- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] a__U101(tt,N,XS) -> a__fst(a__splitAt(mark(N),mark(XS))) [2] a__U11(tt,N,XS) -> a__snd(a__splitAt(mark(N),mark(XS))) [3] a__U21(tt,X) -> mark(X) [4] a__U31(tt,N) -> mark(N) [5] a__U41(tt,N) -> cons(mark(N),natsFrom(s(N))) [6] a__U51(tt,N,XS) -> a__head(a__afterNth(mark(N),mark(XS))) [7] a__U61(tt,Y) -> mark(Y) [8] a__U71(tt,XS) -> pair(nil,mark(XS)) [9] a__U81(tt,N,X,XS) -> a__U82(a__splitAt(mark(N),mark(XS)),X) [10] a__U82(pair(YS,ZS),X) -> pair(cons(mark(X),YS),mark(ZS)) [11] a__U91(tt,XS) -> mark(XS) [12] a__afterNth(N,XS) -> a__U11(a__and(a__isNatural(N),isLNat(XS)),N,XS) [13] a__and(tt,X) -> mark(X) [14] a__fst(pair(X,Y)) -> a__U21(a__and(a__isLNat(X),isLNat(Y)),X) [15] a__head(cons(N,XS)) -> a__U31(a__and(a__isNatural(N),isLNat(XS)),N) [16] a__isLNat(nil) -> tt [17] a__isLNat(afterNth(V1,V2)) -> a__and(a__isNatural(V1),isLNat(V2)) [18] a__isLNat(cons(V1,V2)) -> a__and(a__isNatural(V1),isLNat(V2)) [19] a__isLNat(fst(V1)) -> a__isPLNat(V1) [20] a__isLNat(natsFrom(V1)) -> a__isNatural(V1) [21] a__isLNat(snd(V1)) -> a__isPLNat(V1) [22] a__isLNat(tail(V1)) -> a__isLNat(V1) [23] a__isLNat(take(V1,V2)) -> a__and(a__isNatural(V1),isLNat(V2)) [24] a__isNatural(0) -> tt [25] a__isNatural(head(V1)) -> a__isLNat(V1) [26] a__isNatural(s(V1)) -> a__isNatural(V1) [27] a__isNatural(sel(V1,V2)) -> a__and(a__isNatural(V1),isLNat(V2)) [28] a__isPLNat(pair(V1,V2)) -> a__and(a__isLNat(V1),isLNat(V2)) [29] a__isPLNat(splitAt(V1,V2)) -> a__and(a__isNatural(V1),isLNat(V2)) [30] a__natsFrom(N) -> a__U41(a__isNatural(N),N) [31] a__sel(N,XS) -> a__U51(a__and(a__isNatural(N),isLNat(XS)),N,XS) [32] a__snd(pair(X,Y)) -> a__U61(a__and(a__isLNat(X),isLNat(Y)),Y) [33] a__splitAt(0,XS) -> a__U71(a__isLNat(XS),XS) [34] a__splitAt(s(N),cons(X,XS)) -> a__U81(a__and(a__isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS) [35] a__tail(cons(N,XS)) -> a__U91(a__and(a__isNatural(N),isLNat(XS)),XS) [36] a__take(N,XS) -> a__U101(a__and(a__isNatural(N),isLNat(XS)),N,XS) [37] mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) [38] mark(fst(X)) -> a__fst(mark(X)) [39] mark(splitAt(X1,X2)) -> a__splitAt(mark(X1),mark(X2)) [40] mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3) [41] mark(snd(X)) -> a__snd(mark(X)) [42] mark(U21(X1,X2)) -> a__U21(mark(X1),X2) [43] mark(U31(X1,X2)) -> a__U31(mark(X1),X2) [44] mark(U41(X1,X2)) -> a__U41(mark(X1),X2) [45] mark(natsFrom(X)) -> a__natsFrom(mark(X)) [46] mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) [47] mark(head(X)) -> a__head(mark(X)) [48] mark(afterNth(X1,X2)) -> a__afterNth(mark(X1),mark(X2)) [49] mark(U61(X1,X2)) -> a__U61(mark(X1),X2) [50] mark(U71(X1,X2)) -> a__U71(mark(X1),X2) [51] mark(U81(X1,X2,X3,X4)) -> a__U81(mark(X1),X2,X3,X4) [52] mark(U82(X1,X2)) -> a__U82(mark(X1),X2) [53] mark(U91(X1,X2)) -> a__U91(mark(X1),X2) [54] mark(and(X1,X2)) -> a__and(mark(X1),X2) [55] mark(isNatural(X)) -> a__isNatural(X) [56] mark(isLNat(X)) -> a__isLNat(X) [57] mark(isPLNat(X)) -> a__isPLNat(X) [58] mark(tail(X)) -> a__tail(mark(X)) [59] mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) [60] mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2)) [61] mark(tt) -> tt [62] mark(cons(X1,X2)) -> cons(mark(X1),X2) [63] mark(s(X)) -> s(mark(X)) [64] mark(pair(X1,X2)) -> pair(mark(X1),mark(X2)) [65] mark(nil) -> nil [66] mark(0) -> 0 [67] a__U101(X1,X2,X3) -> U101(X1,X2,X3) [68] a__fst(X) -> fst(X) [69] a__splitAt(X1,X2) -> splitAt(X1,X2) [70] a__U11(X1,X2,X3) -> U11(X1,X2,X3) [71] a__snd(X) -> snd(X) [72] a__U21(X1,X2) -> U21(X1,X2) [73] a__U31(X1,X2) -> U31(X1,X2) [74] a__U41(X1,X2) -> U41(X1,X2) [75] a__natsFrom(X) -> natsFrom(X) [76] a__U51(X1,X2,X3) -> U51(X1,X2,X3) [77] a__head(X) -> head(X) [78] a__afterNth(X1,X2) -> afterNth(X1,X2) [79] a__U61(X1,X2) -> U61(X1,X2) [80] a__U71(X1,X2) -> U71(X1,X2) [81] a__U81(X1,X2,X3,X4) -> U81(X1,X2,X3,X4) [82] a__U82(X1,X2) -> U82(X1,X2) [83] a__U91(X1,X2) -> U91(X1,X2) [84] a__and(X1,X2) -> and(X1,X2) [85] a__isNatural(X) -> isNatural(X) [86] a__isLNat(X) -> isLNat(X) [87] a__isPLNat(X) -> isPLNat(X) [88] a__tail(X) -> tail(X) [89] a__take(X1,X2) -> take(X1,X2) [90] a__sel(X1,X2) -> sel(X1,X2) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__fst(pair(X,Y)) >= a__U21(a__and(a__isLNat(X),isLNat(Y)),X) ; a__fst(X) >= fst(X) ; a__splitAt(s(N),cons(X,XS)) >= a__U81(a__and(a__isNatural(N), and(isNatural(X),isLNat(XS))), N,X,XS) ; a__splitAt(0,XS) >= a__U71(a__isLNat(XS),XS) ; a__splitAt(X1,X2) >= splitAt(X1,X2) ; mark(tt) >= tt ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(natsFrom(X)) >= a__natsFrom(mark(X)) ; mark(s(X)) >= s(mark(X)) ; mark(pair(X1,X2)) >= pair(mark(X1),mark(X2)) ; mark(nil) >= nil ; mark(isLNat(X)) >= a__isLNat(X) ; mark(afterNth(X1,X2)) >= a__afterNth(mark(X1),mark(X2)) ; mark(fst(X)) >= a__fst(mark(X)) ; mark(snd(X)) >= a__snd(mark(X)) ; mark(tail(X)) >= a__tail(mark(X)) ; mark(take(X1,X2)) >= a__take(mark(X1),mark(X2)) ; mark(0) >= 0 ; mark(head(X)) >= a__head(mark(X)) ; mark(sel(X1,X2)) >= a__sel(mark(X1),mark(X2)) ; mark(splitAt(X1,X2)) >= a__splitAt(mark(X1),mark(X2)) ; mark(and(X1,X2)) >= a__and(mark(X1),X2) ; mark(isNatural(X)) >= a__isNatural(X) ; mark(U101(X1,X2,X3)) >= a__U101(mark(X1),X2,X3) ; mark(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) ; mark(U21(X1,X2)) >= a__U21(mark(X1),X2) ; mark(U31(X1,X2)) >= a__U31(mark(X1),X2) ; mark(U41(X1,X2)) >= a__U41(mark(X1),X2) ; mark(U51(X1,X2,X3)) >= a__U51(mark(X1),X2,X3) ; mark(U61(X1,X2)) >= a__U61(mark(X1),X2) ; mark(U71(X1,X2)) >= a__U71(mark(X1),X2) ; mark(U81(X1,X2,X3,X4)) >= a__U81(mark(X1),X2,X3,X4) ; mark(U82(X1,X2)) >= a__U82(mark(X1),X2) ; mark(U91(X1,X2)) >= a__U91(mark(X1),X2) ; mark(isPLNat(X)) >= a__isPLNat(X) ; a__U101(tt,N,XS) >= a__fst(a__splitAt(mark(N),mark(XS))) ; a__U101(X1,X2,X3) >= U101(X1,X2,X3) ; a__snd(pair(X,Y)) >= a__U61(a__and(a__isLNat(X),isLNat(Y)),Y) ; a__snd(X) >= snd(X) ; a__U11(tt,N,XS) >= a__snd(a__splitAt(mark(N),mark(XS))) ; a__U11(X1,X2,X3) >= U11(X1,X2,X3) ; a__U21(tt,X) >= mark(X) ; a__U21(X1,X2) >= U21(X1,X2) ; a__U31(tt,N) >= mark(N) ; a__U31(X1,X2) >= U31(X1,X2) ; a__U41(tt,N) >= cons(mark(N),natsFrom(s(N))) ; a__U41(X1,X2) >= U41(X1,X2) ; a__head(cons(N,XS)) >= a__U31(a__and(a__isNatural(N),isLNat(XS)),N) ; a__head(X) >= head(X) ; a__afterNth(N,XS) >= a__U11(a__and(a__isNatural(N),isLNat(XS)),N,XS) ; a__afterNth(X1,X2) >= afterNth(X1,X2) ; a__U51(tt,N,XS) >= a__head(a__afterNth(mark(N),mark(XS))) ; a__U51(X1,X2,X3) >= U51(X1,X2,X3) ; a__U61(tt,Y) >= mark(Y) ; a__U61(X1,X2) >= U61(X1,X2) ; a__U71(tt,XS) >= pair(nil,mark(XS)) ; a__U71(X1,X2) >= U71(X1,X2) ; a__U82(pair(YS,ZS),X) >= pair(cons(mark(X),YS),mark(ZS)) ; a__U82(X1,X2) >= U82(X1,X2) ; a__U81(tt,N,X,XS) >= a__U82(a__splitAt(mark(N),mark(XS)),X) ; a__U81(X1,X2,X3,X4) >= U81(X1,X2,X3,X4) ; a__U91(tt,XS) >= mark(XS) ; a__U91(X1,X2) >= U91(X1,X2) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__isNatural(s(V1)) >= a__isNatural(V1) ; a__isNatural(0) >= tt ; a__isNatural(head(V1)) >= a__isLNat(V1) ; a__isNatural(sel(V1,V2)) >= a__and(a__isNatural(V1),isLNat(V2)) ; a__isNatural(X) >= isNatural(X) ; a__isLNat(cons(V1,V2)) >= a__and(a__isNatural(V1),isLNat(V2)) ; a__isLNat(natsFrom(V1)) >= a__isNatural(V1) ; a__isLNat(nil) >= tt ; a__isLNat(afterNth(V1,V2)) >= a__and(a__isNatural(V1),isLNat(V2)) ; a__isLNat(fst(V1)) >= a__isPLNat(V1) ; a__isLNat(snd(V1)) >= a__isPLNat(V1) ; a__isLNat(tail(V1)) >= a__isLNat(V1) ; a__isLNat(take(V1,V2)) >= a__and(a__isNatural(V1),isLNat(V2)) ; a__isLNat(X) >= isLNat(X) ; a__isPLNat(pair(V1,V2)) >= a__and(a__isLNat(V1),isLNat(V2)) ; a__isPLNat(splitAt(V1,V2)) >= a__and(a__isNatural(V1),isLNat(V2)) ; a__isPLNat(X) >= isPLNat(X) ; a__natsFrom(N) >= a__U41(a__isNatural(N),N) ; a__natsFrom(X) >= natsFrom(X) ; a__sel(N,XS) >= a__U51(a__and(a__isNatural(N),isLNat(XS)),N,XS) ; a__sel(X1,X2) >= sel(X1,X2) ; a__tail(cons(N,XS)) >= a__U91(a__and(a__isNatural(N),isLNat(XS)),XS) ; a__tail(X) >= tail(X) ; a__take(N,XS) >= a__U101(a__and(a__isNatural(N),isLNat(XS)),N,XS) ; a__take(X1,X2) >= take(X1,X2) ; Marked_a__sel(N,XS) >= Marked_a__isNatural(N) ; Marked_a__sel(N,XS) >= Marked_a__and(a__isNatural(N),isLNat(XS)) ; Marked_a__sel(N,XS) >= Marked_a__U51(a__and(a__isNatural(N),isLNat(XS)),N,XS) ; Marked_a__take(N,XS) >= Marked_a__isNatural(N) ; Marked_a__take(N,XS) >= Marked_a__and(a__isNatural(N),isLNat(XS)) ; Marked_a__take(N,XS) >= Marked_a__U101(a__and(a__isNatural(N),isLNat(XS)), N,XS) ; Marked_a__tail(cons(N,XS)) >= Marked_a__isNatural(N) ; Marked_a__tail(cons(N,XS)) >= Marked_a__and(a__isNatural(N),isLNat(XS)) ; Marked_a__tail(cons(N,XS)) >= Marked_a__U91(a__and(a__isNatural(N), isLNat(XS)),XS) ; Marked_a__isPLNat(pair(V1,V2)) >= Marked_a__isLNat(V1) ; Marked_a__isPLNat(pair(V1,V2)) >= Marked_a__and(a__isLNat(V1),isLNat(V2)) ; Marked_a__isPLNat(splitAt(V1,V2)) >= Marked_a__isNatural(V1) ; Marked_a__isPLNat(splitAt(V1,V2)) >= Marked_a__and(a__isNatural(V1), isLNat(V2)) ; Marked_a__isLNat(cons(V1,V2)) >= Marked_a__isNatural(V1) ; Marked_a__isLNat(cons(V1,V2)) >= Marked_a__and(a__isNatural(V1),isLNat(V2)) ; Marked_a__isLNat(natsFrom(V1)) >= Marked_a__isNatural(V1) ; Marked_a__isLNat(afterNth(V1,V2)) >= Marked_a__isNatural(V1) ; Marked_a__isLNat(afterNth(V1,V2)) >= Marked_a__and(a__isNatural(V1), isLNat(V2)) ; Marked_a__isLNat(fst(V1)) >= Marked_a__isPLNat(V1) ; Marked_a__isLNat(snd(V1)) >= Marked_a__isPLNat(V1) ; Marked_a__isLNat(tail(V1)) >= Marked_a__isLNat(V1) ; Marked_a__isLNat(take(V1,V2)) >= Marked_a__isNatural(V1) ; Marked_a__isLNat(take(V1,V2)) >= Marked_a__and(a__isNatural(V1),isLNat(V2)) ; Marked_a__isNatural(s(V1)) >= Marked_a__isNatural(V1) ; Marked_a__isNatural(head(V1)) >= Marked_a__isLNat(V1) ; Marked_a__isNatural(sel(V1,V2)) >= Marked_a__isNatural(V1) ; Marked_a__isNatural(sel(V1,V2)) >= Marked_a__and(a__isNatural(V1),isLNat(V2)) ; Marked_a__and(tt,X) >= Marked_mark(X) ; Marked_a__U91(tt,XS) >= Marked_mark(XS) ; Marked_a__U82(pair(YS,ZS),X) >= Marked_mark(X) ; Marked_a__U82(pair(YS,ZS),X) >= Marked_mark(ZS) ; Marked_a__U81(tt,N,X,XS) >= Marked_a__U82(a__splitAt(mark(N),mark(XS)),X) ; Marked_a__U81(tt,N,X,XS) >= Marked_a__splitAt(mark(N),mark(XS)) ; Marked_a__U81(tt,N,X,XS) >= Marked_mark(N) ; Marked_a__U81(tt,N,X,XS) >= Marked_mark(XS) ; Marked_a__U71(tt,XS) >= Marked_mark(XS) ; Marked_a__U61(tt,Y) >= Marked_mark(Y) ; Marked_a__afterNth(N,XS) >= Marked_a__isNatural(N) ; Marked_a__afterNth(N,XS) >= Marked_a__and(a__isNatural(N),isLNat(XS)) ; Marked_a__afterNth(N,XS) >= Marked_a__U11(a__and(a__isNatural(N),isLNat(XS)), N,XS) ; Marked_a__head(cons(N,XS)) >= Marked_a__isNatural(N) ; Marked_a__head(cons(N,XS)) >= Marked_a__and(a__isNatural(N),isLNat(XS)) ; Marked_a__head(cons(N,XS)) >= Marked_a__U31(a__and(a__isNatural(N), isLNat(XS)),N) ; Marked_a__U51(tt,N,XS) >= Marked_a__afterNth(mark(N),mark(XS)) ; Marked_a__U51(tt,N,XS) >= Marked_a__head(a__afterNth(mark(N),mark(XS))) ; Marked_a__U51(tt,N,XS) >= Marked_mark(N) ; Marked_a__U51(tt,N,XS) >= Marked_mark(XS) ; Marked_a__natsFrom(N) >= Marked_a__isNatural(N) ; Marked_a__natsFrom(N) >= Marked_a__U41(a__isNatural(N),N) ; Marked_a__U41(tt,N) >= Marked_mark(N) ; Marked_a__U31(tt,N) >= Marked_mark(N) ; Marked_a__U21(tt,X) >= Marked_mark(X) ; Marked_a__snd(pair(X,Y)) >= Marked_a__isLNat(X) ; Marked_a__snd(pair(X,Y)) >= Marked_a__and(a__isLNat(X),isLNat(Y)) ; Marked_a__snd(pair(X,Y)) >= Marked_a__U61(a__and(a__isLNat(X),isLNat(Y)),Y) ; Marked_a__U11(tt,N,XS) >= Marked_a__snd(a__splitAt(mark(N),mark(XS))) ; Marked_a__U11(tt,N,XS) >= Marked_a__splitAt(mark(N),mark(XS)) ; Marked_a__U11(tt,N,XS) >= Marked_mark(N) ; Marked_a__U11(tt,N,XS) >= Marked_mark(XS) ; Marked_a__splitAt(s(N),cons(X,XS)) >= Marked_a__isNatural(N) ; Marked_a__splitAt(s(N),cons(X,XS)) >= Marked_a__and(a__isNatural(N), and(isNatural(X),isLNat(XS))) ; Marked_a__splitAt(s(N),cons(X,XS)) >= Marked_a__U81(a__and(a__isNatural(N), and(isNatural(X), isLNat(XS))), N,X,XS) ; Marked_a__splitAt(0,XS) >= Marked_a__isLNat(XS) ; Marked_a__splitAt(0,XS) >= Marked_a__U71(a__isLNat(XS),XS) ; Marked_a__fst(pair(X,Y)) >= Marked_a__isLNat(X) ; Marked_a__fst(pair(X,Y)) >= Marked_a__and(a__isLNat(X),isLNat(Y)) ; Marked_a__fst(pair(X,Y)) >= Marked_a__U21(a__and(a__isLNat(X),isLNat(Y)),X) ; Marked_a__U101(tt,N,XS) >= Marked_a__splitAt(mark(N),mark(XS)) ; Marked_a__U101(tt,N,XS) >= Marked_a__fst(a__splitAt(mark(N),mark(XS))) ; Marked_a__U101(tt,N,XS) >= Marked_mark(N) ; Marked_a__U101(tt,N,XS) >= Marked_mark(XS) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(natsFrom(X)) >= Marked_a__natsFrom(mark(X)) ; Marked_mark(natsFrom(X)) >= Marked_mark(X) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(pair(X1,X2)) >= Marked_mark(X1) ; Marked_mark(pair(X1,X2)) >= Marked_mark(X2) ; Marked_mark(isLNat(X)) >= Marked_a__isLNat(X) ; Marked_mark(afterNth(X1,X2)) >= Marked_a__afterNth(mark(X1),mark(X2)) ; Marked_mark(afterNth(X1,X2)) >= Marked_mark(X1) ; Marked_mark(afterNth(X1,X2)) >= Marked_mark(X2) ; Marked_mark(fst(X)) >= Marked_a__fst(mark(X)) ; Marked_mark(fst(X)) >= Marked_mark(X) ; Marked_mark(snd(X)) >= Marked_a__snd(mark(X)) ; Marked_mark(snd(X)) >= Marked_mark(X) ; Marked_mark(tail(X)) >= Marked_a__tail(mark(X)) ; Marked_mark(tail(X)) >= Marked_mark(X) ; Marked_mark(take(X1,X2)) >= Marked_a__take(mark(X1),mark(X2)) ; Marked_mark(take(X1,X2)) >= Marked_mark(X1) ; Marked_mark(take(X1,X2)) >= Marked_mark(X2) ; Marked_mark(head(X)) >= Marked_a__head(mark(X)) ; Marked_mark(head(X)) >= Marked_mark(X) ; Marked_mark(sel(X1,X2)) >= Marked_a__sel(mark(X1),mark(X2)) ; Marked_mark(sel(X1,X2)) >= Marked_mark(X1) ; Marked_mark(sel(X1,X2)) >= Marked_mark(X2) ; Marked_mark(splitAt(X1,X2)) >= Marked_a__splitAt(mark(X1),mark(X2)) ; Marked_mark(splitAt(X1,X2)) >= Marked_mark(X1) ; Marked_mark(splitAt(X1,X2)) >= Marked_mark(X2) ; Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(isNatural(X)) >= Marked_a__isNatural(X) ; Marked_mark(U101(X1,X2,X3)) >= Marked_a__U101(mark(X1),X2,X3) ; Marked_mark(U101(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_a__U11(mark(X1),X2,X3) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U21(X1,X2)) >= Marked_a__U21(mark(X1),X2) ; Marked_mark(U21(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U31(X1,X2)) >= Marked_a__U31(mark(X1),X2) ; Marked_mark(U31(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U41(X1,X2)) >= Marked_a__U41(mark(X1),X2) ; Marked_mark(U41(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U51(X1,X2,X3)) >= Marked_a__U51(mark(X1),X2,X3) ; Marked_mark(U51(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U61(X1,X2)) >= Marked_a__U61(mark(X1),X2) ; Marked_mark(U61(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U71(X1,X2)) >= Marked_a__U71(mark(X1),X2) ; Marked_mark(U71(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U81(X1,X2,X3,X4)) >= Marked_a__U81(mark(X1),X2,X3,X4) ; Marked_mark(U81(X1,X2,X3,X4)) >= Marked_mark(X1) ; Marked_mark(U82(X1,X2)) >= Marked_a__U82(mark(X1),X2) ; Marked_mark(U82(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U91(X1,X2)) >= Marked_a__U91(mark(X1),X2) ; Marked_mark(U91(X1,X2)) >= Marked_mark(X1) ; Marked_mark(isPLNat(X)) >= Marked_a__isPLNat(X) ; } + Disjunctions:{ { Marked_a__sel(N,XS) > Marked_a__isNatural(N) ; } { Marked_a__sel(N,XS) > Marked_a__and(a__isNatural(N),isLNat(XS)) ; } { Marked_a__sel(N,XS) > Marked_a__U51(a__and(a__isNatural(N),isLNat(XS)),N,XS) ; } { Marked_a__take(N,XS) > Marked_a__isNatural(N) ; } { Marked_a__take(N,XS) > Marked_a__and(a__isNatural(N),isLNat(XS)) ; } { Marked_a__take(N,XS) > Marked_a__U101(a__and(a__isNatural(N),isLNat(XS)), N,XS) ; } { Marked_a__tail(cons(N,XS)) > Marked_a__isNatural(N) ; } { Marked_a__tail(cons(N,XS)) > Marked_a__and(a__isNatural(N),isLNat(XS)) ; } { Marked_a__tail(cons(N,XS)) > Marked_a__U91(a__and(a__isNatural(N),isLNat(XS)), XS) ; } { Marked_a__isPLNat(pair(V1,V2)) > Marked_a__isLNat(V1) ; } { Marked_a__isPLNat(pair(V1,V2)) > Marked_a__and(a__isLNat(V1),isLNat(V2)) ; } { Marked_a__isPLNat(splitAt(V1,V2)) > Marked_a__isNatural(V1) ; } { Marked_a__isPLNat(splitAt(V1,V2)) > Marked_a__and(a__isNatural(V1), isLNat(V2)) ; } { Marked_a__isLNat(cons(V1,V2)) > Marked_a__isNatural(V1) ; } { Marked_a__isLNat(cons(V1,V2)) > Marked_a__and(a__isNatural(V1),isLNat(V2)) ; } { Marked_a__isLNat(natsFrom(V1)) > Marked_a__isNatural(V1) ; } { Marked_a__isLNat(afterNth(V1,V2)) > Marked_a__isNatural(V1) ; } { Marked_a__isLNat(afterNth(V1,V2)) > Marked_a__and(a__isNatural(V1), isLNat(V2)) ; } { Marked_a__isLNat(fst(V1)) > Marked_a__isPLNat(V1) ; } { Marked_a__isLNat(snd(V1)) > Marked_a__isPLNat(V1) ; } { Marked_a__isLNat(tail(V1)) > Marked_a__isLNat(V1) ; } { Marked_a__isLNat(take(V1,V2)) > Marked_a__isNatural(V1) ; } { Marked_a__isLNat(take(V1,V2)) > Marked_a__and(a__isNatural(V1),isLNat(V2)) ; } { Marked_a__isNatural(s(V1)) > Marked_a__isNatural(V1) ; } { Marked_a__isNatural(head(V1)) > Marked_a__isLNat(V1) ; } { Marked_a__isNatural(sel(V1,V2)) > Marked_a__isNatural(V1) ; } { Marked_a__isNatural(sel(V1,V2)) > Marked_a__and(a__isNatural(V1),isLNat(V2)) ; } { Marked_a__and(tt,X) > Marked_mark(X) ; } { Marked_a__U91(tt,XS) > Marked_mark(XS) ; } { Marked_a__U82(pair(YS,ZS),X) > Marked_mark(X) ; } { Marked_a__U82(pair(YS,ZS),X) > Marked_mark(ZS) ; } { Marked_a__U81(tt,N,X,XS) > Marked_a__U82(a__splitAt(mark(N),mark(XS)),X) ; } { Marked_a__U81(tt,N,X,XS) > Marked_a__splitAt(mark(N),mark(XS)) ; } { Marked_a__U81(tt,N,X,XS) > Marked_mark(N) ; } { Marked_a__U81(tt,N,X,XS) > Marked_mark(XS) ; } { Marked_a__U71(tt,XS) > Marked_mark(XS) ; } { Marked_a__U61(tt,Y) > Marked_mark(Y) ; } { Marked_a__afterNth(N,XS) > Marked_a__isNatural(N) ; } { Marked_a__afterNth(N,XS) > Marked_a__and(a__isNatural(N),isLNat(XS)) ; } { Marked_a__afterNth(N,XS) > Marked_a__U11(a__and(a__isNatural(N),isLNat(XS)), N,XS) ; } { Marked_a__head(cons(N,XS)) > Marked_a__isNatural(N) ; } { Marked_a__head(cons(N,XS)) > Marked_a__and(a__isNatural(N),isLNat(XS)) ; } { Marked_a__head(cons(N,XS)) > Marked_a__U31(a__and(a__isNatural(N),isLNat(XS)), N) ; } { Marked_a__U51(tt,N,XS) > Marked_a__afterNth(mark(N),mark(XS)) ; } { Marked_a__U51(tt,N,XS) > Marked_a__head(a__afterNth(mark(N),mark(XS))) ; } { Marked_a__U51(tt,N,XS) > Marked_mark(N) ; } { Marked_a__U51(tt,N,XS) > Marked_mark(XS) ; } { Marked_a__natsFrom(N) > Marked_a__isNatural(N) ; } { Marked_a__natsFrom(N) > Marked_a__U41(a__isNatural(N),N) ; } { Marked_a__U41(tt,N) > Marked_mark(N) ; } { Marked_a__U31(tt,N) > Marked_mark(N) ; } { Marked_a__U21(tt,X) > Marked_mark(X) ; } { Marked_a__snd(pair(X,Y)) > Marked_a__isLNat(X) ; } { Marked_a__snd(pair(X,Y)) > Marked_a__and(a__isLNat(X),isLNat(Y)) ; } { Marked_a__snd(pair(X,Y)) > Marked_a__U61(a__and(a__isLNat(X),isLNat(Y)),Y) ; } { Marked_a__U11(tt,N,XS) > Marked_a__snd(a__splitAt(mark(N),mark(XS))) ; } { Marked_a__U11(tt,N,XS) > Marked_a__splitAt(mark(N),mark(XS)) ; } { Marked_a__U11(tt,N,XS) > Marked_mark(N) ; } { Marked_a__U11(tt,N,XS) > Marked_mark(XS) ; } { Marked_a__splitAt(s(N),cons(X,XS)) > Marked_a__isNatural(N) ; } { Marked_a__splitAt(s(N),cons(X,XS)) > Marked_a__and(a__isNatural(N), and(isNatural(X),isLNat(XS))) ; } { Marked_a__splitAt(s(N),cons(X,XS)) > Marked_a__U81(a__and(a__isNatural(N), and(isNatural(X), isLNat(XS))),N, X,XS) ; } { Marked_a__splitAt(0,XS) > Marked_a__isLNat(XS) ; } { Marked_a__splitAt(0,XS) > Marked_a__U71(a__isLNat(XS),XS) ; } { Marked_a__fst(pair(X,Y)) > Marked_a__isLNat(X) ; } { Marked_a__fst(pair(X,Y)) > Marked_a__and(a__isLNat(X),isLNat(Y)) ; } { Marked_a__fst(pair(X,Y)) > Marked_a__U21(a__and(a__isLNat(X),isLNat(Y)),X) ; } { Marked_a__U101(tt,N,XS) > Marked_a__splitAt(mark(N),mark(XS)) ; } { Marked_a__U101(tt,N,XS) > Marked_a__fst(a__splitAt(mark(N),mark(XS))) ; } { Marked_a__U101(tt,N,XS) > Marked_mark(N) ; } { Marked_a__U101(tt,N,XS) > Marked_mark(XS) ; } { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(natsFrom(X)) > Marked_a__natsFrom(mark(X)) ; } { Marked_mark(natsFrom(X)) > Marked_mark(X) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(pair(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(pair(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(isLNat(X)) > Marked_a__isLNat(X) ; } { Marked_mark(afterNth(X1,X2)) > Marked_a__afterNth(mark(X1),mark(X2)) ; } { Marked_mark(afterNth(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(afterNth(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(fst(X)) > Marked_a__fst(mark(X)) ; } { Marked_mark(fst(X)) > Marked_mark(X) ; } { Marked_mark(snd(X)) > Marked_a__snd(mark(X)) ; } { Marked_mark(snd(X)) > Marked_mark(X) ; } { Marked_mark(tail(X)) > Marked_a__tail(mark(X)) ; } { Marked_mark(tail(X)) > Marked_mark(X) ; } { Marked_mark(take(X1,X2)) > Marked_a__take(mark(X1),mark(X2)) ; } { Marked_mark(take(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(take(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(head(X)) > Marked_a__head(mark(X)) ; } { Marked_mark(head(X)) > Marked_mark(X) ; } { Marked_mark(sel(X1,X2)) > Marked_a__sel(mark(X1),mark(X2)) ; } { Marked_mark(sel(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(sel(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(splitAt(X1,X2)) > Marked_a__splitAt(mark(X1),mark(X2)) ; } { Marked_mark(splitAt(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(splitAt(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(isNatural(X)) > Marked_a__isNatural(X) ; } { Marked_mark(U101(X1,X2,X3)) > Marked_a__U101(mark(X1),X2,X3) ; } { Marked_mark(U101(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_a__U11(mark(X1),X2,X3) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U21(X1,X2)) > Marked_a__U21(mark(X1),X2) ; } { Marked_mark(U21(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U31(X1,X2)) > Marked_a__U31(mark(X1),X2) ; } { Marked_mark(U31(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U41(X1,X2)) > Marked_a__U41(mark(X1),X2) ; } { Marked_mark(U41(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U51(X1,X2,X3)) > Marked_a__U51(mark(X1),X2,X3) ; } { Marked_mark(U51(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U61(X1,X2)) > Marked_a__U61(mark(X1),X2) ; } { Marked_mark(U61(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U71(X1,X2)) > Marked_a__U71(mark(X1),X2) ; } { Marked_mark(U71(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U81(X1,X2,X3,X4)) > Marked_a__U81(mark(X1),X2,X3,X4) ; } { Marked_mark(U81(X1,X2,X3,X4)) > Marked_mark(X1) ; } { Marked_mark(U82(X1,X2)) > Marked_a__U82(mark(X1),X2) ; } { Marked_mark(U82(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U91(X1,X2)) > Marked_a__U91(mark(X1),X2) ; } { Marked_mark(U91(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(isPLNat(X)) > Marked_a__isPLNat(X) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. Entering rpo_solver === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === Time out for these parameters. === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 15.000000 === === STOPING TIMER real === Sat timeout reached === 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 (Simple graph) Found the following constraints: { a__fst(pair(X,Y)) >= a__U21(a__and(a__isLNat(X),isLNat(Y)),X) ; a__fst(X) >= fst(X) ; a__splitAt(s(N),cons(X,XS)) >= a__U81(a__and(a__isNatural(N), and(isNatural(X),isLNat(XS))), N,X,XS) ; a__splitAt(0,XS) >= a__U71(a__isLNat(XS),XS) ; a__splitAt(X1,X2) >= splitAt(X1,X2) ; mark(tt) >= tt ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(natsFrom(X)) >= a__natsFrom(mark(X)) ; mark(s(X)) >= s(mark(X)) ; mark(pair(X1,X2)) >= pair(mark(X1),mark(X2)) ; mark(nil) >= nil ; mark(isLNat(X)) >= a__isLNat(X) ; mark(afterNth(X1,X2)) >= a__afterNth(mark(X1),mark(X2)) ; mark(fst(X)) >= a__fst(mark(X)) ; mark(snd(X)) >= a__snd(mark(X)) ; mark(tail(X)) >= a__tail(mark(X)) ; mark(take(X1,X2)) >= a__take(mark(X1),mark(X2)) ; mark(0) >= 0 ; mark(head(X)) >= a__head(mark(X)) ; mark(sel(X1,X2)) >= a__sel(mark(X1),mark(X2)) ; mark(splitAt(X1,X2)) >= a__splitAt(mark(X1),mark(X2)) ; mark(and(X1,X2)) >= a__and(mark(X1),X2) ; mark(isNatural(X)) >= a__isNatural(X) ; mark(U101(X1,X2,X3)) >= a__U101(mark(X1),X2,X3) ; mark(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) ; mark(U21(X1,X2)) >= a__U21(mark(X1),X2) ; mark(U31(X1,X2)) >= a__U31(mark(X1),X2) ; mark(U41(X1,X2)) >= a__U41(mark(X1),X2) ; mark(U51(X1,X2,X3)) >= a__U51(mark(X1),X2,X3) ; mark(U61(X1,X2)) >= a__U61(mark(X1),X2) ; mark(U71(X1,X2)) >= a__U71(mark(X1),X2) ; mark(U81(X1,X2,X3,X4)) >= a__U81(mark(X1),X2,X3,X4) ; mark(U82(X1,X2)) >= a__U82(mark(X1),X2) ; mark(U91(X1,X2)) >= a__U91(mark(X1),X2) ; mark(isPLNat(X)) >= a__isPLNat(X) ; a__U101(tt,N,XS) >= a__fst(a__splitAt(mark(N),mark(XS))) ; a__U101(X1,X2,X3) >= U101(X1,X2,X3) ; a__snd(pair(X,Y)) >= a__U61(a__and(a__isLNat(X),isLNat(Y)),Y) ; a__snd(X) >= snd(X) ; a__U11(tt,N,XS) >= a__snd(a__splitAt(mark(N),mark(XS))) ; a__U11(X1,X2,X3) >= U11(X1,X2,X3) ; a__U21(tt,X) >= mark(X) ; a__U21(X1,X2) >= U21(X1,X2) ; a__U31(tt,N) >= mark(N) ; a__U31(X1,X2) >= U31(X1,X2) ; a__U41(tt,N) >= cons(mark(N),natsFrom(s(N))) ; a__U41(X1,X2) >= U41(X1,X2) ; a__head(cons(N,XS)) >= a__U31(a__and(a__isNatural(N),isLNat(XS)),N) ; a__head(X) >= head(X) ; a__afterNth(N,XS) >= a__U11(a__and(a__isNatural(N),isLNat(XS)),N,XS) ; a__afterNth(X1,X2) >= afterNth(X1,X2) ; a__U51(tt,N,XS) >= a__head(a__afterNth(mark(N),mark(XS))) ; a__U51(X1,X2,X3) >= U51(X1,X2,X3) ; a__U61(tt,Y) >= mark(Y) ; a__U61(X1,X2) >= U61(X1,X2) ; a__U71(tt,XS) >= pair(nil,mark(XS)) ; a__U71(X1,X2) >= U71(X1,X2) ; a__U82(pair(YS,ZS),X) >= pair(cons(mark(X),YS),mark(ZS)) ; a__U82(X1,X2) >= U82(X1,X2) ; a__U81(tt,N,X,XS) >= a__U82(a__splitAt(mark(N),mark(XS)),X) ; a__U81(X1,X2,X3,X4) >= U81(X1,X2,X3,X4) ; a__U91(tt,XS) >= mark(XS) ; a__U91(X1,X2) >= U91(X1,X2) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__isNatural(s(V1)) >= a__isNatural(V1) ; a__isNatural(0) >= tt ; a__isNatural(head(V1)) >= a__isLNat(V1) ; a__isNatural(sel(V1,V2)) >= a__and(a__isNatural(V1),isLNat(V2)) ; a__isNatural(X) >= isNatural(X) ; a__isLNat(cons(V1,V2)) >= a__and(a__isNatural(V1),isLNat(V2)) ; a__isLNat(natsFrom(V1)) >= a__isNatural(V1) ; a__isLNat(nil) >= tt ; a__isLNat(afterNth(V1,V2)) >= a__and(a__isNatural(V1),isLNat(V2)) ; a__isLNat(fst(V1)) >= a__isPLNat(V1) ; a__isLNat(snd(V1)) >= a__isPLNat(V1) ; a__isLNat(tail(V1)) >= a__isLNat(V1) ; a__isLNat(take(V1,V2)) >= a__and(a__isNatural(V1),isLNat(V2)) ; a__isLNat(X) >= isLNat(X) ; a__isPLNat(pair(V1,V2)) >= a__and(a__isLNat(V1),isLNat(V2)) ; a__isPLNat(splitAt(V1,V2)) >= a__and(a__isNatural(V1),isLNat(V2)) ; a__isPLNat(X) >= isPLNat(X) ; a__natsFrom(N) >= a__U41(a__isNatural(N),N) ; a__natsFrom(X) >= natsFrom(X) ; a__sel(N,XS) >= a__U51(a__and(a__isNatural(N),isLNat(XS)),N,XS) ; a__sel(X1,X2) >= sel(X1,X2) ; a__tail(cons(N,XS)) >= a__U91(a__and(a__isNatural(N),isLNat(XS)),XS) ; a__tail(X) >= tail(X) ; a__take(N,XS) >= a__U101(a__and(a__isNatural(N),isLNat(XS)),N,XS) ; a__take(X1,X2) >= take(X1,X2) ; Marked_a__sel(N,XS) >= Marked_a__isNatural(N) ; Marked_a__sel(N,XS) >= Marked_a__and(a__isNatural(N),isLNat(XS)) ; Marked_a__sel(N,XS) >= Marked_a__U51(a__and(a__isNatural(N),isLNat(XS)),N,XS) ; Marked_a__take(N,XS) > Marked_a__isNatural(N) ; Marked_a__take(N,XS) > Marked_a__and(a__isNatural(N),isLNat(XS)) ; Marked_a__take(N,XS) >= Marked_a__U101(a__and(a__isNatural(N),isLNat(XS)), N,XS) ; Marked_a__tail(cons(N,XS)) > Marked_a__isNatural(N) ; Marked_a__tail(cons(N,XS)) > Marked_a__and(a__isNatural(N),isLNat(XS)) ; Marked_a__tail(cons(N,XS)) >= Marked_a__U91(a__and(a__isNatural(N), isLNat(XS)),XS) ; Marked_a__isPLNat(pair(V1,V2)) > Marked_a__isLNat(V1) ; Marked_a__isPLNat(pair(V1,V2)) > Marked_a__and(a__isLNat(V1),isLNat(V2)) ; Marked_a__isPLNat(splitAt(V1,V2)) > Marked_a__isNatural(V1) ; Marked_a__isPLNat(splitAt(V1,V2)) > Marked_a__and(a__isNatural(V1), isLNat(V2)) ; Marked_a__isLNat(cons(V1,V2)) > Marked_a__isNatural(V1) ; Marked_a__isLNat(cons(V1,V2)) > Marked_a__and(a__isNatural(V1),isLNat(V2)) ; Marked_a__isLNat(natsFrom(V1)) > Marked_a__isNatural(V1) ; Marked_a__isLNat(afterNth(V1,V2)) > Marked_a__isNatural(V1) ; Marked_a__isLNat(afterNth(V1,V2)) > Marked_a__and(a__isNatural(V1), isLNat(V2)) ; Marked_a__isLNat(fst(V1)) > Marked_a__isPLNat(V1) ; Marked_a__isLNat(snd(V1)) >= Marked_a__isPLNat(V1) ; Marked_a__isLNat(tail(V1)) > Marked_a__isLNat(V1) ; Marked_a__isLNat(take(V1,V2)) > Marked_a__isNatural(V1) ; Marked_a__isLNat(take(V1,V2)) > Marked_a__and(a__isNatural(V1),isLNat(V2)) ; Marked_a__isNatural(s(V1)) > Marked_a__isNatural(V1) ; Marked_a__isNatural(head(V1)) >= Marked_a__isLNat(V1) ; Marked_a__isNatural(sel(V1,V2)) > Marked_a__isNatural(V1) ; Marked_a__isNatural(sel(V1,V2)) >= Marked_a__and(a__isNatural(V1),isLNat(V2)) ; Marked_a__and(tt,X) > Marked_mark(X) ; Marked_a__U91(tt,XS) > Marked_mark(XS) ; Marked_a__U82(pair(YS,ZS),X) > Marked_mark(X) ; Marked_a__U82(pair(YS,ZS),X) > Marked_mark(ZS) ; Marked_a__U81(tt,N,X,XS) > Marked_a__U82(a__splitAt(mark(N),mark(XS)),X) ; Marked_a__U81(tt,N,X,XS) > Marked_a__splitAt(mark(N),mark(XS)) ; Marked_a__U81(tt,N,X,XS) > Marked_mark(N) ; Marked_a__U81(tt,N,X,XS) > Marked_mark(XS) ; Marked_a__U71(tt,XS) > Marked_mark(XS) ; Marked_a__U61(tt,Y) > Marked_mark(Y) ; Marked_a__afterNth(N,XS) > Marked_a__isNatural(N) ; Marked_a__afterNth(N,XS) > Marked_a__and(a__isNatural(N),isLNat(XS)) ; Marked_a__afterNth(N,XS) >= Marked_a__U11(a__and(a__isNatural(N),isLNat(XS)), N,XS) ; Marked_a__head(cons(N,XS)) > Marked_a__isNatural(N) ; Marked_a__head(cons(N,XS)) > Marked_a__and(a__isNatural(N),isLNat(XS)) ; Marked_a__head(cons(N,XS)) >= Marked_a__U31(a__and(a__isNatural(N), isLNat(XS)),N) ; Marked_a__U51(tt,N,XS) > Marked_a__afterNth(mark(N),mark(XS)) ; Marked_a__U51(tt,N,XS) > Marked_a__head(a__afterNth(mark(N),mark(XS))) ; Marked_a__U51(tt,N,XS) > Marked_mark(N) ; Marked_a__U51(tt,N,XS) > Marked_mark(XS) ; Marked_a__natsFrom(N) > Marked_a__isNatural(N) ; Marked_a__natsFrom(N) >= Marked_a__U41(a__isNatural(N),N) ; Marked_a__U41(tt,N) > Marked_mark(N) ; Marked_a__U31(tt,N) > Marked_mark(N) ; Marked_a__U21(tt,X) > Marked_mark(X) ; Marked_a__snd(pair(X,Y)) >= Marked_a__isLNat(X) ; Marked_a__snd(pair(X,Y)) > Marked_a__and(a__isLNat(X),isLNat(Y)) ; Marked_a__snd(pair(X,Y)) > Marked_a__U61(a__and(a__isLNat(X),isLNat(Y)),Y) ; Marked_a__U11(tt,N,XS) >= Marked_a__snd(a__splitAt(mark(N),mark(XS))) ; Marked_a__U11(tt,N,XS) >= Marked_a__splitAt(mark(N),mark(XS)) ; Marked_a__U11(tt,N,XS) > Marked_mark(N) ; Marked_a__U11(tt,N,XS) > Marked_mark(XS) ; Marked_a__splitAt(s(N),cons(X,XS)) > Marked_a__isNatural(N) ; Marked_a__splitAt(s(N),cons(X,XS)) > Marked_a__and(a__isNatural(N), and(isNatural(X),isLNat(XS))) ; Marked_a__splitAt(s(N),cons(X,XS)) > Marked_a__U81(a__and(a__isNatural(N), and(isNatural(X), isLNat(XS))),N, X,XS) ; Marked_a__splitAt(0,XS) >= Marked_a__isLNat(XS) ; Marked_a__splitAt(0,XS) > Marked_a__U71(a__isLNat(XS),XS) ; Marked_a__fst(pair(X,Y)) >= Marked_a__isLNat(X) ; Marked_a__fst(pair(X,Y)) > Marked_a__and(a__isLNat(X),isLNat(Y)) ; Marked_a__fst(pair(X,Y)) > Marked_a__U21(a__and(a__isLNat(X),isLNat(Y)),X) ; Marked_a__U101(tt,N,XS) > Marked_a__splitAt(mark(N),mark(XS)) ; Marked_a__U101(tt,N,XS) >= Marked_a__fst(a__splitAt(mark(N),mark(XS))) ; Marked_a__U101(tt,N,XS) > Marked_mark(N) ; Marked_a__U101(tt,N,XS) > Marked_mark(XS) ; Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; Marked_mark(natsFrom(X)) >= Marked_a__natsFrom(mark(X)) ; Marked_mark(natsFrom(X)) > Marked_mark(X) ; Marked_mark(s(X)) > Marked_mark(X) ; Marked_mark(pair(X1,X2)) > Marked_mark(X1) ; Marked_mark(pair(X1,X2)) > Marked_mark(X2) ; Marked_mark(isLNat(X)) >= Marked_a__isLNat(X) ; Marked_mark(afterNth(X1,X2)) >= Marked_a__afterNth(mark(X1),mark(X2)) ; Marked_mark(afterNth(X1,X2)) > Marked_mark(X1) ; Marked_mark(afterNth(X1,X2)) > Marked_mark(X2) ; Marked_mark(fst(X)) >= Marked_a__fst(mark(X)) ; Marked_mark(fst(X)) > Marked_mark(X) ; Marked_mark(snd(X)) >= Marked_a__snd(mark(X)) ; Marked_mark(snd(X)) > Marked_mark(X) ; Marked_mark(tail(X)) >= Marked_a__tail(mark(X)) ; Marked_mark(tail(X)) > Marked_mark(X) ; Marked_mark(take(X1,X2)) >= Marked_a__take(mark(X1),mark(X2)) ; Marked_mark(take(X1,X2)) > Marked_mark(X1) ; Marked_mark(take(X1,X2)) > Marked_mark(X2) ; Marked_mark(head(X)) >= Marked_a__head(mark(X)) ; Marked_mark(head(X)) > Marked_mark(X) ; Marked_mark(sel(X1,X2)) >= Marked_a__sel(mark(X1),mark(X2)) ; Marked_mark(sel(X1,X2)) > Marked_mark(X1) ; Marked_mark(sel(X1,X2)) > Marked_mark(X2) ; Marked_mark(splitAt(X1,X2)) >= Marked_a__splitAt(mark(X1),mark(X2)) ; Marked_mark(splitAt(X1,X2)) > Marked_mark(X1) ; Marked_mark(splitAt(X1,X2)) > Marked_mark(X2) ; Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ; Marked_mark(and(X1,X2)) > Marked_mark(X1) ; Marked_mark(isNatural(X)) > Marked_a__isNatural(X) ; Marked_mark(U101(X1,X2,X3)) > Marked_a__U101(mark(X1),X2,X3) ; Marked_mark(U101(X1,X2,X3)) > Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) > Marked_a__U11(mark(X1),X2,X3) ; Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; Marked_mark(U21(X1,X2)) >= Marked_a__U21(mark(X1),X2) ; Marked_mark(U21(X1,X2)) > Marked_mark(X1) ; Marked_mark(U31(X1,X2)) > Marked_a__U31(mark(X1),X2) ; Marked_mark(U31(X1,X2)) > Marked_mark(X1) ; Marked_mark(U41(X1,X2)) > Marked_a__U41(mark(X1),X2) ; Marked_mark(U41(X1,X2)) > Marked_mark(X1) ; Marked_mark(U51(X1,X2,X3)) >= Marked_a__U51(mark(X1),X2,X3) ; Marked_mark(U51(X1,X2,X3)) > Marked_mark(X1) ; Marked_mark(U61(X1,X2)) >= Marked_a__U61(mark(X1),X2) ; Marked_mark(U61(X1,X2)) > Marked_mark(X1) ; Marked_mark(U71(X1,X2)) >= Marked_a__U71(mark(X1),X2) ; Marked_mark(U71(X1,X2)) > Marked_mark(X1) ; Marked_mark(U81(X1,X2,X3,X4)) >= Marked_a__U81(mark(X1),X2,X3,X4) ; Marked_mark(U81(X1,X2,X3,X4)) > Marked_mark(X1) ; Marked_mark(U82(X1,X2)) >= Marked_a__U82(mark(X1),X2) ; Marked_mark(U82(X1,X2)) > Marked_mark(X1) ; Marked_mark(U91(X1,X2)) > Marked_a__U91(mark(X1),X2) ; Marked_mark(U91(X1,X2)) > Marked_mark(X1) ; Marked_mark(isPLNat(X)) >= Marked_a__isPLNat(X) ; } APPLY CRITERIA (SOLVE_ORD) Trying to solve the following constraints: { a__fst(pair(X,Y)) >= a__U21(a__and(a__isLNat(X),isLNat(Y)),X) ; a__fst(X) >= fst(X) ; a__splitAt(s(N),cons(X,XS)) >= a__U81(a__and(a__isNatural(N), and(isNatural(X),isLNat(XS))), N,X,XS) ; a__splitAt(0,XS) >= a__U71(a__isLNat(XS),XS) ; a__splitAt(X1,X2) >= splitAt(X1,X2) ; mark(tt) >= tt ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(natsFrom(X)) >= a__natsFrom(mark(X)) ; mark(s(X)) >= s(mark(X)) ; mark(pair(X1,X2)) >= pair(mark(X1),mark(X2)) ; mark(nil) >= nil ; mark(isLNat(X)) >= a__isLNat(X) ; mark(afterNth(X1,X2)) >= a__afterNth(mark(X1),mark(X2)) ; mark(fst(X)) >= a__fst(mark(X)) ; mark(snd(X)) >= a__snd(mark(X)) ; mark(tail(X)) >= a__tail(mark(X)) ; mark(take(X1,X2)) >= a__take(mark(X1),mark(X2)) ; mark(0) >= 0 ; mark(head(X)) >= a__head(mark(X)) ; mark(sel(X1,X2)) >= a__sel(mark(X1),mark(X2)) ; mark(splitAt(X1,X2)) >= a__splitAt(mark(X1),mark(X2)) ; mark(and(X1,X2)) >= a__and(mark(X1),X2) ; mark(isNatural(X)) >= a__isNatural(X) ; mark(U101(X1,X2,X3)) >= a__U101(mark(X1),X2,X3) ; mark(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) ; mark(U21(X1,X2)) >= a__U21(mark(X1),X2) ; mark(U31(X1,X2)) >= a__U31(mark(X1),X2) ; mark(U41(X1,X2)) >= a__U41(mark(X1),X2) ; mark(U51(X1,X2,X3)) >= a__U51(mark(X1),X2,X3) ; mark(U61(X1,X2)) >= a__U61(mark(X1),X2) ; mark(U71(X1,X2)) >= a__U71(mark(X1),X2) ; mark(U81(X1,X2,X3,X4)) >= a__U81(mark(X1),X2,X3,X4) ; mark(U82(X1,X2)) >= a__U82(mark(X1),X2) ; mark(U91(X1,X2)) >= a__U91(mark(X1),X2) ; mark(isPLNat(X)) >= a__isPLNat(X) ; a__U101(tt,N,XS) >= a__fst(a__splitAt(mark(N),mark(XS))) ; a__U101(X1,X2,X3) >= U101(X1,X2,X3) ; a__snd(pair(X,Y)) >= a__U61(a__and(a__isLNat(X),isLNat(Y)),Y) ; a__snd(X) >= snd(X) ; a__U11(tt,N,XS) >= a__snd(a__splitAt(mark(N),mark(XS))) ; a__U11(X1,X2,X3) >= U11(X1,X2,X3) ; a__U21(tt,X) >= mark(X) ; a__U21(X1,X2) >= U21(X1,X2) ; a__U31(tt,N) >= mark(N) ; a__U31(X1,X2) >= U31(X1,X2) ; a__U41(tt,N) >= cons(mark(N),natsFrom(s(N))) ; a__U41(X1,X2) >= U41(X1,X2) ; a__head(cons(N,XS)) >= a__U31(a__and(a__isNatural(N),isLNat(XS)),N) ; a__head(X) >= head(X) ; a__afterNth(N,XS) >= a__U11(a__and(a__isNatural(N),isLNat(XS)),N,XS) ; a__afterNth(X1,X2) >= afterNth(X1,X2) ; a__U51(tt,N,XS) >= a__head(a__afterNth(mark(N),mark(XS))) ; a__U51(X1,X2,X3) >= U51(X1,X2,X3) ; a__U61(tt,Y) >= mark(Y) ; a__U61(X1,X2) >= U61(X1,X2) ; a__U71(tt,XS) >= pair(nil,mark(XS)) ; a__U71(X1,X2) >= U71(X1,X2) ; a__U82(pair(YS,ZS),X) >= pair(cons(mark(X),YS),mark(ZS)) ; a__U82(X1,X2) >= U82(X1,X2) ; a__U81(tt,N,X,XS) >= a__U82(a__splitAt(mark(N),mark(XS)),X) ; a__U81(X1,X2,X3,X4) >= U81(X1,X2,X3,X4) ; a__U91(tt,XS) >= mark(XS) ; a__U91(X1,X2) >= U91(X1,X2) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__isNatural(s(V1)) >= a__isNatural(V1) ; a__isNatural(0) >= tt ; a__isNatural(head(V1)) >= a__isLNat(V1) ; a__isNatural(sel(V1,V2)) >= a__and(a__isNatural(V1),isLNat(V2)) ; a__isNatural(X) >= isNatural(X) ; a__isLNat(cons(V1,V2)) >= a__and(a__isNatural(V1),isLNat(V2)) ; a__isLNat(natsFrom(V1)) >= a__isNatural(V1) ; a__isLNat(nil) >= tt ; a__isLNat(afterNth(V1,V2)) >= a__and(a__isNatural(V1),isLNat(V2)) ; a__isLNat(fst(V1)) >= a__isPLNat(V1) ; a__isLNat(snd(V1)) >= a__isPLNat(V1) ; a__isLNat(tail(V1)) >= a__isLNat(V1) ; a__isLNat(take(V1,V2)) >= a__and(a__isNatural(V1),isLNat(V2)) ; a__isLNat(X) >= isLNat(X) ; a__isPLNat(pair(V1,V2)) >= a__and(a__isLNat(V1),isLNat(V2)) ; a__isPLNat(splitAt(V1,V2)) >= a__and(a__isNatural(V1),isLNat(V2)) ; a__isPLNat(X) >= isPLNat(X) ; a__natsFrom(N) >= a__U41(a__isNatural(N),N) ; a__natsFrom(X) >= natsFrom(X) ; a__sel(N,XS) >= a__U51(a__and(a__isNatural(N),isLNat(XS)),N,XS) ; a__sel(X1,X2) >= sel(X1,X2) ; a__tail(cons(N,XS)) >= a__U91(a__and(a__isNatural(N),isLNat(XS)),XS) ; a__tail(X) >= tail(X) ; a__take(N,XS) >= a__U101(a__and(a__isNatural(N),isLNat(XS)),N,XS) ; a__take(X1,X2) >= take(X1,X2) ; Marked_a__sel(N,XS) >= Marked_a__isNatural(N) ; Marked_a__sel(N,XS) >= Marked_a__and(a__isNatural(N),isLNat(XS)) ; Marked_a__sel(N,XS) >= Marked_a__U51(a__and(a__isNatural(N),isLNat(XS)),N,XS) ; Marked_a__take(N,XS) > Marked_a__isNatural(N) ; Marked_a__take(N,XS) > Marked_a__and(a__isNatural(N),isLNat(XS)) ; Marked_a__take(N,XS) >= Marked_a__U101(a__and(a__isNatural(N),isLNat(XS)), N,XS) ; Marked_a__tail(cons(N,XS)) > Marked_a__isNatural(N) ; Marked_a__tail(cons(N,XS)) > Marked_a__and(a__isNatural(N),isLNat(XS)) ; Marked_a__tail(cons(N,XS)) >= Marked_a__U91(a__and(a__isNatural(N), isLNat(XS)),XS) ; Marked_a__isPLNat(pair(V1,V2)) > Marked_a__isLNat(V1) ; Marked_a__isPLNat(pair(V1,V2)) > Marked_a__and(a__isLNat(V1),isLNat(V2)) ; Marked_a__isPLNat(splitAt(V1,V2)) > Marked_a__isNatural(V1) ; Marked_a__isPLNat(splitAt(V1,V2)) > Marked_a__and(a__isNatural(V1), isLNat(V2)) ; Marked_a__isLNat(cons(V1,V2)) > Marked_a__isNatural(V1) ; Marked_a__isLNat(cons(V1,V2)) > Marked_a__and(a__isNatural(V1),isLNat(V2)) ; Marked_a__isLNat(natsFrom(V1)) > Marked_a__isNatural(V1) ; Marked_a__isLNat(afterNth(V1,V2)) > Marked_a__isNatural(V1) ; Marked_a__isLNat(afterNth(V1,V2)) > Marked_a__and(a__isNatural(V1), isLNat(V2)) ; Marked_a__isLNat(fst(V1)) > Marked_a__isPLNat(V1) ; Marked_a__isLNat(snd(V1)) >= Marked_a__isPLNat(V1) ; Marked_a__isLNat(tail(V1)) > Marked_a__isLNat(V1) ; Marked_a__isLNat(take(V1,V2)) > Marked_a__isNatural(V1) ; Marked_a__isLNat(take(V1,V2)) > Marked_a__and(a__isNatural(V1),isLNat(V2)) ; Marked_a__isNatural(s(V1)) > Marked_a__isNatural(V1) ; Marked_a__isNatural(head(V1)) >= Marked_a__isLNat(V1) ; Marked_a__isNatural(sel(V1,V2)) > Marked_a__isNatural(V1) ; Marked_a__isNatural(sel(V1,V2)) >= Marked_a__and(a__isNatural(V1),isLNat(V2)) ; Marked_a__and(tt,X) > Marked_mark(X) ; Marked_a__U91(tt,XS) > Marked_mark(XS) ; Marked_a__U82(pair(YS,ZS),X) > Marked_mark(X) ; Marked_a__U82(pair(YS,ZS),X) > Marked_mark(ZS) ; Marked_a__U81(tt,N,X,XS) > Marked_a__U82(a__splitAt(mark(N),mark(XS)),X) ; Marked_a__U81(tt,N,X,XS) > Marked_a__splitAt(mark(N),mark(XS)) ; Marked_a__U81(tt,N,X,XS) > Marked_mark(N) ; Marked_a__U81(tt,N,X,XS) > Marked_mark(XS) ; Marked_a__U71(tt,XS) > Marked_mark(XS) ; Marked_a__U61(tt,Y) > Marked_mark(Y) ; Marked_a__afterNth(N,XS) > Marked_a__isNatural(N) ; Marked_a__afterNth(N,XS) > Marked_a__and(a__isNatural(N),isLNat(XS)) ; Marked_a__afterNth(N,XS) >= Marked_a__U11(a__and(a__isNatural(N),isLNat(XS)), N,XS) ; Marked_a__head(cons(N,XS)) > Marked_a__isNatural(N) ; Marked_a__head(cons(N,XS)) > Marked_a__and(a__isNatural(N),isLNat(XS)) ; Marked_a__head(cons(N,XS)) >= Marked_a__U31(a__and(a__isNatural(N), isLNat(XS)),N) ; Marked_a__U51(tt,N,XS) > Marked_a__afterNth(mark(N),mark(XS)) ; Marked_a__U51(tt,N,XS) > Marked_a__head(a__afterNth(mark(N),mark(XS))) ; Marked_a__U51(tt,N,XS) > Marked_mark(N) ; Marked_a__U51(tt,N,XS) > Marked_mark(XS) ; Marked_a__natsFrom(N) > Marked_a__isNatural(N) ; Marked_a__natsFrom(N) >= Marked_a__U41(a__isNatural(N),N) ; Marked_a__U41(tt,N) > Marked_mark(N) ; Marked_a__U31(tt,N) > Marked_mark(N) ; Marked_a__U21(tt,X) > Marked_mark(X) ; Marked_a__snd(pair(X,Y)) >= Marked_a__isLNat(X) ; Marked_a__snd(pair(X,Y)) > Marked_a__and(a__isLNat(X),isLNat(Y)) ; Marked_a__snd(pair(X,Y)) > Marked_a__U61(a__and(a__isLNat(X),isLNat(Y)),Y) ; Marked_a__U11(tt,N,XS) >= Marked_a__snd(a__splitAt(mark(N),mark(XS))) ; Marked_a__U11(tt,N,XS) >= Marked_a__splitAt(mark(N),mark(XS)) ; Marked_a__U11(tt,N,XS) > Marked_mark(N) ; Marked_a__U11(tt,N,XS) > Marked_mark(XS) ; Marked_a__splitAt(s(N),cons(X,XS)) > Marked_a__isNatural(N) ; Marked_a__splitAt(s(N),cons(X,XS)) > Marked_a__and(a__isNatural(N), and(isNatural(X),isLNat(XS))) ; Marked_a__splitAt(s(N),cons(X,XS)) > Marked_a__U81(a__and(a__isNatural(N), and(isNatural(X), isLNat(XS))),N, X,XS) ; Marked_a__splitAt(0,XS) >= Marked_a__isLNat(XS) ; Marked_a__splitAt(0,XS) > Marked_a__U71(a__isLNat(XS),XS) ; Marked_a__fst(pair(X,Y)) >= Marked_a__isLNat(X) ; Marked_a__fst(pair(X,Y)) > Marked_a__and(a__isLNat(X),isLNat(Y)) ; Marked_a__fst(pair(X,Y)) > Marked_a__U21(a__and(a__isLNat(X),isLNat(Y)),X) ; Marked_a__U101(tt,N,XS) > Marked_a__splitAt(mark(N),mark(XS)) ; Marked_a__U101(tt,N,XS) >= Marked_a__fst(a__splitAt(mark(N),mark(XS))) ; Marked_a__U101(tt,N,XS) > Marked_mark(N) ; Marked_a__U101(tt,N,XS) > Marked_mark(XS) ; Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; Marked_mark(natsFrom(X)) >= Marked_a__natsFrom(mark(X)) ; Marked_mark(natsFrom(X)) > Marked_mark(X) ; Marked_mark(s(X)) > Marked_mark(X) ; Marked_mark(pair(X1,X2)) > Marked_mark(X1) ; Marked_mark(pair(X1,X2)) > Marked_mark(X2) ; Marked_mark(isLNat(X)) >= Marked_a__isLNat(X) ; Marked_mark(afterNth(X1,X2)) >= Marked_a__afterNth(mark(X1),mark(X2)) ; Marked_mark(afterNth(X1,X2)) > Marked_mark(X1) ; Marked_mark(afterNth(X1,X2)) > Marked_mark(X2) ; Marked_mark(fst(X)) >= Marked_a__fst(mark(X)) ; Marked_mark(fst(X)) > Marked_mark(X) ; Marked_mark(snd(X)) >= Marked_a__snd(mark(X)) ; Marked_mark(snd(X)) > Marked_mark(X) ; Marked_mark(tail(X)) >= Marked_a__tail(mark(X)) ; Marked_mark(tail(X)) > Marked_mark(X) ; Marked_mark(take(X1,X2)) >= Marked_a__take(mark(X1),mark(X2)) ; Marked_mark(take(X1,X2)) > Marked_mark(X1) ; Marked_mark(take(X1,X2)) > Marked_mark(X2) ; Marked_mark(head(X)) >= Marked_a__head(mark(X)) ; Marked_mark(head(X)) > Marked_mark(X) ; Marked_mark(sel(X1,X2)) >= Marked_a__sel(mark(X1),mark(X2)) ; Marked_mark(sel(X1,X2)) > Marked_mark(X1) ; Marked_mark(sel(X1,X2)) > Marked_mark(X2) ; Marked_mark(splitAt(X1,X2)) >= Marked_a__splitAt(mark(X1),mark(X2)) ; Marked_mark(splitAt(X1,X2)) > Marked_mark(X1) ; Marked_mark(splitAt(X1,X2)) > Marked_mark(X2) ; Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ; Marked_mark(and(X1,X2)) > Marked_mark(X1) ; Marked_mark(isNatural(X)) > Marked_a__isNatural(X) ; Marked_mark(U101(X1,X2,X3)) > Marked_a__U101(mark(X1),X2,X3) ; Marked_mark(U101(X1,X2,X3)) > Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) > Marked_a__U11(mark(X1),X2,X3) ; Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; Marked_mark(U21(X1,X2)) >= Marked_a__U21(mark(X1),X2) ; Marked_mark(U21(X1,X2)) > Marked_mark(X1) ; Marked_mark(U31(X1,X2)) > Marked_a__U31(mark(X1),X2) ; Marked_mark(U31(X1,X2)) > Marked_mark(X1) ; Marked_mark(U41(X1,X2)) > Marked_a__U41(mark(X1),X2) ; Marked_mark(U41(X1,X2)) > Marked_mark(X1) ; Marked_mark(U51(X1,X2,X3)) >= Marked_a__U51(mark(X1),X2,X3) ; Marked_mark(U51(X1,X2,X3)) > Marked_mark(X1) ; Marked_mark(U61(X1,X2)) >= Marked_a__U61(mark(X1),X2) ; Marked_mark(U61(X1,X2)) > Marked_mark(X1) ; Marked_mark(U71(X1,X2)) >= Marked_a__U71(mark(X1),X2) ; Marked_mark(U71(X1,X2)) > Marked_mark(X1) ; Marked_mark(U81(X1,X2,X3,X4)) >= Marked_a__U81(mark(X1),X2,X3,X4) ; Marked_mark(U81(X1,X2,X3,X4)) > Marked_mark(X1) ; Marked_mark(U82(X1,X2)) >= Marked_a__U82(mark(X1),X2) ; Marked_mark(U82(X1,X2)) > Marked_mark(X1) ; Marked_mark(U91(X1,X2)) > Marked_a__U91(mark(X1),X2) ; Marked_mark(U91(X1,X2)) > Marked_mark(X1) ; Marked_mark(isPLNat(X)) >= Marked_a__isPLNat(X) ; } + Disjunctions:{ } === 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 Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 15.000000 === === STOPING TIMER real === Sat solver returned === STOPING TIMER real === === STOPING TIMER virtual === No solution found 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 solver returned === STOPING TIMER real === === 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 152.043116 seconds (real time) Cime Exit Status: 0