(U31(X1,X2)) >= Marked_a__U31(mark(X1),X2) ; Marked_mark(U31(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U32(X)) >= Marked_mark(X) ; 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(isNatIList(X)) >= Marked_a__isNatIList(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,X3)) >= Marked_a__U61(mark(X1),X2,X3) ; Marked_mark(U61(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U62(X1,X2)) >= Marked_a__U62(mark(X1),X2) ; Marked_mark(U62(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U63(X)) >= Marked_mark(X) ; Marked_mark(U71(X1,X2)) >= Marked_a__U71(mark(X1),X2) ; Marked_mark(U71(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U81(X)) >= Marked_mark(X) ; } + Disjunctions:{ { Marked_a__isNatKind(s(V1)) > Marked_a__isNatKind(V1) ; } { Marked_a__isNatKind(length(V1)) > Marked_a__isNatIListKind(V1) ; } { Marked_a__isNatIListKind(cons(V1,V2)) > Marked_a__isNatKind(V1) ; } { Marked_a__isNatIListKind(cons(V1,V2)) > Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; } { Marked_a__isNatIListKind(take(V1,V2)) > Marked_a__isNatKind(V1) ; } { Marked_a__isNatIListKind(take(V1,V2)) > Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; } { Marked_a__and(tt,X) > Marked_mark(X) ; } { Marked_a__length(cons(N,L)) > Marked_a__and(a__isNatList(L), isNatIListKind(L)) ; } { Marked_a__length(cons(N,L)) > Marked_a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N),isNatKind(N))) ; } { Marked_a__length(cons(N,L)) > Marked_a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N),isNatKind(N))), L) ; } { Marked_a__length(cons(N,L)) > Marked_a__isNatList(L) ; } { Marked_a__U71(tt,L) > Marked_a__length(mark(L)) ; } { Marked_a__U71(tt,L) > Marked_mark(L) ; } { Marked_a__U62(tt,V2) > Marked_a__isNatIList(V2) ; } { Marked_a__U61(tt,V1,V2) > Marked_a__U62(a__isNat(V1),V2) ; } { Marked_a__U61(tt,V1,V2) > Marked_a__isNat(V1) ; } { Marked_a__U52(tt,V2) > Marked_a__isNatList(V2) ; } { Marked_a__U51(tt,V1,V2) > Marked_a__U52(a__isNat(V1),V2) ; } { Marked_a__U51(tt,V1,V2) > Marked_a__isNat(V1) ; } { Marked_a__isNatIList(cons(V1,V2)) > Marked_a__isNatKind(V1) ; } { Marked_a__isNatIList(cons(V1,V2)) > Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; } { Marked_a__isNatIList(cons(V1,V2)) > Marked_a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1,V2) ; } { Marked_a__isNatIList(V) > Marked_a__isNatIListKind(V) ; } { Marked_a__isNatIList(V) > Marked_a__U31(a__isNatIListKind(V),V) ; } { Marked_a__U42(tt,V2) > Marked_a__isNatIList(V2) ; } { Marked_a__U41(tt,V1,V2) > Marked_a__U42(a__isNat(V1),V2) ; } { Marked_a__U41(tt,V1,V2) > Marked_a__isNat(V1) ; } { Marked_a__U31(tt,V) > Marked_a__isNatList(V) ; } { Marked_a__isNat(s(V1)) > Marked_a__isNatKind(V1) ; } { Marked_a__isNat(s(V1)) > Marked_a__U21(a__isNatKind(V1),V1) ; } { Marked_a__isNat(length(V1)) > Marked_a__isNatIListKind(V1) ; } { Marked_a__isNat(length(V1)) > Marked_a__U11(a__isNatIListKind(V1),V1) ; } { Marked_a__U21(tt,V1) > Marked_a__isNat(V1) ; } { Marked_a__isNatList(cons(V1,V2)) > Marked_a__isNatKind(V1) ; } { Marked_a__isNatList(cons(V1,V2)) > Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; } { Marked_a__isNatList(cons(V1,V2)) > Marked_a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1,V2) ; } { Marked_a__isNatList(take(V1,V2)) > Marked_a__isNatKind(V1) ; } { Marked_a__isNatList(take(V1,V2)) > Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; } { Marked_a__isNatList(take(V1,V2)) > Marked_a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1,V2) ; } { Marked_a__U11(tt,V1) > Marked_a__isNatList(V1) ; } { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(length(X)) > Marked_a__length(mark(X)) ; } { Marked_mark(length(X)) > Marked_mark(X) ; } { Marked_mark(isNatIListKind(X)) > Marked_a__isNatIListKind(X) ; } { Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(isNat(X)) > Marked_a__isNat(X) ; } { Marked_mark(isNatKind(X)) > Marked_a__isNatKind(X) ; } { Marked_mark(U11(X1,X2)) > Marked_a__U11(mark(X1),X2) ; } { Marked_mark(U11(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U12(X)) > Marked_mark(X) ; } { Marked_mark(isNatList(X)) > Marked_a__isNatList(X) ; } { Marked_mark(U21(X1,X2)) > Marked_a__U21(mark(X1),X2) ; } { Marked_mark(U21(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U22(X)) > Marked_mark(X) ; } { Marked_mark(U31(X1,X2)) > Marked_a__U31(mark(X1),X2) ; } { Marked_mark(U31(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U32(X)) > Marked_mark(X) ; } { 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(isNatIList(X)) > Marked_a__isNatIList(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,X3)) > Marked_a__U61(mark(X1),X2,X3) ; } { Marked_mark(U61(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U62(X1,X2)) > Marked_a__U62(mark(X1),X2) ; } { Marked_mark(U62(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U63(X)) > Marked_mark(X) ; } { Marked_mark(U71(X1,X2)) > Marked_a__U71(mark(X1),X2) ; } { Marked_mark(U71(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U81(X)) > Marked_mark(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 Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: a__zeros >= cons(0,zeros) constraint: a__zeros >= zeros constraint: a__U12(tt) >= tt constraint: a__U12(X) >= U12(X) constraint: a__isNatList(cons(V1,V2)) >= a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1,V2) constraint: a__isNatList(nil) >= tt constraint: a__isNatList(take(V1,V2)) >= a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1,V2) constraint: a__isNatList(X) >= isNatList(X) constraint: a__U11(tt,V1) >= a__U12(a__isNatList(V1)) constraint: a__U11(X1,X2) >= U11(X1,X2) constraint: a__U22(tt) >= tt constraint: a__U22(X) >= U22(X) constraint: a__isNat(0) >= tt constraint: a__isNat(s(V1)) >= a__U21(a__isNatKind(V1),V1) constraint: a__isNat(length(V1)) >= a__U11(a__isNatIListKind(V1),V1) constraint: a__isNat(X) >= isNat(X) constraint: a__U21(tt,V1) >= a__U22(a__isNat(V1)) constraint: a__U21(X1,X2) >= U21(X1,X2) constraint: a__U32(tt) >= tt constraint: a__U32(X) >= U32(X) constraint: a__U31(tt,V) >= a__U32(a__isNatList(V)) constraint: a__U31(X1,X2) >= U31(X1,X2) constraint: a__U42(tt,V2) >= a__U43(a__isNatIList(V2)) constraint: a__U42(X1,X2) >= U42(X1,X2) constraint: a__U41(tt,V1,V2) >= a__U42(a__isNat(V1),V2) constraint: a__U41(X1,X2,X3) >= U41(X1,X2,X3) constraint: a__U43(tt) >= tt constraint: a__U43(X) >= U43(X) constraint: a__isNatIList(cons(V1,V2)) >= a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1,V2) constraint: a__isNatIList(zeros) >= tt constraint: a__isNatIList(V) >= a__U31(a__isNatIListKind(V),V) constraint: a__isNatIList(X) >= isNatIList(X) constraint: a__U52(tt,V2) >= a__U53(a__isNatList(V2)) constraint: a__U52(X1,X2) >= U52(X1,X2) constraint: a__U51(tt,V1,V2) >= a__U52(a__isNat(V1),V2) constraint: a__U51(X1,X2,X3) >= U51(X1,X2,X3) constraint: a__U53(tt) >= tt constraint: a__U53(X) >= U53(X) constraint: a__U62(tt,V2) >= a__U63(a__isNatIList(V2)) constraint: a__U62(X1,X2) >= U62(X1,X2) constraint: a__U61(tt,V1,V2) >= a__U62(a__isNat(V1),V2) constraint: a__U61(X1,X2,X3) >= U61(X1,X2,X3) constraint: a__U63(tt) >= tt constraint: a__U63(X) >= U63(X) constraint: a__length(cons(N,L)) >= a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N),isNatKind(N))), L) constraint: a__length(nil) >= 0 constraint: a__length(X) >= length(X) constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2) constraint: mark(0) >= 0 constraint: mark(zeros) >= a__zeros constraint: mark(tt) >= tt constraint: mark(s(X)) >= s(mark(X)) constraint: mark(nil) >= nil constraint: mark(take(X1,X2)) >= a__take(mark(X1),mark(X2)) constraint: mark(length(X)) >= a__length(mark(X)) constraint: mark(isNatIListKind(X)) >= a__isNatIListKind(X) constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2) constraint: mark(isNat(X)) >= a__isNat(X) constraint: mark(isNatKind(X)) >= a__isNatKind(X) constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2) constraint: mark(U12(X)) >= a__U12(mark(X)) constraint: mark(isNatList(X)) >= a__isNatList(X) constraint: mark(U21(X1,X2)) >= a__U21(mark(X1),X2) constraint: mark(U22(X)) >= a__U22(mark(X)) constraint: mark(U31(X1,X2)) >= a__U31(mark(X1),X2) constraint: mark(U32(X)) >= a__U32(mark(X)) constraint: mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3) constraint: mark(U42(X1,X2)) >= a__U42(mark(X1),X2) constraint: mark(U43(X)) >= a__U43(mark(X)) constraint: mark(isNatIList(X)) >= a__isNatIList(X) constraint: mark(U51(X1,X2,X3)) >= a__U51(mark(X1),X2,X3) constraint: mark(U52(X1,X2)) >= a__U52(mark(X1),X2) constraint: mark(U53(X)) >= a__U53(mark(X)) constraint: mark(U61(X1,X2,X3)) >= a__U61(mark(X1),X2,X3) constraint: mark(U62(X1,X2)) >= a__U62(mark(X1),X2) constraint: mark(U63(X)) >= a__U63(mark(X)) constraint: mark(U71(X1,X2)) >= a__U71(mark(X1),X2) constraint: mark(U81(X)) >= a__U81(mark(X)) constraint: mark(U91(X1,X2,X3,X4)) >= a__U91(mark(X1),X2,X3,X4) constraint: a__U71(tt,L) >= s(a__length(mark(L))) constraint: a__U71(X1,X2) >= U71(X1,X2) constraint: a__U81(tt) >= nil constraint: a__U81(X) >= U81(X) constraint: a__U91(tt,IL,M,N) >= cons(mark(N),take(M,IL)) constraint: a__U91(X1,X2,X3,X4) >= U91(X1,X2,X3,X4) constraint: a__and(tt,X) >= mark(X) constraint: a__and(X1,X2) >= and(X1,X2) constraint: a__isNatIListKind(cons(V1,V2)) >= a__and(a__isNatKind(V1), isNatIListKind(V2)) constraint: a__isNatIListKind(zeros) >= tt constraint: a__isNatIListKind(nil) >= tt constraint: a__isNatIListKind(take(V1,V2)) >= a__and(a__isNatKind(V1), isNatIListKind(V2)) constraint: a__isNatIListKind(X) >= isNatIListKind(X) constraint: a__isNatKind(0) >= tt constraint: a__isNatKind(s(V1)) >= a__isNatKind(V1) constraint: a__isNatKind(length(V1)) >= a__isNatIListKind(V1) constraint: a__isNatKind(X) >= isNatKind(X) constraint: a__take(0,IL) >= a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL))) constraint: a__take(s(M),cons(N,IL)) >= a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N)))), IL,M,N) constraint: a__take(X1,X2) >= take(X1,X2) constraint: Marked_a__isNatKind(s(V1)) >= Marked_a__isNatKind(V1) constraint: Marked_a__isNatKind(length(V1)) >= Marked_a__isNatIListKind(V1) constraint: Marked_a__isNatIListKind(cons(V1,V2)) >= Marked_a__isNatKind(V1) constraint: Marked_a__isNatIListKind(cons(V1,V2)) >= Marked_a__and(a__isNatKind( V1), isNatIListKind(V2)) constraint: Marked_a__isNatIListKind(take(V1,V2)) >= Marked_a__isNatKind(V1) constraint: Marked_a__isNatIListKind(take(V1,V2)) >= Marked_a__and(a__isNatKind( V1), isNatIListKind(V2)) constraint: Marked_a__and(tt,X) >= Marked_mark(X) constraint: Marked_a__length(cons(N,L)) >= Marked_a__and(a__isNatList(L), isNatIListKind(L)) constraint: Marked_a__length(cons(N,L)) >= Marked_a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N),isNatKind(N))) constraint: Marked_a__length(cons(N,L)) >= Marked_a__U71(a__and(a__and( a__isNatList( L), isNatIListKind( L)), and(isNat(N), isNatKind(N))), L) constraint: Marked_a__length(cons(N,L)) >= Marked_a__isNatList(L) constraint: Marked_a__U71(tt,L) >= Marked_a__length(mark(L)) constraint: Marked_a__U71(tt,L) >= Marked_mark(L) constraint: Marked_a__U62(tt,V2) >= Marked_a__isNatIList(V2) constraint: Marked_a__U61(tt,V1,V2) >= Marked_a__U62(a__isNat(V1),V2) constraint: Marked_a__U61(tt,V1,V2) >= Marked_a__isNat(V1) constraint: Marked_a__U52(tt,V2) >= Marked_a__isNatList(V2) constraint: Marked_a__U51(tt,V1,V2) >= Marked_a__U52(a__isNat(V1),V2) constraint: Marked_a__U51(tt,V1,V2) >= Marked_a__isNat(V1) constraint: Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__isNatKind(V1) constraint: Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) constraint: Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__U41(a__and( a__isNatKind( V1), isNatIListKind( V2)), V1,V2) constraint: Marked_a__isNatIList(V) >= Marked_a__isNatIListKind(V) constraint: Marked_a__isNatIList(V) >= Marked_a__U31(a__isNatIListKind(V),V) constraint: Marked_a__U42(tt,V2) >= Marked_a__isNatIList(V2) constraint: Marked_a__U41(tt,V1,V2) >= Marked_a__U42(a__isNat(V1),V2) constraint: Marked_a__U41(tt,V1,V2) >= Marked_a__isNat(V1) constraint: Marked_a__U31(tt,V) >= Marked_a__isNatList(V) constraint: Marked_a__isNat(s(V1)) >= Marked_a__isNatKind(V1) constraint: Marked_a__isNat(s(V1)) >= Marked_a__U21(a__isNatKind(V1),V1) constraint: Marked_a__isNat(length(V1)) >= Marked_a__isNatIListKind(V1) constraint: Marked_a__isNat(length(V1)) >= Marked_a__U11(a__isNatIListKind(V1), V1) constraint: Marked_a__U21(tt,V1) >= Marked_a__isNat(V1) constraint: Marked_a__isNatList(cons(V1,V2)) >= Marked_a__isNatKind(V1) constraint: Marked_a__isNatList(cons(V1,V2)) >= Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) constraint: Marked_a__isNatList(cons(V1,V2)) >= Marked_a__U51(a__and( a__isNatKind( V1), isNatIListKind( V2)), V1,V2) constraint: Marked_a__isNatList(take(V1,V2)) >= Marked_a__isNatKind(V1) constraint: Marked_a__isNatList(take(V1,V2)) >= Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) constraint: Marked_a__isNatList(take(V1,V2)) >= Marked_a__U61(a__and( a__isNatKind( V1), isNatIListKind( V2)), V1,V2) constraint: Marked_a__U11(tt,V1) >= Marked_a__isNatList(V1) constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(s(X)) >= Marked_mark(X) constraint: Marked_mark(length(X)) >= Marked_a__length(mark(X)) constraint: Marked_mark(length(X)) >= Marked_mark(X) constraint: Marked_mark(isNatIListKind(X)) >= Marked_a__isNatIListKind(X) constraint: Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(isNat(X)) >= Marked_a__isNat(X) constraint: Marked_mark(isNatKind(X)) >= Marked_a__isNatKind(X) constraint: Marked_mark(U11(X1,X2)) >= Marked_a__U11(mark(X1),X2) constraint: Marked_mark(U11(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U12(X)) >= Marked_mark(X) constraint: Marked_mark(isNatList(X)) >= Marked_a__isNatList(X) constraint: Marked_mark(U21(X1,X2)) >= Marked_a__U21(mark(X1),X2) constraint: Marked_mark(U21(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U22(X)) >= Marked_mark(X) constraint: Marked_mark(U31(X1,X2)) >= Marked_a__U31(mark(X1),X2) constraint: Marked_mark(U31(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U32(X)) >= Marked_mark(X) constraint: Marked_mark(U41(X1,X2,X3)) >= Marked_a__U41(mark(X1),X2,X3) constraint: Marked_mark(U41(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U42(X1,X2)) >= Marked_a__U42(mark(X1),X2) constraint: Marked_mark(U42(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U43(X)) >= Marked_mark(X) constraint: Marked_mark(isNatIList(X)) >= Marked_a__isNatIList(X) constraint: Marked_mark(U51(X1,X2,X3)) >= Marked_a__U51(mark(X1),X2,X3) constraint: Marked_mark(U51(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U52(X1,X2)) >= Marked_a__U52(mark(X1),X2) constraint: Marked_mark(U52(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U53(X)) >= Marked_mark(X) constraint: Marked_mark(U61(X1,X2,X3)) >= Marked_a__U61(mark(X1),X2,X3) constraint: Marked_mark(U61(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U62(X1,X2)) >= Marked_a__U62(mark(X1),X2) constraint: Marked_mark(U62(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U63(X)) >= Marked_mark(X) constraint: Marked_mark(U71(X1,X2)) >= Marked_a__U71(mark(X1),X2) constraint: Marked_mark(U71(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U81(X)) >= Marked_mark(X) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__zeros >= cons(0,zeros) ; a__zeros >= zeros ; a__U12(tt) >= tt ; a__U12(X) >= U12(X) ; a__isNatList(cons(V1,V2)) >= a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)),V1,V2) ; a__isNatList(nil) >= tt ; a__isNatList(take(V1,V2)) >= a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)),V1,V2) ; a__isNatList(X) >= isNatList(X) ; a__U11(tt,V1) >= a__U12(a__isNatList(V1)) ; a__U11(X1,X2) >= U11(X1,X2) ; a__U22(tt) >= tt ; a__U22(X) >= U22(X) ; a__isNat(0) >= tt ; a__isNat(s(V1)) >= a__U21(a__isNatKind(V1),V1) ; a__isNat(length(V1)) >= a__U11(a__isNatIListKind(V1),V1) ; a__isNat(X) >= isNat(X) ; a__U21(tt,V1) >= a__U22(a__isNat(V1)) ; a__U21(X1,X2) >= U21(X1,X2) ; a__U32(tt) >= tt ; a__U32(X) >= U32(X) ; a__U31(tt,V) >= a__U32(a__isNatList(V)) ; a__U31(X1,X2) >= U31(X1,X2) ; a__U42(tt,V2) >= a__U43(a__isNatIList(V2)) ; a__U42(X1,X2) >= U42(X1,X2) ; a__U41(tt,V1,V2) >= a__U42(a__isNat(V1),V2) ; a__U41(X1,X2,X3) >= U41(X1,X2,X3) ; a__U43(tt) >= tt ; a__U43(X) >= U43(X) ; a__isNatIList(cons(V1,V2)) >= a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)),V1,V2) ; a__isNatIList(zeros) >= tt ; a__isNatIList(V) >= a__U31(a__isNatIListKind(V),V) ; a__isNatIList(X) >= isNatIList(X) ; a__U52(tt,V2) >= a__U53(a__isNatList(V2)) ; a__U52(X1,X2) >= U52(X1,X2) ; a__U51(tt,V1,V2) >= a__U52(a__isNat(V1),V2) ; a__U51(X1,X2,X3) >= U51(X1,X2,X3) ; a__U53(tt) >= tt ; a__U53(X) >= U53(X) ; a__U62(tt,V2) >= a__U63(a__isNatIList(V2)) ; a__U62(X1,X2) >= U62(X1,X2) ; a__U61(tt,V1,V2) >= a__U62(a__isNat(V1),V2) ; a__U61(X1,X2,X3) >= U61(X1,X2,X3) ; a__U63(tt) >= tt ; a__U63(X) >= U63(X) ; a__length(cons(N,L)) >= a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N),isNatKind(N))),L) ; a__length(nil) >= 0 ; a__length(X) >= length(X) ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(0) >= 0 ; mark(zeros) >= a__zeros ; mark(tt) >= tt ; mark(s(X)) >= s(mark(X)) ; mark(nil) >= nil ; mark(take(X1,X2)) >= a__take(mark(X1),mark(X2)) ; mark(length(X)) >= a__length(mark(X)) ; mark(isNatIListKind(X)) >= a__isNatIListKind(X) ; mark(and(X1,X2)) >= a__and(mark(X1),X2) ; mark(isNat(X)) >= a__isNat(X) ; mark(isNatKind(X)) >= a__isNatKind(X) ; mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ; mark(U12(X)) >= a__U12(mark(X)) ; mark(isNatList(X)) >= a__isNatList(X) ; mark(U21(X1,X2)) >= a__U21(mark(X1),X2) ; mark(U22(X)) >= a__U22(mark(X)) ; mark(U31(X1,X2)) >= a__U31(mark(X1),X2) ; mark(U32(X)) >= a__U32(mark(X)) ; 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(isNatIList(X)) >= a__isNatIList(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,X3)) >= a__U61(mark(X1),X2,X3) ; mark(U62(X1,X2)) >= a__U62(mark(X1),X2) ; mark(U63(X)) >= a__U63(mark(X)) ; mark(U71(X1,X2)) >= a__U71(mark(X1),X2) ; mark(U81(X)) >= a__U81(mark(X)) ; mark(U91(X1,X2,X3,X4)) >= a__U91(mark(X1),X2,X3,X4) ; a__U71(tt,L) >= s(a__length(mark(L))) ; a__U71(X1,X2) >= U71(X1,X2) ; a__U81(tt) >= nil ; a__U81(X) >= U81(X) ; a__U91(tt,IL,M,N) >= cons(mark(N),take(M,IL)) ; a__U91(X1,X2,X3,X4) >= U91(X1,X2,X3,X4) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__isNatIListKind(cons(V1,V2)) >= a__and(a__isNatKind(V1),isNatIListKind(V2)) ; a__isNatIListKind(zeros) >= tt ; a__isNatIListKind(nil) >= tt ; a__isNatIListKind(take(V1,V2)) >= a__and(a__isNatKind(V1),isNatIListKind(V2)) ; a__isNatIListKind(X) >= isNatIListKind(X) ; a__isNatKind(0) >= tt ; a__isNatKind(s(V1)) >= a__isNatKind(V1) ; a__isNatKind(length(V1)) >= a__isNatIListKind(V1) ; a__isNatKind(X) >= isNatKind(X) ; a__take(0,IL) >= a__U81(a__and(a__isNatIList(IL),isNatIListKind(IL))) ; a__take(s(M),cons(N,IL)) >= a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N)))),IL, M,N) ; a__take(X1,X2) >= take(X1,X2) ; Marked_a__isNatKind(s(V1)) >= Marked_a__isNatKind(V1) ; Marked_a__isNatKind(length(V1)) >= Marked_a__isNatIListKind(V1) ; Marked_a__isNatIListKind(cons(V1,V2)) >= Marked_a__isNatKind(V1) ; Marked_a__isNatIListKind(cons(V1,V2)) >= Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; Marked_a__isNatIListKind(take(V1,V2)) >= Marked_a__isNatKind(V1) ; Marked_a__isNatIListKind(take(V1,V2)) >= Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; Marked_a__and(tt,X) >= Marked_mark(X) ; Marked_a__length(cons(N,L)) >= Marked_a__and(a__isNatList(L), isNatIListKind(L)) ; Marked_a__length(cons(N,L)) >= Marked_a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N),isNatKind(N))) ; Marked_a__length(cons(N,L)) >= Marked_a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N),isNatKind(N))), L) ; Marked_a__length(cons(N,L)) >= Marked_a__isNatList(L) ; Marked_a__U71(tt,L) >= Marked_a__length(mark(L)) ; Marked_a__U71(tt,L) >= Marked_mark(L) ; Marked_a__U62(tt,V2) >= Marked_a__isNatIList(V2) ; Marked_a__U61(tt,V1,V2) >= Marked_a__U62(a__isNat(V1),V2) ; Marked_a__U61(tt,V1,V2) >= Marked_a__isNat(V1) ; Marked_a__U52(tt,V2) >= Marked_a__isNatList(V2) ; Marked_a__U51(tt,V1,V2) >= Marked_a__U52(a__isNat(V1),V2) ; Marked_a__U51(tt,V1,V2) >= Marked_a__isNat(V1) ; Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__isNatKind(V1) ; Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1,V2) ; Marked_a__isNatIList(V) >= Marked_a__isNatIListKind(V) ; Marked_a__isNatIList(V) >= Marked_a__U31(a__isNatIListKind(V),V) ; Marked_a__U42(tt,V2) >= Marked_a__isNatIList(V2) ; Marked_a__U41(tt,V1,V2) >= Marked_a__U42(a__isNat(V1),V2) ; Marked_a__U41(tt,V1,V2) >= Marked_a__isNat(V1) ; Marked_a__U31(tt,V) >= Marked_a__isNatList(V) ; Marked_a__isNat(s(V1)) >= Marked_a__isNatKind(V1) ; Marked_a__isNat(s(V1)) >= Marked_a__U21(a__isNatKind(V1),V1) ; Marked_a__isNat(length(V1)) >= Marked_a__isNatIListKind(V1) ; Marked_a__isNat(length(V1)) >= Marked_a__U11(a__isNatIListKind(V1),V1) ; Marked_a__U21(tt,V1) >= Marked_a__isNat(V1) ; Marked_a__isNatList(cons(V1,V2)) >= Marked_a__isNatKind(V1) ; Marked_a__isNatList(cons(V1,V2)) >= Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; Marked_a__isNatList(cons(V1,V2)) >= Marked_a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1,V2) ; Marked_a__isNatList(take(V1,V2)) >= Marked_a__isNatKind(V1) ; Marked_a__isNatList(take(V1,V2)) >= Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; Marked_a__isNatList(take(V1,V2)) >= Marked_a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1,V2) ; Marked_a__U11(tt,V1) >= Marked_a__isNatList(V1) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(length(X)) >= Marked_a__length(mark(X)) ; Marked_mark(length(X)) >= Marked_mark(X) ; Marked_mark(isNatIListKind(X)) >= Marked_a__isNatIListKind(X) ; Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(isNat(X)) >= Marked_a__isNat(X) ; Marked_mark(isNatKind(X)) >= Marked_a__isNatKind(X) ; Marked_mark(U11(X1,X2)) >= Marked_a__U11(mark(X1),X2) ; Marked_mark(U11(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U12(X)) >= Marked_mark(X) ; Marked_mark(isNatList(X)) >= Marked_a__isNatList(X) ; Marked_mark(U21(X1,X2)) >= Marked_a__U21(mark(X1),X2) ; Marked_mark(U21(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U22(X)) >= Marked_mark(X) ; Marked_mark(U31(X1,X2)) >= Marked_a__U31(mark(X1),X2) ; Marked_mark(U31(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U32(X)) >= Marked_mark(X) ; 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(isNatIList(X)) >= Marked_a__isNatIList(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,X3)) >= Marked_a__U61(mark(X1),X2,X3) ; Marked_mark(U61(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U62(X1,X2)) >= Marked_a__U62(mark(X1),X2) ; Marked_mark(U62(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U63(X)) >= Marked_mark(X) ; Marked_mark(U71(X1,X2)) >= Marked_a__U71(mark(X1),X2) ; Marked_mark(U71(X1,X2)) >= Marked_mark(X1) ; } + Disjunctions:{ { Marked_a__isNatKind(s(V1)) > Marked_a__isNatKind(V1) ; } { Marked_a__isNatKind(length(V1)) > Marked_a__isNatIListKind(V1) ; } { Marked_a__isNatIListKind(cons(V1,V2)) > Marked_a__isNatKind(V1) ; } { Marked_a__isNatIListKind(cons(V1,V2)) > Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; } { Marked_a__isNatIListKind(take(V1,V2)) > Marked_a__isNatKind(V1) ; } { Marked_a__isNatIListKind(take(V1,V2)) > Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; } { Marked_a__and(tt,X) > Marked_mark(X) ; } { Marked_a__length(cons(N,L)) > Marked_a__and(a__isNatList(L), isNatIListKind(L)) ; } { Marked_a__length(cons(N,L)) > Marked_a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N),isNatKind(N))) ; } { Marked_a__length(cons(N,L)) > Marked_a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N),isNatKind(N))), L) ; } { Marked_a__length(cons(N,L)) > Marked_a__isNatList(L) ; } { Marked_a__U71(tt,L) > Marked_a__length(mark(L)) ; } { Marked_a__U71(tt,L) > Marked_mark(L) ; } { Marked_a__U62(tt,V2) > Marked_a__isNatIList(V2) ; } { Marked_a__U61(tt,V1,V2) > Marked_a__U62(a__isNat(V1),V2) ; } { Marked_a__U61(tt,V1,V2) > Marked_a__isNat(V1) ; } { Marked_a__U52(tt,V2) > Marked_a__isNatList(V2) ; } { Marked_a__U51(tt,V1,V2) > Marked_a__U52(a__isNat(V1),V2) ; } { Marked_a__U51(tt,V1,V2) > Marked_a__isNat(V1) ; } { Marked_a__isNatIList(cons(V1,V2)) > Marked_a__isNatKind(V1) ; } { Marked_a__isNatIList(cons(V1,V2)) > Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; } { Marked_a__isNatIList(cons(V1,V2)) > Marked_a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1,V2) ; } { Marked_a__isNatIList(V) > Marked_a__isNatIListKind(V) ; } { Marked_a__isNatIList(V) > Marked_a__U31(a__isNatIListKind(V),V) ; } { Marked_a__U42(tt,V2) > Marked_a__isNatIList(V2) ; } { Marked_a__U41(tt,V1,V2) > Marked_a__U42(a__isNat(V1),V2) ; } { Marked_a__U41(tt,V1,V2) > Marked_a__isNat(V1) ; } { Marked_a__U31(tt,V) > Marked_a__isNatList(V) ; } { Marked_a__isNat(s(V1)) > Marked_a__isNatKind(V1) ; } { Marked_a__isNat(s(V1)) > Marked_a__U21(a__isNatKind(V1),V1) ; } { Marked_a__isNat(length(V1)) > Marked_a__isNatIListKind(V1) ; } { Marked_a__isNat(length(V1)) > Marked_a__U11(a__isNatIListKind(V1),V1) ; } { Marked_a__U21(tt,V1) > Marked_a__isNat(V1) ; } { Marked_a__isNatList(cons(V1,V2)) > Marked_a__isNatKind(V1) ; } { Marked_a__isNatList(cons(V1,V2)) > Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; } { Marked_a__isNatList(cons(V1,V2)) > Marked_a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1,V2) ; } { Marked_a__isNatList(take(V1,V2)) > Marked_a__isNatKind(V1) ; } { Marked_a__isNatList(take(V1,V2)) > Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) ; } { Marked_a__isNatList(take(V1,V2)) > Marked_a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1,V2) ; } { Marked_a__U11(tt,V1) > Marked_a__isNatList(V1) ; } { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(length(X)) > Marked_a__length(mark(X)) ; } { Marked_mark(length(X)) > Marked_mark(X) ; } { Marked_mark(isNatIListKind(X)) > Marked_a__isNatIListKind(X) ; } { Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(isNat(X)) > Marked_a__isNat(X) ; } { Marked_mark(isNatKind(X)) > Marked_a__isNatKind(X) ; } { Marked_mark(U11(X1,X2)) > Marked_a__U11(mark(X1),X2) ; } { Marked_mark(U11(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U12(X)) > Marked_mark(X) ; } { Marked_mark(isNatList(X)) > Marked_a__isNatList(X) ; } { Marked_mark(U21(X1,X2)) > Marked_a__U21(mark(X1),X2) ; } { Marked_mark(U21(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U22(X)) > Marked_mark(X) ; } { Marked_mark(U31(X1,X2)) > Marked_a__U31(mark(X1),X2) ; } { Marked_mark(U31(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U32(X)) > Marked_mark(X) ; } { 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(isNatIList(X)) > Marked_a__isNatIList(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,X3)) > Marked_a__U61(mark(X1),X2,X3) ; } { Marked_mark(U61(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U62(X1,X2)) > Marked_a__U62(mark(X1),X2) ; } { Marked_mark(U62(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U63(X)) > Marked_mark(X) ; } { Marked_mark(U71(X1,X2)) > Marked_a__U71(mark(X1),X2) ; } { Marked_mark(U71(X1,X2)) > Marked_mark(X1) ; } } === 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: a__zeros >= cons(0,zeros) constraint: a__zeros >= zeros constraint: a__U12(tt) >= tt constraint: a__U12(X) >= U12(X) constraint: a__isNatList(cons(V1,V2)) >= a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1,V2) constraint: a__isNatList(nil) >= tt constraint: a__isNatList(take(V1,V2)) >= a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1,V2) constraint: a__isNatList(X) >= isNatList(X) constraint: a__U11(tt,V1) >= a__U12(a__isNatList(V1)) constraint: a__U11(X1,X2) >= U11(X1,X2) constraint: a__U22(tt) >= tt constraint: a__U22(X) >= U22(X) constraint: a__isNat(0) >= tt constraint: a__isNat(s(V1)) >= a__U21(a__isNatKind(V1),V1) constraint: a__isNat(length(V1)) >= a__U11(a__isNatIListKind(V1),V1) constraint: a__isNat(X) >= isNat(X) constraint: a__U21(tt,V1) >= a__U22(a__isNat(V1)) constraint: a__U21(X1,X2) >= U21(X1,X2) constraint: a__U32(tt) >= tt constraint: a__U32(X) >= U32(X) constraint: a__U31(tt,V) >= a__U32(a__isNatList(V)) constraint: a__U31(X1,X2) >= U31(X1,X2) constraint: a__U42(tt,V2) >= a__U43(a__isNatIList(V2)) constraint: a__U42(X1,X2) >= U42(X1,X2) constraint: a__U41(tt,V1,V2) >= a__U42(a__isNat(V1),V2) constraint: a__U41(X1,X2,X3) >= U41(X1,X2,X3) constraint: a__U43(tt) >= tt constraint: a__U43(X) >= U43(X) constraint: a__isNatIList(cons(V1,V2)) >= a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1,V2) constraint: a__isNatIList(zeros) >= tt constraint: a__isNatIList(V) >= a__U31(a__isNatIListKind(V),V) constraint: a__isNatIList(X) >= isNatIList(X) constraint: a__U52(tt,V2) >= a__U53(a__isNatList(V2)) constraint: a__U52(X1,X2) >= U52(X1,X2) constraint: a__U51(tt,V1,V2) >= a__U52(a__isNat(V1),V2) constraint: a__U51(X1,X2,X3) >= U51(X1,X2,X3) constraint: a__U53(tt) >= tt constraint: a__U53(X) >= U53(X) constraint: a__U62(tt,V2) >= a__U63(a__isNatIList(V2)) constraint: a__U62(X1,X2) >= U62(X1,X2) constraint: a__U61(tt,V1,V2) >= a__U62(a__isNat(V1),V2) constraint: a__U61(X1,X2,X3) >= U61(X1,X2,X3) constraint: a__U63(tt) >= tt constraint: a__U63(X) >= U63(X) constraint: a__length(cons(N,L)) >= a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N),isNatKind(N))), L) constraint: a__length(nil) >= 0 constraint: a__length(X) >= length(X) constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2) constraint: mark(0) >= 0 constraint: mark(zeros) >= a__zeros constraint: mark(tt) >= tt constraint: mark(s(X)) >= s(mark(X)) constraint: mark(nil) >= nil constraint: mark(take(X1,X2)) >= a__take(mark(X1),mark(X2)) constraint: mark(length(X)) >= a__length(mark(X)) constraint: mark(isNatIListKind(X)) >= a__isNatIListKind(X) constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2) constraint: mark(isNat(X)) >= a__isNat(X) constraint: mark(isNatKind(X)) >= a__isNatKind(X) constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2) constraint: mark(U12(X)) >= a__U12(mark(X)) constraint: mark(isNatList(X)) >= a__isNatList(X) constraint: mark(U21(X1,X2)) >= a__U21(mark(X1),X2) constraint: mark(U22(X)) >= a__U22(mark(X)) constraint: mark(U31(X1,X2)) >= a__U31(mark(X1),X2) constraint: mark(U32(X)) >= a__U32(mark(X)) constraint: mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3) constraint: mark(U42(X1,X2)) >= a__U42(mark(X1),X2) constraint: mark(U43(X)) >= a__U43(mark(X)) constraint: mark(isNatIList(X)) >= a__isNatIList(X) constraint: mark(U51(X1,X2,X3)) >= a__U51(mark(X1),X2,X3) constraint: mark(U52(X1,X2)) >= a__U52(mark(X1),X2) constraint: mark(U53(X)) >= a__U53(mark(X)) constraint: mark(U61(X1,X2,X3)) >= a__U61(mark(X1),X2,X3) constraint: mark(U62(X1,X2)) >= a__U62(mark(X1),X2) constraint: mark(U63(X)) >= a__U63(mark(X)) constraint: mark(U71(X1,X2)) >= a__U71(mark(X1),X2) constraint: mark(U81(X)) >= a__U81(mark(X)) constraint: mark(U91(X1,X2,X3,X4)) >= a__U91(mark(X1),X2,X3,X4) constraint: a__U71(tt,L) >= s(a__length(mark(L))) constraint: a__U71(X1,X2) >= U71(X1,X2) constraint: a__U81(tt) >= nil constraint: a__U81(X) >= U81(X) constraint: a__U91(tt,IL,M,N) >= cons(mark(N),take(M,IL)) constraint: a__U91(X1,X2,X3,X4) >= U91(X1,X2,X3,X4) constraint: a__and(tt,X) >= mark(X) constraint: a__and(X1,X2) >= and(X1,X2) constraint: a__isNatIListKind(cons(V1,V2)) >= a__and(a__isNatKind(V1), isNatIListKind(V2)) constraint: a__isNatIListKind(zeros) >= tt constraint: a__isNatIListKind(nil) >= tt constraint: a__isNatIListKind(take(V1,V2)) >= a__and(a__isNatKind(V1), isNatIListKind(V2)) constraint: a__isNatIListKind(X) >= isNatIListKind(X) constraint: a__isNatKind(0) >= tt constraint: a__isNatKind(s(V1)) >= a__isNatKind(V1) constraint: a__isNatKind(length(V1)) >= a__isNatIListKind(V1) constraint: a__isNatKind(X) >= isNatKind(X) constraint: a__take(0,IL) >= a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL))) constraint: a__take(s(M),cons(N,IL)) >= a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N)))), IL,M,N) constraint: a__take(X1,X2) >= take(X1,X2) constraint: Marked_a__isNatKind(s(V1)) >= Marked_a__isNatKind(V1) constraint: Marked_a__isNatKind(length(V1)) >= Marked_a__isNatIListKind(V1) constraint: Marked_a__isNatIListKind(cons(V1,V2)) >= Marked_a__isNatKind(V1) constraint: Marked_a__isNatIListKind(cons(V1,V2)) >= Marked_a__and(a__isNatKind( V1), isNatIListKind(V2)) constraint: Marked_a__isNatIListKind(take(V1,V2)) >= Marked_a__isNatKind(V1) constraint: Marked_a__isNatIListKind(take(V1,V2)) >= Marked_a__and(a__isNatKind( V1), isNatIListKind(V2)) constraint: Marked_a__and(tt,X) >= Marked_mark(X) constraint: Marked_a__length(cons(N,L)) >= Marked_a__and(a__isNatList(L), isNatIListKind(L)) constraint: Marked_a__length(cons(N,L)) >= Marked_a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N),isNatKind(N))) constraint: Marked_a__length(cons(N,L)) >= Marked_a__U71(a__and(a__and( a__isNatList( L), isNatIListKind( L)), and(isNat(N), isNatKind(N))), L) constraint: Marked_a__length(cons(N,L)) >= Marked_a__isNatList(L) constraint: Marked_a__U71(tt,L) >= Marked_a__length(mark(L)) constraint: Marked_a__U71(tt,L) >= Marked_mark(L) constraint: Marked_a__U62(tt,V2) >= Marked_a__isNatIList(V2) constraint: Marked_a__U61(tt,V1,V2) >= Marked_a__U62(a__isNat(V1),V2) constraint: Marked_a__U61(tt,V1,V2) >= Marked_a__isNat(V1) constraint: Marked_a__U52(tt,V2) >= Marked_a__isNatList(V2) constraint: Marked_a__U51(tt,V1,V2) >= Marked_a__U52(a__isNat(V1),V2) constraint: Marked_a__U51(tt,V1,V2) >= Marked_a__isNat(V1) constraint: Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__isNatKind(V1) constraint: Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) constraint: Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__U41(a__and( a__isNatKind( V1), isNatIListKind( V2)), V1,V2) constraint: Marked_a__isNatIList(V) >= Marked_a__isNatIListKind(V) constraint: Marked_a__isNatIList(V) >= Marked_a__U31(a__isNatIListKind(V),V) constraint: Marked_a__U42(tt,V2) >= Marked_a__isNatIList(V2) constraint: Marked_a__U41(tt,V1,V2) >= Marked_a__U42(a__isNat(V1),V2) constraint: Marked_a__U41(tt,V1,V2) >= Marked_a__isNat(V1) constraint: Marked_a__U31(tt,V) >= Marked_a__isNatList(V) constraint: Marked_a__isNat(s(V1)) >= Marked_a__isNatKind(V1) constraint: Marked_a__isNat(s(V1)) >= Marked_a__U21(a__isNatKind(V1),V1) constraint: Marked_a__isNat(length(V1)) >= Marked_a__isNatIListKind(V1) constraint: Marked_a__isNat(length(V1)) >= Marked_a__U11(a__isNatIListKind(V1), V1) constraint: Marked_a__U21(tt,V1) >= Marked_a__isNat(V1) constraint: Marked_a__isNatList(cons(V1,V2)) >= Marked_a__isNatKind(V1) constraint: Marked_a__isNatList(cons(V1,V2)) >= Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) constraint: Marked_a__isNatList(cons(V1,V2)) >= Marked_a__U51(a__and( a__isNatKind( V1), isNatIListKind( V2)), V1,V2) constraint: Marked_a__isNatList(take(V1,V2)) >= Marked_a__isNatKind(V1) constraint: Marked_a__isNatList(take(V1,V2)) >= Marked_a__and(a__isNatKind(V1), isNatIListKind(V2)) constraint: Marked_a__isNatList(take(V1,V2)) >= Marked_a__U61(a__and( a__isNatKind( V1), isNatIListKind( V2)), V1,V2) constraint: Marked_a__U11(tt,V1) >= Marked_a__isNatList(V1) constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(s(X)) >= Marked_mark(X) constraint: Marked_mark(length(X)) >= Marked_a__length(mark(X)) constraint: Marked_mark(length(X)) >= Marked_mark(X) constraint: Marked_mark(isNatIListKind(X)) >= Marked_a__isNatIListKind(X) constraint: Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(isNat(X)) >= Marked_a__isNat(X) constraint: Marked_mark(isNatKind(X)) >= Marked_a__isNatKind(X) constraint: Marked_mark(U11(X1,X2)) >= Marked_a__U11(mark(X1),X2) constraint: Marked_mark(U11(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U12(X)) >= Marked_mark(X) constraint: Marked_mark(isNatList(X)) >= Marked_a__isNatList(X) constraint: Marked_mark(U21(X1,X2)) >= Marked_a__U21(mark(X1),X2) constraint: Marked_mark(U21(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U22(X)) >= Marked_mark(X) constraint: Marked_mark(U31(X1,X2)) >= Marked_a__U31(mark(X1),X2) constraint: Marked_mark(U31(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U32(X)) >= Marked_mark(X) constraint: Marked_mark(U41(X1,X2,X3)) >= Marked_a__U41(mark(X1),X2,X3) constraint: Marked_mark(U41(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U42(X1,X2)) >= Marked_a__U42(mark(X1),X2) constraint: Marked_mark(U42(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U43(X)) >= Marked_mark(X) constraint: Marked_mark(isNatIList(X)) >= Marked_a__isNatIList(X) constraint: Marked_mark(U51(X1,X2,X3)) >= Marked_a__U51(mark(X1),X2,X3) constraint: Marked_mark(U51(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U52(X1,X2)) >= Marked_a__U52(mark(X1),X2) constraint: Marked_mark(U52(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U53(X)) >= Marked_mark(X) constraint: Marked_mark(U61(X1,X2,X3)) >= Marked_a__U61(mark(X1),X2,X3) constraint: Marked_mark(U61(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U62(X1,X2)) >= Marked_a__U62(mark(X1),X2) constraint: Marked_mark(U62(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U63(X)) >= Marked_mark(X) constraint: Marked_mark(U71(X1,X2)) >= Marked_a__U71(mark(X1),X2) constraint: Marked_mark(U71(X1,X2)) >= Marked_mark(X1) APPLY CRITERIA (Graph splitting) Found 2 components: { --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__zeros >= cons(0,zeros) ; a__zeros >= zeros ; a__U12(tt) >= tt ; a__U12(X) >= U12(X) ; a__isNatList(cons(V1,V2)) >= a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)),V1,V2) ; a__isNatList(nil) >= tt ; a__isNatList(take(V1,V2)) >= a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)),V1,V2) ; a__isNatList(X) >= isNatList(X) ; a__U11(tt,V1) >= a__U12(a__isNatList(V1)) ; a__U11(X1,X2) >= U11(X1,X2) ; a__U22(tt) >= tt ; a__U22(X) >= U22(X) ; a__isNat(0) >= tt ; a__isNat(s(V1)) >= a__U21(a__isNatKind(V1),V1) ; a__isNat(length(V1)) >= a__U11(a__isNatIListKind(V1),V1) ; a__isNat(X) >= isNat(X) ; a__U21(tt,V1) >= a__U22(a__isNat(V1)) ; a__U21(X1,X2) >= U21(X1,X2) ; a__U32(tt) >= tt ; a__U32(X) >= U32(X) ; a__U31(tt,V) >= a__U32(a__isNatList(V)) ; a__U31(X1,X2) >= U31(X1,X2) ; a__U42(tt,V2) >= a__U43(a__isNatIList(V2)) ; a__U42(X1,X2) >= U42(X1,X2) ; a__U41(tt,V1,V2) >= a__U42(a__isNat(V1),V2) ; a__U41(X1,X2,X3) >= U41(X1,X2,X3) ; a__U43(tt) >= tt ; a__U43(X) >= U43(X) ; a__isNatIList(cons(V1,V2)) >= a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)),V1,V2) ; a__isNatIList(zeros) >= tt ; a__isNatIList(V) >= a__U31(a__isNatIListKind(V),V) ; a__isNatIList(X) >= isNatIList(X) ; a__U52(tt,V2) >= a__U53(a__isNatList(V2)) ; a__U52(X1,X2) >= U52(X1,X2) ; a__U51(tt,V1,V2) >= a__U52(a__isNat(V1),V2) ; a__U51(X1,X2,X3) >= U51(X1,X2,X3) ; a__U53(tt) >= tt ; a__U53(X) >= U53(X) ; a__U62(tt,V2) >= a__U63(a__isNatIList(V2)) ; a__U62(X1,X2) >= U62(X1,X2) ; a__U61(tt,V1,V2) >= a__U62(a__isNat(V1),V2) ; a__U61(X1,X2,X3) >= U61(X1,X2,X3) ; a__U63(tt) >= tt ; a__U63(X) >= U63(X) ; a__length(cons(N,L)) >= a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N),isNatKind(N))),L) ; a__length(nil) >= 0 ; a__length(X) >= length(X) ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(0) >= 0 ; mark(zeros) >= a__zeros ; mark(tt) >= tt ; mark(s(X)) >= s(mark(X)) ; mark(nil) >= nil ; mark(take(X1,X2)) >= a__take(mark(X1),mark(X2)) ; mark(length(X)) >= a__length(mark(X)) ; mark(isNatIListKind(X)) >= a__isNatIListKind(X) ; mark(and(X1,X2)) >= a__and(mark(X1),X2) ; mark(isNat(X)) >= a__isNat(X) ; mark(isNatKind(X)) >= a__isNatKind(X) ; mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ; mark(U12(X)) >= a__U12(mark(X)) ; mark(isNatList(X)) >= a__isNatList(X) ; mark(U21(X1,X2)) >= a__U21(mark(X1),X2) ; mark(U22(X)) >= a__U22(mark(X)) ; mark(U31(X1,X2)) >= a__U31(mark(X1),X2) ; mark(U32(X)) >= a__U32(mark(X)) ; 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(isNatIList(X)) >= a__isNatIList(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,X3)) >= a__U61(mark(X1),X2,X3) ; mark(U62(X1,X2)) >= a__U62(mark(X1),X2) ; mark(U63(X)) >= a__U63(mark(X)) ; mark(U71(X1,X2)) >= a__U71(mark(X1),X2) ; mark(U81(X)) >= a__U81(mark(X)) ; mark(U91(X1,X2,X3,X4)) >= a__U91(mark(X1),X2,X3,X4) ; a__U71(tt,L) >= s(a__length(mark(L))) ; a__U71(X1,X2) >= U71(X1,X2) ; a__U81(tt) >= nil ; a__U81(X) >= U81(X) ; a__U91(tt,IL,M,N) >= cons(mark(N),take(M,IL)) ; a__U91(X1,X2,X3,X4) >= U91(X1,X2,X3,X4) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__isNatIListKind(cons(V1,V2)) >= a__and(a__isNatKind(V1),isNatIListKind(V2)) ; a__isNatIListKind(zeros) >= tt ; a__isNatIListKind(nil) >= tt ; a__isNatIListKind(take(V1,V2)) >= a__and(a__isNatKind(V1),isNatIListKind(V2)) ; a__isNatIListKind(X) >= isNatIListKind(X) ; a__isNatKind(0) >= tt ; a__isNatKind(s(V1)) >= a__isNatKind(V1) ; a__isNatKind(length(V1)) >= a__isNatIListKind(V1) ; a__isNatKind(X) >= isNatKind(X) ; a__take(0,IL) >= a__U81(a__and(a__isNatIList(IL),isNatIListKind(IL))) ; a__take(s(M),cons(N,IL)) >= a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N)))),IL, M,N) ; a__take(X1,X2) >= take(X1,X2) ; Marked_a__length(cons(N,L)) >= Marked_a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N),isNatKind(N))), L) ; Marked_a__U71(tt,L) >= Marked_a__length(mark(L)) ; } + Disjunctions:{ { Marked_a__length(cons(N,L)) > Marked_a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N),isNatKind(N))), L) ; } { Marked_a__U71(tt,L) > Marked_a__length(mark(L)) ; } } === 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 106.668856 seconds (real time) Cime Exit Status: 0