- : unit = ()
h : heuristic = <heuristic>
- : unit = ()
APPLY CRITERIA (Marked dependency pairs)

TRS termination of:
[1] active(U101(tt,N,XS)) -> mark(fst(splitAt(N,XS)))
[2] active(U11(tt,N,XS)) -> mark(snd(splitAt(N,XS)))
[3] active(U21(tt,X)) -> mark(X)
[4] active(U31(tt,N)) -> mark(N)
[5] active(U41(tt,N)) -> mark(cons(N,natsFrom(s(N))))
[6] active(U51(tt,N,XS)) -> mark(head(afterNth(N,XS)))
[7] active(U61(tt,Y)) -> mark(Y)
[8] active(U71(tt,XS)) -> mark(pair(nil,XS))
[9] active(U81(tt,N,X,XS)) -> mark(U82(splitAt(N,XS),X))
[10] active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
[11] active(U91(tt,XS)) -> mark(XS)
[12] active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
[13] active(and(tt,X)) -> mark(X)
[14] active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
[15] active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
[16] active(isLNat(nil)) -> mark(tt)
[17] active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
[18] active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
[19] active(isLNat(fst(V1))) -> mark(isPLNat(V1))
[20] active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
[21] active(isLNat(snd(V1))) -> mark(isPLNat(V1))
[22] active(isLNat(tail(V1))) -> mark(isLNat(V1))
[23] active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
[24] active(isNatural(0)) -> mark(tt)
[25] active(isNatural(head(V1))) -> mark(isLNat(V1))
[26] active(isNatural(s(V1))) -> mark(isNatural(V1))
[27] active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
[28] active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
[29] active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
[30] active(natsFrom(N)) -> mark(U41(isNatural(N),N))
[31] active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
[32] active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
[33] active(splitAt(0,XS)) -> mark(U71(isLNat(XS),XS))
[34] active(splitAt(s(N),cons(X,XS))) ->
 mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
[35] active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
[36] active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
[37] active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
[38] active(fst(X)) -> fst(active(X))
[39] active(splitAt(X1,X2)) -> splitAt(active(X1),X2)
[40] active(splitAt(X1,X2)) -> splitAt(X1,active(X2))
[41] active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
[42] active(snd(X)) -> snd(active(X))
[43] active(U21(X1,X2)) -> U21(active(X1),X2)
[44] active(U31(X1,X2)) -> U31(active(X1),X2)
[45] active(U41(X1,X2)) -> U41(active(X1),X2)
[46] active(cons(X1,X2)) -> cons(active(X1),X2)
[47] active(natsFrom(X)) -> natsFrom(active(X))
[48] active(s(X)) -> s(active(X))
[49] active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
[50] active(head(X)) -> head(active(X))
[51] active(afterNth(X1,X2)) -> afterNth(active(X1),X2)
[52] active(afterNth(X1,X2)) -> afterNth(X1,active(X2))
[53] active(U61(X1,X2)) -> U61(active(X1),X2)
[54] active(U71(X1,X2)) -> U71(active(X1),X2)
[55] active(pair(X1,X2)) -> pair(active(X1),X2)
[56] active(pair(X1,X2)) -> pair(X1,active(X2))
[57] active(U81(X1,X2,X3,X4)) -> U81(active(X1),X2,X3,X4)
[58] active(U82(X1,X2)) -> U82(active(X1),X2)
[59] active(U91(X1,X2)) -> U91(active(X1),X2)
[60] active(and(X1,X2)) -> and(active(X1),X2)
[61] active(tail(X)) -> tail(active(X))
[62] active(take(X1,X2)) -> take(active(X1),X2)
[63] active(take(X1,X2)) -> take(X1,active(X2))
[64] active(sel(X1,X2)) -> sel(active(X1),X2)
[65] active(sel(X1,X2)) -> sel(X1,active(X2))
[66] U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
[67] fst(mark(X)) -> mark(fst(X))
[68] splitAt(mark(X1),X2) -> mark(splitAt(X1,X2))
[69] splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2))
[70] U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
[71] snd(mark(X)) -> mark(snd(X))
[72] U21(mark(X1),X2) -> mark(U21(X1,X2))
[73] U31(mark(X1),X2) -> mark(U31(X1,X2))
[74] U41(mark(X1),X2) -> mark(U41(X1,X2))
[75] cons(mark(X1),X2) -> mark(cons(X1,X2))
[76] natsFrom(mark(X)) -> mark(natsFrom(X))
[77] s(mark(X)) -> mark(s(X))
[78] U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
[79] head(mark(X)) -> mark(head(X))
[80] afterNth(mark(X1),X2) -> mark(afterNth(X1,X2))
[81] afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2))
[82] U61(mark(X1),X2) -> mark(U61(X1,X2))
[83] U71(mark(X1),X2) -> mark(U71(X1,X2))
[84] pair(mark(X1),X2) -> mark(pair(X1,X2))
[85] pair(X1,mark(X2)) -> mark(pair(X1,X2))
[86] U81(mark(X1),X2,X3,X4) -> mark(U81(X1,X2,X3,X4))
[87] U82(mark(X1),X2) -> mark(U82(X1,X2))
[88] U91(mark(X1),X2) -> mark(U91(X1,X2))
[89] and(mark(X1),X2) -> mark(and(X1,X2))
[90] tail(mark(X)) -> mark(tail(X))
[91] take(mark(X1),X2) -> mark(take(X1,X2))
[92] take(X1,mark(X2)) -> mark(take(X1,X2))
[93] sel(mark(X1),X2) -> mark(sel(X1,X2))
[94] sel(X1,mark(X2)) -> mark(sel(X1,X2))
[95] proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
[96] proper(tt) -> ok(tt)
[97] proper(fst(X)) -> fst(proper(X))
[98] proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2))
[99] proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
[100] proper(snd(X)) -> snd(proper(X))
[101] proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
[102] proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
[103] proper(U41(X1,X2)) -> U41(proper(X1),proper(X2))
[104] proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
[105] proper(natsFrom(X)) -> natsFrom(proper(X))
[106] proper(s(X)) -> s(proper(X))
[107] proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
[108] proper(head(X)) -> head(proper(X))
[109] proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2))
[110] proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
[111] proper(U71(X1,X2)) -> U71(proper(X1),proper(X2))
[112] proper(pair(X1,X2)) -> pair(proper(X1),proper(X2))
[113] proper(nil) -> ok(nil)
[114] proper(U81(X1,X2,X3,X4)) ->
 U81(proper(X1),proper(X2),proper(X3),proper(X4))
[115] proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
[116] proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
[117] proper(and(X1,X2)) -> and(proper(X1),proper(X2))
[118] proper(isNatural(X)) -> isNatural(proper(X))
[119] proper(isLNat(X)) -> isLNat(proper(X))
[120] proper(isPLNat(X)) -> isPLNat(proper(X))
[121] proper(tail(X)) -> tail(proper(X))
[122] proper(take(X1,X2)) -> take(proper(X1),proper(X2))
[123] proper(0) -> ok(0)
[124] proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
[125] U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
[126] fst(ok(X)) -> ok(fst(X))
[127] splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2))
[128] U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
[129] snd(ok(X)) -> ok(snd(X))
[130] U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
[131] U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
[132] U41(ok(X1),ok(X2)) -> ok(U41(X1,X2))
[133] cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
[134] natsFrom(ok(X)) -> ok(natsFrom(X))
[135] s(ok(X)) -> ok(s(X))
[136] U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
[137] head(ok(X)) -> ok(head(X))
[138] afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2))
[139] U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
[140] U71(ok(X1),ok(X2)) -> ok(U71(X1,X2))
[141] pair(ok(X1),ok(X2)) -> ok(pair(X1,X2))
[142] U81(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U81(X1,X2,X3,X4))
[143] U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
[144] U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
[145] and(ok(X1),ok(X2)) -> ok(and(X1,X2))
[146] isNatural(ok(X)) -> ok(isNatural(X))
[147] isLNat(ok(X)) -> ok(isLNat(X))
[148] isPLNat(ok(X)) -> ok(isPLNat(X))
[149] tail(ok(X)) -> ok(tail(X))
[150] take(ok(X1),ok(X2)) -> ok(take(X1,X2))
[151] sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
[152] top(mark(X)) -> top(proper(X))
[153] top(ok(X)) -> top(active(X))


Sub problem: 
guided: 

DP termination of:
<Marked_active(U101(tt,N,XS)) , Marked_fst(splitAt(N,XS))>
<Marked_active(U101(tt,N,XS)) , Marked_splitAt(N,XS)>
<Marked_active(U11(tt,N,XS)) , Marked_snd(splitAt(N,XS))>
<Marked_active(U11(tt,N,XS)) , Marked_splitAt(N,XS)>
<Marked_active(U41(tt,N)) , Marked_cons(N,natsFrom(s(N)))>
<Marked_active(U41(tt,N)) , Marked_natsFrom(s(N))>
<Marked_active(U41(tt,N)) , Marked_s(N)>
<Marked_active(U51(tt,N,XS)) , Marked_head(afterNth(N,XS))>
<Marked_active(U51(tt,N,XS)) , Marked_afterNth(N,XS)>
<Marked_active(U71(tt,XS)) , Marked_pair(nil,XS)>
<Marked_active(U81(tt,N,X,XS)) , Marked_U82(splitAt(N,XS),X)>
<Marked_active(U81(tt,N,X,XS)) , Marked_splitAt(N,XS)>
<Marked_active(U82(pair(YS,ZS),X)) , Marked_pair(cons(X,YS),ZS)>
<Marked_active(U82(pair(YS,ZS),X)) , Marked_cons(X,YS)>
<Marked_active(afterNth(N,XS)) , Marked_U11(and(isNatural(N),isLNat(XS)),N,XS)>
<Marked_active(afterNth(N,XS)) , Marked_and(isNatural(N),isLNat(XS))>
<Marked_active(afterNth(N,XS)) , Marked_isNatural(N)>
<Marked_active(afterNth(N,XS)) , Marked_isLNat(XS)>
<Marked_active(fst(pair(X,Y))) , Marked_U21(and(isLNat(X),isLNat(Y)),X)>
<Marked_active(fst(pair(X,Y))) , Marked_and(isLNat(X),isLNat(Y))>
<Marked_active(fst(pair(X,Y))) , Marked_isLNat(X)>
<Marked_active(fst(pair(X,Y))) , Marked_isLNat(Y)>
<Marked_active(head(cons(N,XS))) , Marked_U31(and(isNatural(N),isLNat(XS)),N)>
<Marked_active(head(cons(N,XS))) , Marked_and(isNatural(N),isLNat(XS))>
<Marked_active(head(cons(N,XS))) , Marked_isNatural(N)>
<Marked_active(head(cons(N,XS))) , Marked_isLNat(XS)>
<Marked_active(isLNat(afterNth(V1,V2))) , Marked_and(isNatural(V1),isLNat(V2))>
<Marked_active(isLNat(afterNth(V1,V2))) , Marked_isNatural(V1)>
<Marked_active(isLNat(afterNth(V1,V2))) , Marked_isLNat(V2)>
<Marked_active(isLNat(cons(V1,V2))) , Marked_and(isNatural(V1),isLNat(V2))>
<Marked_active(isLNat(cons(V1,V2))) , Marked_isNatural(V1)>
<Marked_active(isLNat(cons(V1,V2))) , Marked_isLNat(V2)>
<Marked_active(isLNat(fst(V1))) , Marked_isPLNat(V1)>
<Marked_active(isLNat(natsFrom(V1))) , Marked_isNatural(V1)>
<Marked_active(isLNat(snd(V1))) , Marked_isPLNat(V1)>
<Marked_active(isLNat(tail(V1))) , Marked_isLNat(V1)>
<Marked_active(isLNat(take(V1,V2))) , Marked_and(isNatural(V1),isLNat(V2))>
<Marked_active(isLNat(take(V1,V2))) , Marked_isNatural(V1)>
<Marked_active(isLNat(take(V1,V2))) , Marked_isLNat(V2)>
<Marked_active(isNatural(head(V1))) , Marked_isLNat(V1)>
<Marked_active(isNatural(s(V1))) , Marked_isNatural(V1)>
<Marked_active(isNatural(sel(V1,V2))) , Marked_and(isNatural(V1),isLNat(V2))>
<Marked_active(isNatural(sel(V1,V2))) , Marked_isNatural(V1)>
<Marked_active(isNatural(sel(V1,V2))) , Marked_isLNat(V2)>
<Marked_active(isPLNat(pair(V1,V2))) , Marked_and(isLNat(V1),isLNat(V2))>
<Marked_active(isPLNat(pair(V1,V2))) , Marked_isLNat(V1)>
<Marked_active(isPLNat(pair(V1,V2))) , Marked_isLNat(V2)>
<Marked_active(isPLNat(splitAt(V1,V2))) , Marked_and(isNatural(V1),isLNat(V2))>
<Marked_active(isPLNat(splitAt(V1,V2))) , Marked_isNatural(V1)>
<Marked_active(isPLNat(splitAt(V1,V2))) , Marked_isLNat(V2)>
<Marked_active(natsFrom(N)) , Marked_U41(isNatural(N),N)>
<Marked_active(natsFrom(N)) , Marked_isNatural(N)>
<Marked_active(sel(N,XS)) , Marked_U51(and(isNatural(N),isLNat(XS)),N,XS)>
<Marked_active(sel(N,XS)) , Marked_and(isNatural(N),isLNat(XS))>
<Marked_active(sel(N,XS)) , Marked_isNatural(N)>
<Marked_active(sel(N,XS)) , Marked_isLNat(XS)>
<Marked_active(snd(pair(X,Y))) , Marked_U61(and(isLNat(X),isLNat(Y)),Y)>
<Marked_active(snd(pair(X,Y))) , Marked_and(isLNat(X),isLNat(Y))>
<Marked_active(snd(pair(X,Y))) , Marked_isLNat(X)>
<Marked_active(snd(pair(X,Y))) , Marked_isLNat(Y)>
<Marked_active(splitAt(0,XS)) , Marked_U71(isLNat(XS),XS)>
<Marked_active(splitAt(0,XS)) , Marked_isLNat(XS)>
<Marked_active(splitAt(s(N),cons(X,XS))) , Marked_U81(and(isNatural(N),
                                                       and(isNatural(X),
                                                        isLNat(XS))),
                                            N,X,XS)>
<Marked_active(splitAt(s(N),cons(X,XS))) , Marked_and(isNatural(N),
                                            and(isNatural(X),isLNat(XS)))>
<Marked_active(splitAt(s(N),cons(X,XS))) , Marked_isNatural(N)>
<Marked_active(splitAt(s(N),cons(X,XS))) , Marked_and(isNatural(X),isLNat(XS))>
<Marked_active(splitAt(s(N),cons(X,XS))) , Marked_isNatural(X)>
<Marked_active(splitAt(s(N),cons(X,XS))) , Marked_isLNat(XS)>
<Marked_active(tail(cons(N,XS))) , Marked_U91(and(isNatural(N),isLNat(XS)),XS)>
<Marked_active(tail(cons(N,XS))) , Marked_and(isNatural(N),isLNat(XS))>
<Marked_active(tail(cons(N,XS))) , Marked_isNatural(N)>
<Marked_active(tail(cons(N,XS))) , Marked_isLNat(XS)>
<Marked_active(take(N,XS)) , Marked_U101(and(isNatural(N),isLNat(XS)),N,XS)>
<Marked_active(take(N,XS)) , Marked_and(isNatural(N),isLNat(XS))>
<Marked_active(take(N,XS)) , Marked_isNatural(N)>
<Marked_active(take(N,XS)) , Marked_isLNat(XS)>
<Marked_active(U101(X1,X2,X3)) , Marked_U101(active(X1),X2,X3)>
<Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
<Marked_active(fst(X)) , Marked_fst(active(X))>
<Marked_active(fst(X)) , Marked_active(X)>
<Marked_active(splitAt(X1,X2)) , Marked_splitAt(active(X1),X2)>
<Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
<Marked_active(splitAt(X1,X2)) , Marked_splitAt(X1,active(X2))>
<Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
<Marked_active(U11(X1,X2,X3)) , Marked_U11(active(X1),X2,X3)>
<Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
<Marked_active(snd(X)) , Marked_snd(active(X))>
<Marked_active(snd(X)) , Marked_active(X)>
<Marked_active(U21(X1,X2)) , Marked_U21(active(X1),X2)>
<Marked_active(U21(X1,X2)) , Marked_active(X1)>
<Marked_active(U31(X1,X2)) , Marked_U31(active(X1),X2)>
<Marked_active(U31(X1,X2)) , Marked_active(X1)>
<Marked_active(U41(X1,X2)) , Marked_U41(active(X1),X2)>
<Marked_active(U41(X1,X2)) , Marked_active(X1)>
<Marked_active(cons(X1,X2)) , Marked_cons(active(X1),X2)>
<Marked_active(cons(X1,X2)) , Marked_active(X1)>
<Marked_active(natsFrom(X)) , Marked_natsFrom(active(X))>
<Marked_active(natsFrom(X)) , Marked_active(X)>
<Marked_active(s(X)) , Marked_s(active(X))>
<Marked_active(s(X)) , Marked_active(X)>
<Marked_active(U51(X1,X2,X3)) , Marked_U51(active(X1),X2,X3)>
<Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
<Marked_active(head(X)) , Marked_head(active(X))>
<Marked_active(head(X)) , Marked_active(X)>
<Marked_active(afterNth(X1,X2)) , Marked_afterNth(active(X1),X2)>
<Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
<Marked_active(afterNth(X1,X2)) , Marked_afterNth(X1,active(X2))>
<Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
<Marked_active(U61(X1,X2)) , Marked_U61(active(X1),X2)>
<Marked_active(U61(X1,X2)) , Marked_active(X1)>
<Marked_active(U71(X1,X2)) , Marked_U71(active(X1),X2)>
<Marked_active(U71(X1,X2)) , Marked_active(X1)>
<Marked_active(pair(X1,X2)) , Marked_pair(active(X1),X2)>
<Marked_active(pair(X1,X2)) , Marked_active(X1)>
<Marked_active(pair(X1,X2)) , Marked_pair(X1,active(X2))>
<Marked_active(pair(X1,X2)) , Marked_active(X2)>
<Marked_active(U81(X1,X2,X3,X4)) , Marked_U81(active(X1),X2,X3,X4)>
<Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
<Marked_active(U82(X1,X2)) , Marked_U82(active(X1),X2)>
<Marked_active(U82(X1,X2)) , Marked_active(X1)>
<Marked_active(U91(X1,X2)) , Marked_U91(active(X1),X2)>
<Marked_active(U91(X1,X2)) , Marked_active(X1)>
<Marked_active(and(X1,X2)) , Marked_and(active(X1),X2)>
<Marked_active(and(X1,X2)) , Marked_active(X1)>
<Marked_active(tail(X)) , Marked_tail(active(X))>
<Marked_active(tail(X)) , Marked_active(X)>
<Marked_active(take(X1,X2)) , Marked_take(active(X1),X2)>
<Marked_active(take(X1,X2)) , Marked_active(X1)>
<Marked_active(take(X1,X2)) , Marked_take(X1,active(X2))>
<Marked_active(take(X1,X2)) , Marked_active(X2)>
<Marked_active(sel(X1,X2)) , Marked_sel(active(X1),X2)>
<Marked_active(sel(X1,X2)) , Marked_active(X1)>
<Marked_active(sel(X1,X2)) , Marked_sel(X1,active(X2))>
<Marked_active(sel(X1,X2)) , Marked_active(X2)>
<Marked_U101(mark(X1),X2,X3) , Marked_U101(X1,X2,X3)>
<Marked_fst(mark(X)) , Marked_fst(X)>
<Marked_splitAt(mark(X1),X2) , Marked_splitAt(X1,X2)>
<Marked_splitAt(X1,mark(X2)) , Marked_splitAt(X1,X2)>
<Marked_U11(mark(X1),X2,X3) , Marked_U11(X1,X2,X3)>
<Marked_snd(mark(X)) , Marked_snd(X)>
<Marked_U21(mark(X1),X2) , Marked_U21(X1,X2)>
<Marked_U31(mark(X1),X2) , Marked_U31(X1,X2)>
<Marked_U41(mark(X1),X2) , Marked_U41(X1,X2)>
<Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
<Marked_natsFrom(mark(X)) , Marked_natsFrom(X)>
<Marked_s(mark(X)) , Marked_s(X)>
<Marked_U51(mark(X1),X2,X3) , Marked_U51(X1,X2,X3)>
<Marked_head(mark(X)) , Marked_head(X)>
<Marked_afterNth(mark(X1),X2) , Marked_afterNth(X1,X2)>
<Marked_afterNth(X1,mark(X2)) , Marked_afterNth(X1,X2)>
<Marked_U61(mark(X1),X2) , Marked_U61(X1,X2)>
<Marked_U71(mark(X1),X2) , Marked_U71(X1,X2)>
<Marked_pair(mark(X1),X2) , Marked_pair(X1,X2)>
<Marked_pair(X1,mark(X2)) , Marked_pair(X1,X2)>
<Marked_U81(mark(X1),X2,X3,X4) , Marked_U81(X1,X2,X3,X4)>
<Marked_U82(mark(X1),X2) , Marked_U82(X1,X2)>
<Marked_U91(mark(X1),X2) , Marked_U91(X1,X2)>
<Marked_and(mark(X1),X2) , Marked_and(X1,X2)>
<Marked_tail(mark(X)) , Marked_tail(X)>
<Marked_take(mark(X1),X2) , Marked_take(X1,X2)>
<Marked_take(X1,mark(X2)) , Marked_take(X1,X2)>
<Marked_sel(mark(X1),X2) , Marked_sel(X1,X2)>
<Marked_sel(X1,mark(X2)) , Marked_sel(X1,X2)>
<Marked_proper(U101(X1,X2,X3)) , Marked_U101(proper(X1),proper(X2),proper(X3))>
<Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
<Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
<Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
<Marked_proper(fst(X)) , Marked_fst(proper(X))>
<Marked_proper(fst(X)) , Marked_proper(X)>
<Marked_proper(splitAt(X1,X2)) , Marked_splitAt(proper(X1),proper(X2))>
<Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
<Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U11(X1,X2,X3)) , Marked_U11(proper(X1),proper(X2),proper(X3))>
<Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
<Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
<Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
<Marked_proper(snd(X)) , Marked_snd(proper(X))>
<Marked_proper(snd(X)) , Marked_proper(X)>
<Marked_proper(U21(X1,X2)) , Marked_U21(proper(X1),proper(X2))>
<Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U31(X1,X2)) , Marked_U31(proper(X1),proper(X2))>
<Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U41(X1,X2)) , Marked_U41(proper(X1),proper(X2))>
<Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
<Marked_proper(cons(X1,X2)) , Marked_cons(proper(X1),proper(X2))>
<Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
<Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
<Marked_proper(natsFrom(X)) , Marked_natsFrom(proper(X))>
<Marked_proper(natsFrom(X)) , Marked_proper(X)>
<Marked_proper(s(X)) , Marked_s(proper(X))>
<Marked_proper(s(X)) , Marked_proper(X)>
<Marked_proper(U51(X1,X2,X3)) , Marked_U51(proper(X1),proper(X2),proper(X3))>
<Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
<Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
<Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
<Marked_proper(head(X)) , Marked_head(proper(X))>
<Marked_proper(head(X)) , Marked_proper(X)>
<Marked_proper(afterNth(X1,X2)) , Marked_afterNth(proper(X1),proper(X2))>
<Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
<Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U61(X1,X2)) , Marked_U61(proper(X1),proper(X2))>
<Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U71(X1,X2)) , Marked_U71(proper(X1),proper(X2))>
<Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
<Marked_proper(pair(X1,X2)) , Marked_pair(proper(X1),proper(X2))>
<Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
<Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U81(X1,X2,X3,X4)) , Marked_U81(proper(X1),proper(X2),proper(X3),
                                    proper(X4))>
<Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
<Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
<Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
<Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
<Marked_proper(U82(X1,X2)) , Marked_U82(proper(X1),proper(X2))>
<Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U91(X1,X2)) , Marked_U91(proper(X1),proper(X2))>
<Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
<Marked_proper(and(X1,X2)) , Marked_and(proper(X1),proper(X2))>
<Marked_proper(and(X1,X2)) , Marked_proper(X1)>
<Marked_proper(and(X1,X2)) , Marked_proper(X2)>
<Marked_proper(isNatural(X)) , Marked_isNatural(proper(X))>
<Marked_proper(isNatural(X)) , Marked_proper(X)>
<Marked_proper(isLNat(X)) , Marked_isLNat(proper(X))>
<Marked_proper(isLNat(X)) , Marked_proper(X)>
<Marked_proper(isPLNat(X)) , Marked_isPLNat(proper(X))>
<Marked_proper(isPLNat(X)) , Marked_proper(X)>
<Marked_proper(tail(X)) , Marked_tail(proper(X))>
<Marked_proper(tail(X)) , Marked_proper(X)>
<Marked_proper(take(X1,X2)) , Marked_take(proper(X1),proper(X2))>
<Marked_proper(take(X1,X2)) , Marked_proper(X1)>
<Marked_proper(take(X1,X2)) , Marked_proper(X2)>
<Marked_proper(sel(X1,X2)) , Marked_sel(proper(X1),proper(X2))>
<Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
<Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
<Marked_U101(ok(X1),ok(X2),ok(X3)) , Marked_U101(X1,X2,X3)>
<Marked_fst(ok(X)) , Marked_fst(X)>
<Marked_splitAt(ok(X1),ok(X2)) , Marked_splitAt(X1,X2)>
<Marked_U11(ok(X1),ok(X2),ok(X3)) , Marked_U11(X1,X2,X3)>
<Marked_snd(ok(X)) , Marked_snd(X)>
<Marked_U21(ok(X1),ok(X2)) , Marked_U21(X1,X2)>
<Marked_U31(ok(X1),ok(X2)) , Marked_U31(X1,X2)>
<Marked_U41(ok(X1),ok(X2)) , Marked_U41(X1,X2)>
<Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)>
<Marked_natsFrom(ok(X)) , Marked_natsFrom(X)>
<Marked_s(ok(X)) , Marked_s(X)>
<Marked_U51(ok(X1),ok(X2),ok(X3)) , Marked_U51(X1,X2,X3)>
<Marked_head(ok(X)) , Marked_head(X)>
<Marked_afterNth(ok(X1),ok(X2)) , Marked_afterNth(X1,X2)>
<Marked_U61(ok(X1),ok(X2)) , Marked_U61(X1,X2)>
<Marked_U71(ok(X1),ok(X2)) , Marked_U71(X1,X2)>
<Marked_pair(ok(X1),ok(X2)) , Marked_pair(X1,X2)>
<Marked_U81(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U81(X1,X2,X3,X4)>
<Marked_U82(ok(X1),ok(X2)) , Marked_U82(X1,X2)>
<Marked_U91(ok(X1),ok(X2)) , Marked_U91(X1,X2)>
<Marked_and(ok(X1),ok(X2)) , Marked_and(X1,X2)>
<Marked_isNatural(ok(X)) , Marked_isNatural(X)>
<Marked_isLNat(ok(X)) , Marked_isLNat(X)>
<Marked_isPLNat(ok(X)) , Marked_isPLNat(X)>
<Marked_tail(ok(X)) , Marked_tail(X)>
<Marked_take(ok(X1),ok(X2)) , Marked_take(X1,X2)>
<Marked_sel(ok(X1),ok(X2)) , Marked_sel(X1,X2)>
<Marked_top(mark(X)) , Marked_top(proper(X))>
<Marked_top(mark(X)) , Marked_proper(X)>
<Marked_top(ok(X)) , Marked_top(active(X))>
<Marked_top(ok(X)) , Marked_active(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 30 components:

{  <Marked_top(ok(X)) , Marked_top(active(X))> 
      --> <Marked_top(ok(X)) , Marked_top(active(X))>
  <Marked_top(ok(X)) , Marked_top(active(X))> 
     --> <Marked_top(mark(X)) , Marked_top(proper(X))>
  <Marked_top(mark(X)) , Marked_top(proper(X))> 
     --> <Marked_top(ok(X)) , Marked_top(active(X))>
  <Marked_top(mark(X)) , Marked_top(proper(X))> 
     --> <Marked_top(mark(X)) , Marked_top(proper(X))>
}

{  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
      --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isPLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isLNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNatural(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U91(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U82(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U71(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isPLNat(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isLNat(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatural(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U91(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U82(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U81(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U71(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U101(X1,X2,X3)) , Marked_proper(X1)>
}

{  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
      --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U91(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U82(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U71(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U82(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U91(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U82(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U71(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U82(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U91(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U82(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U71(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X1,X2)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U82(X1,X2)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X1,X2)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U91(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U91(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U91(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U91(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U82(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U91(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U91(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U91(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U91(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U91(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U91(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U91(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U91(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U91(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U91(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U91(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U91(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U82(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U82(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U82(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U82(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U82(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U82(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(U82(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X1,X2)) , Marked_active(X1)>
  <Marked_active(U82(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U82(X1,X2)) , Marked_active(X1)>
  <Marked_active(U82(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U82(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U82(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U82(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X1,X2)) , Marked_active(X1)>
  <Marked_active(U82(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(U82(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U82(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U82(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U82(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U82(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U82(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U82(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U82(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U82(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(U82(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(U82(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U82(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U82(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U82(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U82(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U82(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U91(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U82(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U71(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U91(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U82(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U71(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U82(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U71(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U71(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U71(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U71(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U82(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U71(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U71(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U71(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U71(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U71(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U71(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U71(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U71(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U71(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U71(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U71(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U71(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U82(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U91(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U82(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U71(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U82(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U91(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U82(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U71(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U91(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U82(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U71(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U91(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U82(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U71(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U91(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U82(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U71(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U82(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U82(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U82(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U82(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U91(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U82(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U71(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U91(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U82(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U71(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U91(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U82(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U71(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U91(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U82(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U71(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U91(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U82(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U71(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U91(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U82(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U81(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U71(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U101(X1,X2,X3)) , Marked_active(X1)>
}

{  <Marked_isPLNat(ok(X)) , Marked_isPLNat(X)> 
      --> <Marked_isPLNat(ok(X)) , Marked_isPLNat(X)>
}

{  <Marked_isNatural(ok(X)) , Marked_isNatural(X)> 
      --> <Marked_isNatural(ok(X)) , Marked_isNatural(X)>
}

{  <Marked_isLNat(ok(X)) , Marked_isLNat(X)> 
      --> <Marked_isLNat(ok(X)) , Marked_isLNat(X)>
}

{  <Marked_U101(ok(X1),ok(X2),ok(X3)) , Marked_U101(X1,X2,X3)> 
      --> <Marked_U101(ok(X1),ok(X2),ok(X3)) , Marked_U101(X1,X2,X3)>
  <Marked_U101(ok(X1),ok(X2),ok(X3)) , Marked_U101(X1,X2,X3)> 
     --> <Marked_U101(mark(X1),X2,X3) , Marked_U101(X1,X2,X3)>
  <Marked_U101(mark(X1),X2,X3) , Marked_U101(X1,X2,X3)> 
     --> <Marked_U101(ok(X1),ok(X2),ok(X3)) , Marked_U101(X1,X2,X3)>
  <Marked_U101(mark(X1),X2,X3) , Marked_U101(X1,X2,X3)> 
     --> <Marked_U101(mark(X1),X2,X3) , Marked_U101(X1,X2,X3)>
}

{  <Marked_fst(ok(X)) , Marked_fst(X)> --> <Marked_fst(ok(X)) , Marked_fst(X)>
  <Marked_fst(ok(X)) , Marked_fst(X)> --> <Marked_fst(mark(X)) , Marked_fst(X)>
  <Marked_fst(mark(X)) , Marked_fst(X)> --> <Marked_fst(ok(X)) , Marked_fst(X)>
  <Marked_fst(mark(X)) , Marked_fst(X)> 
     --> <Marked_fst(mark(X)) , Marked_fst(X)>
}

{  <Marked_splitAt(ok(X1),ok(X2)) , Marked_splitAt(X1,X2)> 
      --> <Marked_splitAt(ok(X1),ok(X2)) , Marked_splitAt(X1,X2)>
  <Marked_splitAt(ok(X1),ok(X2)) , Marked_splitAt(X1,X2)> 
     --> <Marked_splitAt(X1,mark(X2)) , Marked_splitAt(X1,X2)>
  <Marked_splitAt(ok(X1),ok(X2)) , Marked_splitAt(X1,X2)> 
     --> <Marked_splitAt(mark(X1),X2) , Marked_splitAt(X1,X2)>
  <Marked_splitAt(X1,mark(X2)) , Marked_splitAt(X1,X2)> 
     --> <Marked_splitAt(ok(X1),ok(X2)) , Marked_splitAt(X1,X2)>
  <Marked_splitAt(X1,mark(X2)) , Marked_splitAt(X1,X2)> 
     --> <Marked_splitAt(X1,mark(X2)) , Marked_splitAt(X1,X2)>
  <Marked_splitAt(X1,mark(X2)) , Marked_splitAt(X1,X2)> 
     --> <Marked_splitAt(mark(X1),X2) , Marked_splitAt(X1,X2)>
  <Marked_splitAt(mark(X1),X2) , Marked_splitAt(X1,X2)> 
     --> <Marked_splitAt(ok(X1),ok(X2)) , Marked_splitAt(X1,X2)>
  <Marked_splitAt(mark(X1),X2) , Marked_splitAt(X1,X2)> 
     --> <Marked_splitAt(X1,mark(X2)) , Marked_splitAt(X1,X2)>
  <Marked_splitAt(mark(X1),X2) , Marked_splitAt(X1,X2)> 
     --> <Marked_splitAt(mark(X1),X2) , Marked_splitAt(X1,X2)>
}

{  <Marked_U11(ok(X1),ok(X2),ok(X3)) , Marked_U11(X1,X2,X3)> 
      --> <Marked_U11(ok(X1),ok(X2),ok(X3)) , Marked_U11(X1,X2,X3)>
  <Marked_U11(ok(X1),ok(X2),ok(X3)) , Marked_U11(X1,X2,X3)> 
     --> <Marked_U11(mark(X1),X2,X3) , Marked_U11(X1,X2,X3)>
  <Marked_U11(mark(X1),X2,X3) , Marked_U11(X1,X2,X3)> 
     --> <Marked_U11(ok(X1),ok(X2),ok(X3)) , Marked_U11(X1,X2,X3)>
  <Marked_U11(mark(X1),X2,X3) , Marked_U11(X1,X2,X3)> 
     --> <Marked_U11(mark(X1),X2,X3) , Marked_U11(X1,X2,X3)>
}

{  <Marked_snd(ok(X)) , Marked_snd(X)> --> <Marked_snd(ok(X)) , Marked_snd(X)>
  <Marked_snd(ok(X)) , Marked_snd(X)> --> <Marked_snd(mark(X)) , Marked_snd(X)>
  <Marked_snd(mark(X)) , Marked_snd(X)> --> <Marked_snd(ok(X)) , Marked_snd(X)>
  <Marked_snd(mark(X)) , Marked_snd(X)> 
     --> <Marked_snd(mark(X)) , Marked_snd(X)>
}

{  <Marked_U21(ok(X1),ok(X2)) , Marked_U21(X1,X2)> 
      --> <Marked_U21(ok(X1),ok(X2)) , Marked_U21(X1,X2)>
  <Marked_U21(ok(X1),ok(X2)) , Marked_U21(X1,X2)> 
     --> <Marked_U21(mark(X1),X2) , Marked_U21(X1,X2)>
  <Marked_U21(mark(X1),X2) , Marked_U21(X1,X2)> 
     --> <Marked_U21(ok(X1),ok(X2)) , Marked_U21(X1,X2)>
  <Marked_U21(mark(X1),X2) , Marked_U21(X1,X2)> 
     --> <Marked_U21(mark(X1),X2) , Marked_U21(X1,X2)>
}

{  <Marked_U31(ok(X1),ok(X2)) , Marked_U31(X1,X2)> 
      --> <Marked_U31(ok(X1),ok(X2)) , Marked_U31(X1,X2)>
  <Marked_U31(ok(X1),ok(X2)) , Marked_U31(X1,X2)> 
     --> <Marked_U31(mark(X1),X2) , Marked_U31(X1,X2)>
  <Marked_U31(mark(X1),X2) , Marked_U31(X1,X2)> 
     --> <Marked_U31(ok(X1),ok(X2)) , Marked_U31(X1,X2)>
  <Marked_U31(mark(X1),X2) , Marked_U31(X1,X2)> 
     --> <Marked_U31(mark(X1),X2) , Marked_U31(X1,X2)>
}

{  <Marked_U41(ok(X1),ok(X2)) , Marked_U41(X1,X2)> 
      --> <Marked_U41(ok(X1),ok(X2)) , Marked_U41(X1,X2)>
  <Marked_U41(ok(X1),ok(X2)) , Marked_U41(X1,X2)> 
     --> <Marked_U41(mark(X1),X2) , Marked_U41(X1,X2)>
  <Marked_U41(mark(X1),X2) , Marked_U41(X1,X2)> 
     --> <Marked_U41(ok(X1),ok(X2)) , Marked_U41(X1,X2)>
  <Marked_U41(mark(X1),X2) , Marked_U41(X1,X2)> 
     --> <Marked_U41(mark(X1),X2) , Marked_U41(X1,X2)>
}

{  <Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)> 
      --> <Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)>
  <Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)> 
     --> <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
  <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)> 
     --> <Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)>
  <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)> 
     --> <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
}

{  <Marked_natsFrom(ok(X)) , Marked_natsFrom(X)> 
      --> <Marked_natsFrom(ok(X)) , Marked_natsFrom(X)>
  <Marked_natsFrom(ok(X)) , Marked_natsFrom(X)> 
     --> <Marked_natsFrom(mark(X)) , Marked_natsFrom(X)>
  <Marked_natsFrom(mark(X)) , Marked_natsFrom(X)> 
     --> <Marked_natsFrom(ok(X)) , Marked_natsFrom(X)>
  <Marked_natsFrom(mark(X)) , Marked_natsFrom(X)> 
     --> <Marked_natsFrom(mark(X)) , Marked_natsFrom(X)>
}

{  <Marked_s(ok(X)) , Marked_s(X)> --> <Marked_s(ok(X)) , Marked_s(X)>
  <Marked_s(ok(X)) , Marked_s(X)> --> <Marked_s(mark(X)) , Marked_s(X)>
  <Marked_s(mark(X)) , Marked_s(X)> --> <Marked_s(ok(X)) , Marked_s(X)>
  <Marked_s(mark(X)) , Marked_s(X)> --> <Marked_s(mark(X)) , Marked_s(X)>
}

{  <Marked_U51(ok(X1),ok(X2),ok(X3)) , Marked_U51(X1,X2,X3)> 
      --> <Marked_U51(ok(X1),ok(X2),ok(X3)) , Marked_U51(X1,X2,X3)>
  <Marked_U51(ok(X1),ok(X2),ok(X3)) , Marked_U51(X1,X2,X3)> 
     --> <Marked_U51(mark(X1),X2,X3) , Marked_U51(X1,X2,X3)>
  <Marked_U51(mark(X1),X2,X3) , Marked_U51(X1,X2,X3)> 
     --> <Marked_U51(ok(X1),ok(X2),ok(X3)) , Marked_U51(X1,X2,X3)>
  <Marked_U51(mark(X1),X2,X3) , Marked_U51(X1,X2,X3)> 
     --> <Marked_U51(mark(X1),X2,X3) , Marked_U51(X1,X2,X3)>
}

{  <Marked_head(ok(X)) , Marked_head(X)> 
      --> <Marked_head(ok(X)) , Marked_head(X)>
  <Marked_head(ok(X)) , Marked_head(X)> 
     --> <Marked_head(mark(X)) , Marked_head(X)>
  <Marked_head(mark(X)) , Marked_head(X)> 
     --> <Marked_head(ok(X)) , Marked_head(X)>
  <Marked_head(mark(X)) , Marked_head(X)> 
     --> <Marked_head(mark(X)) , Marked_head(X)>
}

{  <Marked_afterNth(ok(X1),ok(X2)) , Marked_afterNth(X1,X2)> 
      --> <Marked_afterNth(ok(X1),ok(X2)) , Marked_afterNth(X1,X2)>
  <Marked_afterNth(ok(X1),ok(X2)) , Marked_afterNth(X1,X2)> 
     --> <Marked_afterNth(X1,mark(X2)) , Marked_afterNth(X1,X2)>
  <Marked_afterNth(ok(X1),ok(X2)) , Marked_afterNth(X1,X2)> 
     --> <Marked_afterNth(mark(X1),X2) , Marked_afterNth(X1,X2)>
  <Marked_afterNth(X1,mark(X2)) , Marked_afterNth(X1,X2)> 
     --> <Marked_afterNth(ok(X1),ok(X2)) , Marked_afterNth(X1,X2)>
  <Marked_afterNth(X1,mark(X2)) , Marked_afterNth(X1,X2)> 
     --> <Marked_afterNth(X1,mark(X2)) , Marked_afterNth(X1,X2)>
  <Marked_afterNth(X1,mark(X2)) , Marked_afterNth(X1,X2)> 
     --> <Marked_afterNth(mark(X1),X2) , Marked_afterNth(X1,X2)>
  <Marked_afterNth(mark(X1),X2) , Marked_afterNth(X1,X2)> 
     --> <Marked_afterNth(ok(X1),ok(X2)) , Marked_afterNth(X1,X2)>
  <Marked_afterNth(mark(X1),X2) , Marked_afterNth(X1,X2)> 
     --> <Marked_afterNth(X1,mark(X2)) , Marked_afterNth(X1,X2)>
  <Marked_afterNth(mark(X1),X2) , Marked_afterNth(X1,X2)> 
     --> <Marked_afterNth(mark(X1),X2) , Marked_afterNth(X1,X2)>
}

{  <Marked_U61(ok(X1),ok(X2)) , Marked_U61(X1,X2)> 
      --> <Marked_U61(ok(X1),ok(X2)) , Marked_U61(X1,X2)>
  <Marked_U61(ok(X1),ok(X2)) , Marked_U61(X1,X2)> 
     --> <Marked_U61(mark(X1),X2) , Marked_U61(X1,X2)>
  <Marked_U61(mark(X1),X2) , Marked_U61(X1,X2)> 
     --> <Marked_U61(ok(X1),ok(X2)) , Marked_U61(X1,X2)>
  <Marked_U61(mark(X1),X2) , Marked_U61(X1,X2)> 
     --> <Marked_U61(mark(X1),X2) , Marked_U61(X1,X2)>
}

{  <Marked_U71(ok(X1),ok(X2)) , Marked_U71(X1,X2)> 
      --> <Marked_U71(ok(X1),ok(X2)) , Marked_U71(X1,X2)>
  <Marked_U71(ok(X1),ok(X2)) , Marked_U71(X1,X2)> 
     --> <Marked_U71(mark(X1),X2) , Marked_U71(X1,X2)>
  <Marked_U71(mark(X1),X2) , Marked_U71(X1,X2)> 
     --> <Marked_U71(ok(X1),ok(X2)) , Marked_U71(X1,X2)>
  <Marked_U71(mark(X1),X2) , Marked_U71(X1,X2)> 
     --> <Marked_U71(mark(X1),X2) , Marked_U71(X1,X2)>
}

{  <Marked_pair(ok(X1),ok(X2)) , Marked_pair(X1,X2)> 
      --> <Marked_pair(ok(X1),ok(X2)) , Marked_pair(X1,X2)>
  <Marked_pair(ok(X1),ok(X2)) , Marked_pair(X1,X2)> 
     --> <Marked_pair(X1,mark(X2)) , Marked_pair(X1,X2)>
  <Marked_pair(ok(X1),ok(X2)) , Marked_pair(X1,X2)> 
     --> <Marked_pair(mark(X1),X2) , Marked_pair(X1,X2)>
  <Marked_pair(X1,mark(X2)) , Marked_pair(X1,X2)> 
     --> <Marked_pair(ok(X1),ok(X2)) , Marked_pair(X1,X2)>
  <Marked_pair(X1,mark(X2)) , Marked_pair(X1,X2)> 
     --> <Marked_pair(X1,mark(X2)) , Marked_pair(X1,X2)>
  <Marked_pair(X1,mark(X2)) , Marked_pair(X1,X2)> 
     --> <Marked_pair(mark(X1),X2) , Marked_pair(X1,X2)>
  <Marked_pair(mark(X1),X2) , Marked_pair(X1,X2)> 
     --> <Marked_pair(ok(X1),ok(X2)) , Marked_pair(X1,X2)>
  <Marked_pair(mark(X1),X2) , Marked_pair(X1,X2)> 
     --> <Marked_pair(X1,mark(X2)) , Marked_pair(X1,X2)>
  <Marked_pair(mark(X1),X2) , Marked_pair(X1,X2)> 
     --> <Marked_pair(mark(X1),X2) , Marked_pair(X1,X2)>
}

{  <Marked_U81(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U81(X1,X2,X3,X4)> 
      --> <Marked_U81(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U81(X1,X2,X3,X4)>
  <Marked_U81(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U81(X1,X2,X3,X4)> 
     --> <Marked_U81(mark(X1),X2,X3,X4) , Marked_U81(X1,X2,X3,X4)>
  <Marked_U81(mark(X1),X2,X3,X4) , Marked_U81(X1,X2,X3,X4)> 
     --> <Marked_U81(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U81(X1,X2,X3,X4)>
  <Marked_U81(mark(X1),X2,X3,X4) , Marked_U81(X1,X2,X3,X4)> 
     --> <Marked_U81(mark(X1),X2,X3,X4) , Marked_U81(X1,X2,X3,X4)>
}

{  <Marked_U82(ok(X1),ok(X2)) , Marked_U82(X1,X2)> 
      --> <Marked_U82(ok(X1),ok(X2)) , Marked_U82(X1,X2)>
  <Marked_U82(ok(X1),ok(X2)) , Marked_U82(X1,X2)> 
     --> <Marked_U82(mark(X1),X2) , Marked_U82(X1,X2)>
  <Marked_U82(mark(X1),X2) , Marked_U82(X1,X2)> 
     --> <Marked_U82(ok(X1),ok(X2)) , Marked_U82(X1,X2)>
  <Marked_U82(mark(X1),X2) , Marked_U82(X1,X2)> 
     --> <Marked_U82(mark(X1),X2) , Marked_U82(X1,X2)>
}

{  <Marked_U91(ok(X1),ok(X2)) , Marked_U91(X1,X2)> 
      --> <Marked_U91(ok(X1),ok(X2)) , Marked_U91(X1,X2)>
  <Marked_U91(ok(X1),ok(X2)) , Marked_U91(X1,X2)> 
     --> <Marked_U91(mark(X1),X2) , Marked_U91(X1,X2)>
  <Marked_U91(mark(X1),X2) , Marked_U91(X1,X2)> 
     --> <Marked_U91(ok(X1),ok(X2)) , Marked_U91(X1,X2)>
  <Marked_U91(mark(X1),X2) , Marked_U91(X1,X2)> 
     --> <Marked_U91(mark(X1),X2) , Marked_U91(X1,X2)>
}

{  <Marked_and(ok(X1),ok(X2)) , Marked_and(X1,X2)> 
      --> <Marked_and(ok(X1),ok(X2)) , Marked_and(X1,X2)>
  <Marked_and(ok(X1),ok(X2)) , Marked_and(X1,X2)> 
     --> <Marked_and(mark(X1),X2) , Marked_and(X1,X2)>
  <Marked_and(mark(X1),X2) , Marked_and(X1,X2)> 
     --> <Marked_and(ok(X1),ok(X2)) , Marked_and(X1,X2)>
  <Marked_and(mark(X1),X2) , Marked_and(X1,X2)> 
     --> <Marked_and(mark(X1),X2) , Marked_and(X1,X2)>
}

{  <Marked_tail(ok(X)) , Marked_tail(X)> 
      --> <Marked_tail(ok(X)) , Marked_tail(X)>
  <Marked_tail(ok(X)) , Marked_tail(X)> 
     --> <Marked_tail(mark(X)) , Marked_tail(X)>
  <Marked_tail(mark(X)) , Marked_tail(X)> 
     --> <Marked_tail(ok(X)) , Marked_tail(X)>
  <Marked_tail(mark(X)) , Marked_tail(X)> 
     --> <Marked_tail(mark(X)) , Marked_tail(X)>
}

{  <Marked_take(ok(X1),ok(X2)) , Marked_take(X1,X2)> 
      --> <Marked_take(ok(X1),ok(X2)) , Marked_take(X1,X2)>
  <Marked_take(ok(X1),ok(X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(X1,mark(X2)) , Marked_take(X1,X2)>
  <Marked_take(ok(X1),ok(X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(mark(X1),X2) , Marked_take(X1,X2)>
  <Marked_take(X1,mark(X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(ok(X1),ok(X2)) , Marked_take(X1,X2)>
  <Marked_take(X1,mark(X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(X1,mark(X2)) , Marked_take(X1,X2)>
  <Marked_take(X1,mark(X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(mark(X1),X2) , Marked_take(X1,X2)>
  <Marked_take(mark(X1),X2) , Marked_take(X1,X2)> 
     --> <Marked_take(ok(X1),ok(X2)) , Marked_take(X1,X2)>
  <Marked_take(mark(X1),X2) , Marked_take(X1,X2)> 
     --> <Marked_take(X1,mark(X2)) , Marked_take(X1,X2)>
  <Marked_take(mark(X1),X2) , Marked_take(X1,X2)> 
     --> <Marked_take(mark(X1),X2) , Marked_take(X1,X2)>
}

{  <Marked_sel(ok(X1),ok(X2)) , Marked_sel(X1,X2)> 
      --> <Marked_sel(ok(X1),ok(X2)) , Marked_sel(X1,X2)>
  <Marked_sel(ok(X1),ok(X2)) , Marked_sel(X1,X2)> 
     --> <Marked_sel(X1,mark(X2)) , Marked_sel(X1,X2)>
  <Marked_sel(ok(X1),ok(X2)) , Marked_sel(X1,X2)> 
     --> <Marked_sel(mark(X1),X2) , Marked_sel(X1,X2)>
  <Marked_sel(X1,mark(X2)) , Marked_sel(X1,X2)> 
     --> <Marked_sel(ok(X1),ok(X2)) , Marked_sel(X1,X2)>
  <Marked_sel(X1,mark(X2)) , Marked_sel(X1,X2)> 
     --> <Marked_sel(X1,mark(X2)) , Marked_sel(X1,X2)>
  <Marked_sel(X1,mark(X2)) , Marked_sel(X1,X2)> 
     --> <Marked_sel(mark(X1),X2) , Marked_sel(X1,X2)>
  <Marked_sel(mark(X1),X2) , Marked_sel(X1,X2)> 
     --> <Marked_sel(ok(X1),ok(X2)) , Marked_sel(X1,X2)>
  <Marked_sel(mark(X1),X2) , Marked_sel(X1,X2)> 
     --> <Marked_sel(X1,mark(X2)) , Marked_sel(X1,X2)>
  <Marked_sel(mark(X1),X2) , Marked_sel(X1,X2)> 
     --> <Marked_sel(mark(X1),X2) , Marked_sel(X1,X2)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  fst(mark(X)) >= mark(fst(X)) ;
  fst(ok(X)) >= ok(fst(X)) ;
  splitAt(mark(X1),X2) >= mark(splitAt(X1,X2)) ;
  splitAt(ok(X1),ok(X2)) >= ok(splitAt(X1,X2)) ;
  splitAt(X1,mark(X2)) >= mark(splitAt(X1,X2)) ;
  active(fst(pair(X,Y))) >= mark(U21(and(isLNat(X),isLNat(Y)),X)) ;
  active(fst(X)) >= fst(active(X)) ;
  active(splitAt(s(N),cons(X,XS))) >= mark(U81(and(isNatural(N),
                                                and(isNatural(X),isLNat(XS))),
                                            N,X,XS)) ;
  active(splitAt(0,XS)) >= mark(U71(isLNat(XS),XS)) ;
  active(splitAt(X1,X2)) >= splitAt(active(X1),X2) ;
  active(splitAt(X1,X2)) >= splitAt(X1,active(X2)) ;
  active(U101(tt,N,XS)) >= mark(fst(splitAt(N,XS))) ;
  active(U101(X1,X2,X3)) >= U101(active(X1),X2,X3) ;
  active(snd(pair(X,Y))) >= mark(U61(and(isLNat(X),isLNat(Y)),Y)) ;
  active(snd(X)) >= snd(active(X)) ;
  active(U11(tt,N,XS)) >= mark(snd(splitAt(N,XS))) ;
  active(U11(X1,X2,X3)) >= U11(active(X1),X2,X3) ;
  active(U21(tt,X)) >= mark(X) ;
  active(U21(X1,X2)) >= U21(active(X1),X2) ;
  active(U31(tt,N)) >= mark(N) ;
  active(U31(X1,X2)) >= U31(active(X1),X2) ;
  active(cons(X1,X2)) >= cons(active(X1),X2) ;
  active(natsFrom(N)) >= mark(U41(isNatural(N),N)) ;
  active(natsFrom(X)) >= natsFrom(active(X)) ;
  active(s(X)) >= s(active(X)) ;
  active(U41(tt,N)) >= mark(cons(N,natsFrom(s(N)))) ;
  active(U41(X1,X2)) >= U41(active(X1),X2) ;
  active(head(cons(N,XS))) >= mark(U31(and(isNatural(N),isLNat(XS)),N)) ;
  active(head(X)) >= head(active(X)) ;
  active(afterNth(N,XS)) >= mark(U11(and(isNatural(N),isLNat(XS)),N,XS)) ;
  active(afterNth(X1,X2)) >= afterNth(active(X1),X2) ;
  active(afterNth(X1,X2)) >= afterNth(X1,active(X2)) ;
  active(U51(tt,N,XS)) >= mark(head(afterNth(N,XS))) ;
  active(U51(X1,X2,X3)) >= U51(active(X1),X2,X3) ;
  active(U61(tt,Y)) >= mark(Y) ;
  active(U61(X1,X2)) >= U61(active(X1),X2) ;
  active(pair(X1,X2)) >= pair(active(X1),X2) ;
  active(pair(X1,X2)) >= pair(X1,active(X2)) ;
  active(U71(tt,XS)) >= mark(pair(nil,XS)) ;
  active(U71(X1,X2)) >= U71(active(X1),X2) ;
  active(U82(pair(YS,ZS),X)) >= mark(pair(cons(X,YS),ZS)) ;
  active(U82(X1,X2)) >= U82(active(X1),X2) ;
  active(U81(tt,N,X,XS)) >= mark(U82(splitAt(N,XS),X)) ;
  active(U81(X1,X2,X3,X4)) >= U81(active(X1),X2,X3,X4) ;
  active(U91(tt,XS)) >= mark(XS) ;
  active(U91(X1,X2)) >= U91(active(X1),X2) ;
  active(and(tt,X)) >= mark(X) ;
  active(and(X1,X2)) >= and(active(X1),X2) ;
  active(isNatural(s(V1))) >= mark(isNatural(V1)) ;
  active(isNatural(head(V1))) >= mark(isLNat(V1)) ;
  active(isNatural(0)) >= mark(tt) ;
  active(isNatural(sel(V1,V2))) >= mark(and(isNatural(V1),isLNat(V2))) ;
  active(isLNat(fst(V1))) >= mark(isPLNat(V1)) ;
  active(isLNat(snd(V1))) >= mark(isPLNat(V1)) ;
  active(isLNat(cons(V1,V2))) >= mark(and(isNatural(V1),isLNat(V2))) ;
  active(isLNat(natsFrom(V1))) >= mark(isNatural(V1)) ;
  active(isLNat(afterNth(V1,V2))) >= mark(and(isNatural(V1),isLNat(V2))) ;
  active(isLNat(nil)) >= mark(tt) ;
  active(isLNat(tail(V1))) >= mark(isLNat(V1)) ;
  active(isLNat(take(V1,V2))) >= mark(and(isNatural(V1),isLNat(V2))) ;
  active(isPLNat(splitAt(V1,V2))) >= mark(and(isNatural(V1),isLNat(V2))) ;
  active(isPLNat(pair(V1,V2))) >= mark(and(isLNat(V1),isLNat(V2))) ;
  active(tail(cons(N,XS))) >= mark(U91(and(isNatural(N),isLNat(XS)),XS)) ;
  active(tail(X)) >= tail(active(X)) ;
  active(take(N,XS)) >= mark(U101(and(isNatural(N),isLNat(XS)),N,XS)) ;
  active(take(X1,X2)) >= take(active(X1),X2) ;
  active(take(X1,X2)) >= take(X1,active(X2)) ;
  active(sel(N,XS)) >= mark(U51(and(isNatural(N),isLNat(XS)),N,XS)) ;
  active(sel(X1,X2)) >= sel(active(X1),X2) ;
  active(sel(X1,X2)) >= sel(X1,active(X2)) ;
  U101(mark(X1),X2,X3) >= mark(U101(X1,X2,X3)) ;
  U101(ok(X1),ok(X2),ok(X3)) >= ok(U101(X1,X2,X3)) ;
  snd(mark(X)) >= mark(snd(X)) ;
  snd(ok(X)) >= ok(snd(X)) ;
  U11(mark(X1),X2,X3) >= mark(U11(X1,X2,X3)) ;
  U11(ok(X1),ok(X2),ok(X3)) >= ok(U11(X1,X2,X3)) ;
  U21(mark(X1),X2) >= mark(U21(X1,X2)) ;
  U21(ok(X1),ok(X2)) >= ok(U21(X1,X2)) ;
  U31(mark(X1),X2) >= mark(U31(X1,X2)) ;
  U31(ok(X1),ok(X2)) >= ok(U31(X1,X2)) ;
  cons(mark(X1),X2) >= mark(cons(X1,X2)) ;
  cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ;
  natsFrom(mark(X)) >= mark(natsFrom(X)) ;
  natsFrom(ok(X)) >= ok(natsFrom(X)) ;
  s(mark(X)) >= mark(s(X)) ;
  s(ok(X)) >= ok(s(X)) ;
  U41(mark(X1),X2) >= mark(U41(X1,X2)) ;
  U41(ok(X1),ok(X2)) >= ok(U41(X1,X2)) ;
  head(mark(X)) >= mark(head(X)) ;
  head(ok(X)) >= ok(head(X)) ;
  afterNth(mark(X1),X2) >= mark(afterNth(X1,X2)) ;
  afterNth(ok(X1),ok(X2)) >= ok(afterNth(X1,X2)) ;
  afterNth(X1,mark(X2)) >= mark(afterNth(X1,X2)) ;
  U51(mark(X1),X2,X3) >= mark(U51(X1,X2,X3)) ;
  U51(ok(X1),ok(X2),ok(X3)) >= ok(U51(X1,X2,X3)) ;
  U61(mark(X1),X2) >= mark(U61(X1,X2)) ;
  U61(ok(X1),ok(X2)) >= ok(U61(X1,X2)) ;
  pair(mark(X1),X2) >= mark(pair(X1,X2)) ;
  pair(ok(X1),ok(X2)) >= ok(pair(X1,X2)) ;
  pair(X1,mark(X2)) >= mark(pair(X1,X2)) ;
  U71(mark(X1),X2) >= mark(U71(X1,X2)) ;
  U71(ok(X1),ok(X2)) >= ok(U71(X1,X2)) ;
  U82(mark(X1),X2) >= mark(U82(X1,X2)) ;
  U82(ok(X1),ok(X2)) >= ok(U82(X1,X2)) ;
  U81(mark(X1),X2,X3,X4) >= mark(U81(X1,X2,X3,X4)) ;
  U81(ok(X1),ok(X2),ok(X3),ok(X4)) >= ok(U81(X1,X2,X3,X4)) ;
  U91(mark(X1),X2) >= mark(U91(X1,X2)) ;
  U91(ok(X1),ok(X2)) >= ok(U91(X1,X2)) ;
  and(mark(X1),X2) >= mark(and(X1,X2)) ;
  and(ok(X1),ok(X2)) >= ok(and(X1,X2)) ;
  isNatural(ok(X)) >= ok(isNatural(X)) ;
  isLNat(ok(X)) >= ok(isLNat(X)) ;
  isPLNat(ok(X)) >= ok(isPLNat(X)) ;
  tail(mark(X)) >= mark(tail(X)) ;
  tail(ok(X)) >= ok(tail(X)) ;
  take(mark(X1),X2) >= mark(take(X1,X2)) ;
  take(ok(X1),ok(X2)) >= ok(take(X1,X2)) ;
  take(X1,mark(X2)) >= mark(take(X1,X2)) ;
  sel(mark(X1),X2) >= mark(sel(X1,X2)) ;
  sel(ok(X1),ok(X2)) >= ok(sel(X1,X2)) ;
  sel(X1,mark(X2)) >= mark(sel(X1,X2)) ;
  proper(fst(X)) >= fst(proper(X)) ;
  proper(splitAt(X1,X2)) >= splitAt(proper(X1),proper(X2)) ;
  proper(U101(X1,X2,X3)) >= U101(proper(X1),proper(X2),proper(X3)) ;
  proper(tt) >= ok(tt) ;
  proper(snd(X)) >= snd(proper(X)) ;
  proper(U11(X1,X2,X3)) >= U11(proper(X1),proper(X2),proper(X3)) ;
  proper(U21(X1,X2)) >= U21(proper(X1),proper(X2)) ;
  proper(U31(X1,X2)) >= U31(proper(X1),proper(X2)) ;
  proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ;
  proper(natsFrom(X)) >= natsFrom(proper(X)) ;
  proper(s(X)) >= s(proper(X)) ;
  proper(U41(X1,X2)) >= U41(proper(X1),proper(X2)) ;
  proper(head(X)) >= head(proper(X)) ;
  proper(afterNth(X1,X2)) >= afterNth(proper(X1),proper(X2)) ;
  proper(U51(X1,X2,X3)) >= U51(proper(X1),proper(X2),proper(X3)) ;
  proper(U61(X1,X2)) >= U61(proper(X1),proper(X2)) ;
  proper(pair(X1,X2)) >= pair(proper(X1),proper(X2)) ;
  proper(nil) >= ok(nil) ;
  proper(U71(X1,X2)) >= U71(proper(X1),proper(X2)) ;
  proper(U82(X1,X2)) >= U82(proper(X1),proper(X2)) ;
  proper(U81(X1,X2,X3,X4)) >= U81(proper(X1),proper(X2),proper(X3),proper(X4)) ;
  proper(U91(X1,X2)) >= U91(proper(X1),proper(X2)) ;
  proper(and(X1,X2)) >= and(proper(X1),proper(X2)) ;
  proper(isNatural(X)) >= isNatural(proper(X)) ;
  proper(isLNat(X)) >= isLNat(proper(X)) ;
  proper(isPLNat(X)) >= isPLNat(proper(X)) ;
  proper(tail(X)) >= tail(proper(X)) ;
  proper(take(X1,X2)) >= take(proper(X1),proper(X2)) ;
  proper(0) >= ok(0) ;
  proper(sel(X1,X2)) >= sel(proper(X1),proper(X2)) ;
  top(mark(X)) >= top(proper(X)) ;
  top(ok(X)) >= top(active(X)) ;
  Marked_top(mark(X)) >= Marked_top(proper(X)) ;
  Marked_top(ok(X)) >= Marked_top(active(X)) ;
 }
 + Disjunctions:{ 
{
  Marked_top(mark(X)) > Marked_top(proper(X)) ;
 }
{
  Marked_top(ok(X)) > Marked_top(active(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 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 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 93.636141 seconds (real time)
Cime Exit Status: 0