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

TRS termination of:
[1] active(zeros) -> mark(cons(0,zeros))
[2] active(U11(tt,V1)) -> mark(U12(isNatList(V1)))
[3] active(U12(tt)) -> mark(tt)
[4] active(U21(tt,V1)) -> mark(U22(isNat(V1)))
[5] active(U22(tt)) -> mark(tt)
[6] active(U31(tt,V)) -> mark(U32(isNatList(V)))
[7] active(U32(tt)) -> mark(tt)
[8] active(U41(tt,V1,V2)) -> mark(U42(isNat(V1),V2))
[9] active(U42(tt,V2)) -> mark(U43(isNatIList(V2)))
[10] active(U43(tt)) -> mark(tt)
[11] active(U51(tt,V1,V2)) -> mark(U52(isNat(V1),V2))
[12] active(U52(tt,V2)) -> mark(U53(isNatList(V2)))
[13] active(U53(tt)) -> mark(tt)
[14] active(U61(tt,L)) -> mark(s(length(L)))
[15] active(and(tt,X)) -> mark(X)
[16] active(isNat(0)) -> mark(tt)
[17] active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
[18] active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
[19] active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
[20] active(isNatIList(zeros)) -> mark(tt)
[21] active(isNatIList(cons(V1,V2))) ->
 mark(U41(and(isNatKind(V1),isNatIListKind(V2)),V1,V2))
[22] active(isNatIListKind(nil)) -> mark(tt)
[23] active(isNatIListKind(zeros)) -> mark(tt)
[24] active(isNatIListKind(cons(V1,V2))) ->
 mark(and(isNatKind(V1),isNatIListKind(V2)))
[25] active(isNatKind(0)) -> mark(tt)
[26] active(isNatKind(length(V1))) -> mark(isNatIListKind(V1))
[27] active(isNatKind(s(V1))) -> mark(isNatKind(V1))
[28] active(isNatList(nil)) -> mark(tt)
[29] active(isNatList(cons(V1,V2))) ->
 mark(U51(and(isNatKind(V1),isNatIListKind(V2)),V1,V2))
[30] active(length(nil)) -> mark(0)
[31] active(length(cons(N,L))) ->
 mark(U61(and(and(isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),
       L))
[32] active(cons(X1,X2)) -> cons(active(X1),X2)
[33] active(U11(X1,X2)) -> U11(active(X1),X2)
[34] active(U12(X)) -> U12(active(X))
[35] active(U21(X1,X2)) -> U21(active(X1),X2)
[36] active(U22(X)) -> U22(active(X))
[37] active(U31(X1,X2)) -> U31(active(X1),X2)
[38] active(U32(X)) -> U32(active(X))
[39] active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
[40] active(U42(X1,X2)) -> U42(active(X1),X2)
[41] active(U43(X)) -> U43(active(X))
[42] active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
[43] active(U52(X1,X2)) -> U52(active(X1),X2)
[44] active(U53(X)) -> U53(active(X))
[45] active(U61(X1,X2)) -> U61(active(X1),X2)
[46] active(s(X)) -> s(active(X))
[47] active(length(X)) -> length(active(X))
[48] active(and(X1,X2)) -> and(active(X1),X2)
[49] cons(mark(X1),X2) -> mark(cons(X1,X2))
[50] U11(mark(X1),X2) -> mark(U11(X1,X2))
[51] U12(mark(X)) -> mark(U12(X))
[52] U21(mark(X1),X2) -> mark(U21(X1,X2))
[53] U22(mark(X)) -> mark(U22(X))
[54] U31(mark(X1),X2) -> mark(U31(X1,X2))
[55] U32(mark(X)) -> mark(U32(X))
[56] U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
[57] U42(mark(X1),X2) -> mark(U42(X1,X2))
[58] U43(mark(X)) -> mark(U43(X))
[59] U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
[60] U52(mark(X1),X2) -> mark(U52(X1,X2))
[61] U53(mark(X)) -> mark(U53(X))
[62] U61(mark(X1),X2) -> mark(U61(X1,X2))
[63] s(mark(X)) -> mark(s(X))
[64] length(mark(X)) -> mark(length(X))
[65] and(mark(X1),X2) -> mark(and(X1,X2))
[66] proper(zeros) -> ok(zeros)
[67] proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
[68] proper(0) -> ok(0)
[69] proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
[70] proper(tt) -> ok(tt)
[71] proper(U12(X)) -> U12(proper(X))
[72] proper(isNatList(X)) -> isNatList(proper(X))
[73] proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
[74] proper(U22(X)) -> U22(proper(X))
[75] proper(isNat(X)) -> isNat(proper(X))
[76] proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
[77] proper(U32(X)) -> U32(proper(X))
[78] proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
[79] proper(U42(X1,X2)) -> U42(proper(X1),proper(X2))
[80] proper(U43(X)) -> U43(proper(X))
[81] proper(isNatIList(X)) -> isNatIList(proper(X))
[82] proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
[83] proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
[84] proper(U53(X)) -> U53(proper(X))
[85] proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
[86] proper(s(X)) -> s(proper(X))
[87] proper(length(X)) -> length(proper(X))
[88] proper(and(X1,X2)) -> and(proper(X1),proper(X2))
[89] proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
[90] proper(isNatKind(X)) -> isNatKind(proper(X))
[91] proper(nil) -> ok(nil)
[92] cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
[93] U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
[94] U12(ok(X)) -> ok(U12(X))
[95] isNatList(ok(X)) -> ok(isNatList(X))
[96] U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
[97] U22(ok(X)) -> ok(U22(X))
[98] isNat(ok(X)) -> ok(isNat(X))
[99] U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
[100] U32(ok(X)) -> ok(U32(X))
[101] U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
[102] U42(ok(X1),ok(X2)) -> ok(U42(X1,X2))
[103] U43(ok(X)) -> ok(U43(X))
[104] isNatIList(ok(X)) -> ok(isNatIList(X))
[105] U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
[106] U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
[107] U53(ok(X)) -> ok(U53(X))
[108] U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
[109] s(ok(X)) -> ok(s(X))
[110] length(ok(X)) -> ok(length(X))
[111] and(ok(X1),ok(X2)) -> ok(and(X1,X2))
[112] isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
[113] isNatKind(ok(X)) -> ok(isNatKind(X))
[114] top(mark(X)) -> top(proper(X))
[115] top(ok(X)) -> top(active(X))


Sub problem: 
guided: 

DP termination of:
<Marked_active(zeros) , Marked_cons(0,zeros)>
<Marked_active(U11(tt,V1)) , Marked_U12(isNatList(V1))>
<Marked_active(U11(tt,V1)) , Marked_isNatList(V1)>
<Marked_active(U21(tt,V1)) , Marked_U22(isNat(V1))>
<Marked_active(U21(tt,V1)) , Marked_isNat(V1)>
<Marked_active(U31(tt,V)) , Marked_U32(isNatList(V))>
<Marked_active(U31(tt,V)) , Marked_isNatList(V)>
<Marked_active(U41(tt,V1,V2)) , Marked_U42(isNat(V1),V2)>
<Marked_active(U41(tt,V1,V2)) , Marked_isNat(V1)>
<Marked_active(U42(tt,V2)) , Marked_U43(isNatIList(V2))>
<Marked_active(U42(tt,V2)) , Marked_isNatIList(V2)>
<Marked_active(U51(tt,V1,V2)) , Marked_U52(isNat(V1),V2)>
<Marked_active(U51(tt,V1,V2)) , Marked_isNat(V1)>
<Marked_active(U52(tt,V2)) , Marked_U53(isNatList(V2))>
<Marked_active(U52(tt,V2)) , Marked_isNatList(V2)>
<Marked_active(U61(tt,L)) , Marked_s(length(L))>
<Marked_active(U61(tt,L)) , Marked_length(L)>
<Marked_active(isNat(length(V1))) , Marked_U11(isNatIListKind(V1),V1)>
<Marked_active(isNat(length(V1))) , Marked_isNatIListKind(V1)>
<Marked_active(isNat(s(V1))) , Marked_U21(isNatKind(V1),V1)>
<Marked_active(isNat(s(V1))) , Marked_isNatKind(V1)>
<Marked_active(isNatIList(V)) , Marked_U31(isNatIListKind(V),V)>
<Marked_active(isNatIList(V)) , Marked_isNatIListKind(V)>
<Marked_active(isNatIList(cons(V1,V2))) , Marked_U41(and(isNatKind(V1),
                                                      isNatIListKind(V2)),
                                           V1,V2)>
<Marked_active(isNatIList(cons(V1,V2))) , Marked_and(isNatKind(V1),
                                           isNatIListKind(V2))>
<Marked_active(isNatIList(cons(V1,V2))) , Marked_isNatKind(V1)>
<Marked_active(isNatIList(cons(V1,V2))) , Marked_isNatIListKind(V2)>
<Marked_active(isNatIListKind(cons(V1,V2))) , Marked_and(isNatKind(V1),
                                               isNatIListKind(V2))>
<Marked_active(isNatIListKind(cons(V1,V2))) , Marked_isNatKind(V1)>
<Marked_active(isNatIListKind(cons(V1,V2))) , Marked_isNatIListKind(V2)>
<Marked_active(isNatKind(length(V1))) , Marked_isNatIListKind(V1)>
<Marked_active(isNatKind(s(V1))) , Marked_isNatKind(V1)>
<Marked_active(isNatList(cons(V1,V2))) , Marked_U51(and(isNatKind(V1),
                                                     isNatIListKind(V2)),
                                          V1,V2)>
<Marked_active(isNatList(cons(V1,V2))) , Marked_and(isNatKind(V1),
                                          isNatIListKind(V2))>
<Marked_active(isNatList(cons(V1,V2))) , Marked_isNatKind(V1)>
<Marked_active(isNatList(cons(V1,V2))) , Marked_isNatIListKind(V2)>
<Marked_active(length(cons(N,L))) , Marked_U61(and(and(isNatList(L),
                                                    isNatIListKind(L)),
                                                and(isNat(N),isNatKind(N))),
                                     L)>
<Marked_active(length(cons(N,L))) , Marked_and(and(isNatList(L),
                                                isNatIListKind(L)),
                                     and(isNat(N),isNatKind(N)))>
<Marked_active(length(cons(N,L))) , Marked_and(isNatList(L),isNatIListKind(L))>
<Marked_active(length(cons(N,L))) , Marked_isNatList(L)>
<Marked_active(length(cons(N,L))) , Marked_isNatIListKind(L)>
<Marked_active(length(cons(N,L))) , Marked_and(isNat(N),isNatKind(N))>
<Marked_active(length(cons(N,L))) , Marked_isNat(N)>
<Marked_active(length(cons(N,L))) , Marked_isNatKind(N)>
<Marked_active(cons(X1,X2)) , Marked_cons(active(X1),X2)>
<Marked_active(cons(X1,X2)) , Marked_active(X1)>
<Marked_active(U11(X1,X2)) , Marked_U11(active(X1),X2)>
<Marked_active(U11(X1,X2)) , Marked_active(X1)>
<Marked_active(U12(X)) , Marked_U12(active(X))>
<Marked_active(U12(X)) , Marked_active(X)>
<Marked_active(U21(X1,X2)) , Marked_U21(active(X1),X2)>
<Marked_active(U21(X1,X2)) , Marked_active(X1)>
<Marked_active(U22(X)) , Marked_U22(active(X))>
<Marked_active(U22(X)) , Marked_active(X)>
<Marked_active(U31(X1,X2)) , Marked_U31(active(X1),X2)>
<Marked_active(U31(X1,X2)) , Marked_active(X1)>
<Marked_active(U32(X)) , Marked_U32(active(X))>
<Marked_active(U32(X)) , Marked_active(X)>
<Marked_active(U41(X1,X2,X3)) , Marked_U41(active(X1),X2,X3)>
<Marked_active(U41(X1,X2,X3)) , Marked_active(X1)>
<Marked_active(U42(X1,X2)) , Marked_U42(active(X1),X2)>
<Marked_active(U42(X1,X2)) , Marked_active(X1)>
<Marked_active(U43(X)) , Marked_U43(active(X))>
<Marked_active(U43(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(U52(X1,X2)) , Marked_U52(active(X1),X2)>
<Marked_active(U52(X1,X2)) , Marked_active(X1)>
<Marked_active(U53(X)) , Marked_U53(active(X))>
<Marked_active(U53(X)) , Marked_active(X)>
<Marked_active(U61(X1,X2)) , Marked_U61(active(X1),X2)>
<Marked_active(U61(X1,X2)) , Marked_active(X1)>
<Marked_active(s(X)) , Marked_s(active(X))>
<Marked_active(s(X)) , Marked_active(X)>
<Marked_active(length(X)) , Marked_length(active(X))>
<Marked_active(length(X)) , Marked_active(X)>
<Marked_active(and(X1,X2)) , Marked_and(active(X1),X2)>
<Marked_active(and(X1,X2)) , Marked_active(X1)>
<Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
<Marked_U11(mark(X1),X2) , Marked_U11(X1,X2)>
<Marked_U12(mark(X)) , Marked_U12(X)>
<Marked_U21(mark(X1),X2) , Marked_U21(X1,X2)>
<Marked_U22(mark(X)) , Marked_U22(X)>
<Marked_U31(mark(X1),X2) , Marked_U31(X1,X2)>
<Marked_U32(mark(X)) , Marked_U32(X)>
<Marked_U41(mark(X1),X2,X3) , Marked_U41(X1,X2,X3)>
<Marked_U42(mark(X1),X2) , Marked_U42(X1,X2)>
<Marked_U43(mark(X)) , Marked_U43(X)>
<Marked_U51(mark(X1),X2,X3) , Marked_U51(X1,X2,X3)>
<Marked_U52(mark(X1),X2) , Marked_U52(X1,X2)>
<Marked_U53(mark(X)) , Marked_U53(X)>
<Marked_U61(mark(X1),X2) , Marked_U61(X1,X2)>
<Marked_s(mark(X)) , Marked_s(X)>
<Marked_length(mark(X)) , Marked_length(X)>
<Marked_and(mark(X1),X2) , Marked_and(X1,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(U11(X1,X2)) , Marked_U11(proper(X1),proper(X2))>
<Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U12(X)) , Marked_U12(proper(X))>
<Marked_proper(U12(X)) , Marked_proper(X)>
<Marked_proper(isNatList(X)) , Marked_isNatList(proper(X))>
<Marked_proper(isNatList(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(U22(X)) , Marked_U22(proper(X))>
<Marked_proper(U22(X)) , Marked_proper(X)>
<Marked_proper(isNat(X)) , Marked_isNat(proper(X))>
<Marked_proper(isNat(X)) , Marked_proper(X)>
<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(U32(X)) , Marked_U32(proper(X))>
<Marked_proper(U32(X)) , Marked_proper(X)>
<Marked_proper(U41(X1,X2,X3)) , Marked_U41(proper(X1),proper(X2),proper(X3))>
<Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
<Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
<Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
<Marked_proper(U42(X1,X2)) , Marked_U42(proper(X1),proper(X2))>
<Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U43(X)) , Marked_U43(proper(X))>
<Marked_proper(U43(X)) , Marked_proper(X)>
<Marked_proper(isNatIList(X)) , Marked_isNatIList(proper(X))>
<Marked_proper(isNatIList(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(U52(X1,X2)) , Marked_U52(proper(X1),proper(X2))>
<Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U53(X)) , Marked_U53(proper(X))>
<Marked_proper(U53(X)) , Marked_proper(X)>
<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(s(X)) , Marked_s(proper(X))>
<Marked_proper(s(X)) , Marked_proper(X)>
<Marked_proper(length(X)) , Marked_length(proper(X))>
<Marked_proper(length(X)) , Marked_proper(X)>
<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(isNatIListKind(X)) , Marked_isNatIListKind(proper(X))>
<Marked_proper(isNatIListKind(X)) , Marked_proper(X)>
<Marked_proper(isNatKind(X)) , Marked_isNatKind(proper(X))>
<Marked_proper(isNatKind(X)) , Marked_proper(X)>
<Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)>
<Marked_U11(ok(X1),ok(X2)) , Marked_U11(X1,X2)>
<Marked_U12(ok(X)) , Marked_U12(X)>
<Marked_isNatList(ok(X)) , Marked_isNatList(X)>
<Marked_U21(ok(X1),ok(X2)) , Marked_U21(X1,X2)>
<Marked_U22(ok(X)) , Marked_U22(X)>
<Marked_isNat(ok(X)) , Marked_isNat(X)>
<Marked_U31(ok(X1),ok(X2)) , Marked_U31(X1,X2)>
<Marked_U32(ok(X)) , Marked_U32(X)>
<Marked_U41(ok(X1),ok(X2),ok(X3)) , Marked_U41(X1,X2,X3)>
<Marked_U42(ok(X1),ok(X2)) , Marked_U42(X1,X2)>
<Marked_U43(ok(X)) , Marked_U43(X)>
<Marked_isNatIList(ok(X)) , Marked_isNatIList(X)>
<Marked_U51(ok(X1),ok(X2),ok(X3)) , Marked_U51(X1,X2,X3)>
<Marked_U52(ok(X1),ok(X2)) , Marked_U52(X1,X2)>
<Marked_U53(ok(X)) , Marked_U53(X)>
<Marked_U61(ok(X1),ok(X2)) , Marked_U61(X1,X2)>
<Marked_s(ok(X)) , Marked_s(X)>
<Marked_length(ok(X)) , Marked_length(X)>
<Marked_and(ok(X1),ok(X2)) , Marked_and(X1,X2)>
<Marked_isNatIListKind(ok(X)) , Marked_isNatIListKind(X)>
<Marked_isNatKind(ok(X)) , Marked_isNatKind(X)>
<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 25 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(isNatKind(X)) , Marked_proper(X)> 
      --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIListKind(X)) , Marked_proper(X)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIListKind(X)) , Marked_proper(X)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatIListKind(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatIListKind(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(length(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(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(U53(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <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(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <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(isNat(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <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(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <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(X1)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatIListKind(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(length(X)) , Marked_proper(X)>
  <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(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(U53(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <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(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <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(isNat(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <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(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <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(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIListKind(X)) , Marked_proper(X)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIListKind(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(length(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <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(U53(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <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(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <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(isNat(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <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(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <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(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatIListKind(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(length(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(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(U53(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <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(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <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(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <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(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <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(X1)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatIListKind(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(length(X)) , Marked_proper(X)>
  <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(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(U53(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <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(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <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(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <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(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <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(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIListKind(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U53(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatIListKind(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatIListKind(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatIListKind(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(length(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(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(U53(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <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(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <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(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <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(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <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(X2)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatIListKind(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(length(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(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(U53(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <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(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <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(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <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(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <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(X1)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatIListKind(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(length(X)) , Marked_proper(X)>
  <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(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(U53(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <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(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <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(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <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(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <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(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIListKind(X)) , Marked_proper(X)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIListKind(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U43(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatIListKind(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatIListKind(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatIListKind(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatIListKind(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatIListKind(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIListKind(X)) , Marked_proper(X)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U32(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatIListKind(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(length(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(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(U53(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <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(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <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(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <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(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <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(X1)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatIListKind(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(length(X)) , Marked_proper(X)>
  <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(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(U53(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <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(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <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(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <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(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <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(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIListKind(X)) , Marked_proper(X)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIListKind(X)) , Marked_proper(X)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatIListKind(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(length(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(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(U53(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <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(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <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(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <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(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <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(X1)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatIListKind(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(length(X)) , Marked_proper(X)>
  <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(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(U53(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <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(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <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(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <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(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <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(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIListKind(X)) , Marked_proper(X)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIListKind(X)) , Marked_proper(X)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatIListKind(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatIListKind(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U53(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatIListKind(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(length(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(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(U53(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <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(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <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(isNat(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <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(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <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(X1)> 
     --> <Marked_proper(isNatKind(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatIListKind(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(length(X)) , Marked_proper(X)>
  <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(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(U53(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X1,X2)) , Marked_proper(X1)>
  <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(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U43(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U32(X)) , Marked_proper(X)>
  <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(isNat(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X)) , Marked_proper(X)>
  <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(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <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_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(length(X)) , Marked_active(X)>
  <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(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U53(X)) , Marked_active(X)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X1,X2)) , Marked_active(X1)>
  <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(U43(X)) , Marked_active(X)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X1,X2)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U32(X)) , Marked_active(X)>
  <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(U22(X)) , Marked_active(X)>
  <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(U12(X)) , Marked_active(X)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(U53(X)) , Marked_active(X)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X1,X2)) , Marked_active(X1)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(U43(X)) , Marked_active(X)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X1,X2)) , Marked_active(X1)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(U32(X)) , Marked_active(X)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(U22(X)) , Marked_active(X)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(U12(X)) , Marked_active(X)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2)) , Marked_active(X1)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U53(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X1,X2)) , Marked_active(X1)>
  <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(U43(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U32(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U22(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U12(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <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(length(X)) , Marked_active(X)>
  <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(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U53(X)) , Marked_active(X)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X1,X2)) , Marked_active(X1)>
  <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(U43(X)) , Marked_active(X)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U32(X)) , Marked_active(X)>
  <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(U22(X)) , Marked_active(X)>
  <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(U12(X)) , Marked_active(X)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U53(X)) , Marked_active(X)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(U53(X)) , Marked_active(X)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(U53(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U53(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(U53(X)) , Marked_active(X)> 
     --> <Marked_active(U53(X)) , Marked_active(X)>
  <Marked_active(U53(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X1,X2)) , Marked_active(X1)>
  <Marked_active(U53(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U53(X)) , Marked_active(X)> 
     --> <Marked_active(U43(X)) , Marked_active(X)>
  <Marked_active(U53(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X1,X2)) , Marked_active(X1)>
  <Marked_active(U53(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U53(X)) , Marked_active(X)> 
     --> <Marked_active(U32(X)) , Marked_active(X)>
  <Marked_active(U53(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(U53(X)) , Marked_active(X)> 
     --> <Marked_active(U22(X)) , Marked_active(X)>
  <Marked_active(U53(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(U53(X)) , Marked_active(X)> 
     --> <Marked_active(U12(X)) , Marked_active(X)>
  <Marked_active(U53(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2)) , Marked_active(X1)>
  <Marked_active(U53(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(U52(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U52(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U53(X)) , Marked_active(X)>
  <Marked_active(U52(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U52(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U43(X)) , Marked_active(X)>
  <Marked_active(U52(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U52(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U32(X)) , Marked_active(X)>
  <Marked_active(U52(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X)) , Marked_active(X)>
  <Marked_active(U52(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U12(X)) , Marked_active(X)>
  <Marked_active(U52(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <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(length(X)) , Marked_active(X)>
  <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(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U53(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U52(X1,X2)) , Marked_active(X1)>
  <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(U43(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U42(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U32(X)) , Marked_active(X)>
  <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(U22(X)) , Marked_active(X)>
  <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(U12(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U43(X)) , Marked_active(X)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(U43(X)) , Marked_active(X)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(U43(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U43(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(U43(X)) , Marked_active(X)> 
     --> <Marked_active(U53(X)) , Marked_active(X)>
  <Marked_active(U43(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X1,X2)) , Marked_active(X1)>
  <Marked_active(U43(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U43(X)) , Marked_active(X)> 
     --> <Marked_active(U43(X)) , Marked_active(X)>
  <Marked_active(U43(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X1,X2)) , Marked_active(X1)>
  <Marked_active(U43(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U43(X)) , Marked_active(X)> 
     --> <Marked_active(U32(X)) , Marked_active(X)>
  <Marked_active(U43(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(U43(X)) , Marked_active(X)> 
     --> <Marked_active(U22(X)) , Marked_active(X)>
  <Marked_active(U43(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(U43(X)) , Marked_active(X)> 
     --> <Marked_active(U12(X)) , Marked_active(X)>
  <Marked_active(U43(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2)) , Marked_active(X1)>
  <Marked_active(U43(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(U42(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U42(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U53(X)) , Marked_active(X)>
  <Marked_active(U42(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U42(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U43(X)) , Marked_active(X)>
  <Marked_active(U42(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U42(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U32(X)) , Marked_active(X)>
  <Marked_active(U42(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X)) , Marked_active(X)>
  <Marked_active(U42(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U12(X)) , Marked_active(X)>
  <Marked_active(U42(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U53(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U52(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U43(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U42(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U32(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U22(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U12(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U32(X)) , Marked_active(X)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(U32(X)) , Marked_active(X)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(U32(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U32(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(U32(X)) , Marked_active(X)> 
     --> <Marked_active(U53(X)) , Marked_active(X)>
  <Marked_active(U32(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X1,X2)) , Marked_active(X1)>
  <Marked_active(U32(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U32(X)) , Marked_active(X)> 
     --> <Marked_active(U43(X)) , Marked_active(X)>
  <Marked_active(U32(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X1,X2)) , Marked_active(X1)>
  <Marked_active(U32(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U32(X)) , Marked_active(X)> 
     --> <Marked_active(U32(X)) , Marked_active(X)>
  <Marked_active(U32(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(U32(X)) , Marked_active(X)> 
     --> <Marked_active(U22(X)) , Marked_active(X)>
  <Marked_active(U32(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(U32(X)) , Marked_active(X)> 
     --> <Marked_active(U12(X)) , Marked_active(X)>
  <Marked_active(U32(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2)) , Marked_active(X1)>
  <Marked_active(U32(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <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(length(X)) , Marked_active(X)>
  <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(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U53(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X1,X2)) , Marked_active(X1)>
  <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(U43(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U32(X)) , Marked_active(X)>
  <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(U22(X)) , Marked_active(X)>
  <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(U12(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X)) , Marked_active(X)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X)) , Marked_active(X)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(U22(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U22(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X)) , Marked_active(X)> 
     --> <Marked_active(U53(X)) , Marked_active(X)>
  <Marked_active(U22(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U22(X)) , Marked_active(X)> 
     --> <Marked_active(U43(X)) , Marked_active(X)>
  <Marked_active(U22(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U22(X)) , Marked_active(X)> 
     --> <Marked_active(U32(X)) , Marked_active(X)>
  <Marked_active(U22(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X)) , Marked_active(X)> 
     --> <Marked_active(U22(X)) , Marked_active(X)>
  <Marked_active(U22(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X)) , Marked_active(X)> 
     --> <Marked_active(U12(X)) , Marked_active(X)>
  <Marked_active(U22(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <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(length(X)) , Marked_active(X)>
  <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(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U53(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X1,X2)) , Marked_active(X1)>
  <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(U43(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U32(X)) , Marked_active(X)>
  <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(U22(X)) , Marked_active(X)>
  <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(U12(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X)) , Marked_active(X)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X)) , Marked_active(X)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(U12(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U12(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X)) , Marked_active(X)> 
     --> <Marked_active(U53(X)) , Marked_active(X)>
  <Marked_active(U12(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U12(X)) , Marked_active(X)> 
     --> <Marked_active(U43(X)) , Marked_active(X)>
  <Marked_active(U12(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U12(X)) , Marked_active(X)> 
     --> <Marked_active(U32(X)) , Marked_active(X)>
  <Marked_active(U12(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X)) , Marked_active(X)> 
     --> <Marked_active(U22(X)) , Marked_active(X)>
  <Marked_active(U12(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X)) , Marked_active(X)> 
     --> <Marked_active(U12(X)) , Marked_active(X)>
  <Marked_active(U12(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U53(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U43(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U32(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U12(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <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(length(X)) , Marked_active(X)>
  <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(U61(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U53(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X1,X2)) , Marked_active(X1)>
  <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(U43(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U32(X)) , Marked_active(X)>
  <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(U22(X)) , Marked_active(X)>
  <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(U12(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
}

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

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

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

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

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

{  <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_U11(ok(X1),ok(X2)) , Marked_U11(X1,X2)> 
      --> <Marked_U11(ok(X1),ok(X2)) , Marked_U11(X1,X2)>
  <Marked_U11(ok(X1),ok(X2)) , Marked_U11(X1,X2)> 
     --> <Marked_U11(mark(X1),X2) , Marked_U11(X1,X2)>
  <Marked_U11(mark(X1),X2) , Marked_U11(X1,X2)> 
     --> <Marked_U11(ok(X1),ok(X2)) , Marked_U11(X1,X2)>
  <Marked_U11(mark(X1),X2) , Marked_U11(X1,X2)> 
     --> <Marked_U11(mark(X1),X2) , Marked_U11(X1,X2)>
}

{  <Marked_U12(ok(X)) , Marked_U12(X)> --> <Marked_U12(ok(X)) , Marked_U12(X)>
  <Marked_U12(ok(X)) , Marked_U12(X)> --> <Marked_U12(mark(X)) , Marked_U12(X)>
  <Marked_U12(mark(X)) , Marked_U12(X)> --> <Marked_U12(ok(X)) , Marked_U12(X)>
  <Marked_U12(mark(X)) , Marked_U12(X)> 
     --> <Marked_U12(mark(X)) , Marked_U12(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_U22(ok(X)) , Marked_U22(X)> --> <Marked_U22(ok(X)) , Marked_U22(X)>
  <Marked_U22(ok(X)) , Marked_U22(X)> --> <Marked_U22(mark(X)) , Marked_U22(X)>
  <Marked_U22(mark(X)) , Marked_U22(X)> --> <Marked_U22(ok(X)) , Marked_U22(X)>
  <Marked_U22(mark(X)) , Marked_U22(X)> 
     --> <Marked_U22(mark(X)) , Marked_U22(X)>
}

{  <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_U32(ok(X)) , Marked_U32(X)> --> <Marked_U32(ok(X)) , Marked_U32(X)>
  <Marked_U32(ok(X)) , Marked_U32(X)> --> <Marked_U32(mark(X)) , Marked_U32(X)>
  <Marked_U32(mark(X)) , Marked_U32(X)> --> <Marked_U32(ok(X)) , Marked_U32(X)>
  <Marked_U32(mark(X)) , Marked_U32(X)> 
     --> <Marked_U32(mark(X)) , Marked_U32(X)>
}

{  <Marked_U41(ok(X1),ok(X2),ok(X3)) , Marked_U41(X1,X2,X3)> 
      --> <Marked_U41(ok(X1),ok(X2),ok(X3)) , Marked_U41(X1,X2,X3)>
  <Marked_U41(ok(X1),ok(X2),ok(X3)) , Marked_U41(X1,X2,X3)> 
     --> <Marked_U41(mark(X1),X2,X3) , Marked_U41(X1,X2,X3)>
  <Marked_U41(mark(X1),X2,X3) , Marked_U41(X1,X2,X3)> 
     --> <Marked_U41(ok(X1),ok(X2),ok(X3)) , Marked_U41(X1,X2,X3)>
  <Marked_U41(mark(X1),X2,X3) , Marked_U41(X1,X2,X3)> 
     --> <Marked_U41(mark(X1),X2,X3) , Marked_U41(X1,X2,X3)>
}

{  <Marked_U42(ok(X1),ok(X2)) , Marked_U42(X1,X2)> 
      --> <Marked_U42(ok(X1),ok(X2)) , Marked_U42(X1,X2)>
  <Marked_U42(ok(X1),ok(X2)) , Marked_U42(X1,X2)> 
     --> <Marked_U42(mark(X1),X2) , Marked_U42(X1,X2)>
  <Marked_U42(mark(X1),X2) , Marked_U42(X1,X2)> 
     --> <Marked_U42(ok(X1),ok(X2)) , Marked_U42(X1,X2)>
  <Marked_U42(mark(X1),X2) , Marked_U42(X1,X2)> 
     --> <Marked_U42(mark(X1),X2) , Marked_U42(X1,X2)>
}

{  <Marked_U43(ok(X)) , Marked_U43(X)> --> <Marked_U43(ok(X)) , Marked_U43(X)>
  <Marked_U43(ok(X)) , Marked_U43(X)> --> <Marked_U43(mark(X)) , Marked_U43(X)>
  <Marked_U43(mark(X)) , Marked_U43(X)> --> <Marked_U43(ok(X)) , Marked_U43(X)>
  <Marked_U43(mark(X)) , Marked_U43(X)> 
     --> <Marked_U43(mark(X)) , Marked_U43(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_U52(ok(X1),ok(X2)) , Marked_U52(X1,X2)> 
      --> <Marked_U52(ok(X1),ok(X2)) , Marked_U52(X1,X2)>
  <Marked_U52(ok(X1),ok(X2)) , Marked_U52(X1,X2)> 
     --> <Marked_U52(mark(X1),X2) , Marked_U52(X1,X2)>
  <Marked_U52(mark(X1),X2) , Marked_U52(X1,X2)> 
     --> <Marked_U52(ok(X1),ok(X2)) , Marked_U52(X1,X2)>
  <Marked_U52(mark(X1),X2) , Marked_U52(X1,X2)> 
     --> <Marked_U52(mark(X1),X2) , Marked_U52(X1,X2)>
}

{  <Marked_U53(ok(X)) , Marked_U53(X)> --> <Marked_U53(ok(X)) , Marked_U53(X)>
  <Marked_U53(ok(X)) , Marked_U53(X)> --> <Marked_U53(mark(X)) , Marked_U53(X)>
  <Marked_U53(mark(X)) , Marked_U53(X)> --> <Marked_U53(ok(X)) , Marked_U53(X)>
  <Marked_U53(mark(X)) , Marked_U53(X)> 
     --> <Marked_U53(mark(X)) , Marked_U53(X)>
}

{  <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_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_length(ok(X)) , Marked_length(X)> 
      --> <Marked_length(ok(X)) , Marked_length(X)>
  <Marked_length(ok(X)) , Marked_length(X)> 
     --> <Marked_length(mark(X)) , Marked_length(X)>
  <Marked_length(mark(X)) , Marked_length(X)> 
     --> <Marked_length(ok(X)) , Marked_length(X)>
  <Marked_length(mark(X)) , Marked_length(X)> 
     --> <Marked_length(mark(X)) , Marked_length(X)>
}

{  <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)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  cons(mark(X1),X2) >= mark(cons(X1,X2)) ;
  cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ;
  active(cons(X1,X2)) >= cons(active(X1),X2) ;
  active(zeros) >= mark(cons(0,zeros)) ;
  active(U12(tt)) >= mark(tt) ;
  active(U12(X)) >= U12(active(X)) ;
  active(isNatList(cons(V1,V2))) >= mark(U51(and(isNatKind(V1),
                                              isNatIListKind(V2)),V1,
                                          V2)) ;
  active(isNatList(nil)) >= mark(tt) ;
  active(U11(tt,V1)) >= mark(U12(isNatList(V1))) ;
  active(U11(X1,X2)) >= U11(active(X1),X2) ;
  active(U22(tt)) >= mark(tt) ;
  active(U22(X)) >= U22(active(X)) ;
  active(isNat(0)) >= mark(tt) ;
  active(isNat(s(V1))) >= mark(U21(isNatKind(V1),V1)) ;
  active(isNat(length(V1))) >= mark(U11(isNatIListKind(V1),V1)) ;
  active(U21(tt,V1)) >= mark(U22(isNat(V1))) ;
  active(U21(X1,X2)) >= U21(active(X1),X2) ;
  active(U32(tt)) >= mark(tt) ;
  active(U32(X)) >= U32(active(X)) ;
  active(U31(tt,V)) >= mark(U32(isNatList(V))) ;
  active(U31(X1,X2)) >= U31(active(X1),X2) ;
  active(U42(tt,V2)) >= mark(U43(isNatIList(V2))) ;
  active(U42(X1,X2)) >= U42(active(X1),X2) ;
  active(U41(tt,V1,V2)) >= mark(U42(isNat(V1),V2)) ;
  active(U41(X1,X2,X3)) >= U41(active(X1),X2,X3) ;
  active(U43(tt)) >= mark(tt) ;
  active(U43(X)) >= U43(active(X)) ;
  active(isNatIList(cons(V1,V2))) >= mark(U41(and(isNatKind(V1),
                                               isNatIListKind(V2)),V1,
                                           V2)) ;
  active(isNatIList(zeros)) >= mark(tt) ;
  active(isNatIList(V)) >= mark(U31(isNatIListKind(V),V)) ;
  active(U52(tt,V2)) >= mark(U53(isNatList(V2))) ;
  active(U52(X1,X2)) >= U52(active(X1),X2) ;
  active(U51(tt,V1,V2)) >= mark(U52(isNat(V1),V2)) ;
  active(U51(X1,X2,X3)) >= U51(active(X1),X2,X3) ;
  active(U53(tt)) >= mark(tt) ;
  active(U53(X)) >= U53(active(X)) ;
  active(s(X)) >= s(active(X)) ;
  active(length(cons(N,L))) >= mark(U61(and(and(isNatList(L),isNatIListKind(L)),
                                         and(isNat(N),isNatKind(N))),
                                     L)) ;
  active(length(nil)) >= mark(0) ;
  active(length(X)) >= length(active(X)) ;
  active(U61(tt,L)) >= mark(s(length(L))) ;
  active(U61(X1,X2)) >= U61(active(X1),X2) ;
  active(and(tt,X)) >= mark(X) ;
  active(and(X1,X2)) >= and(active(X1),X2) ;
  active(isNatIListKind(cons(V1,V2))) >= mark(and(isNatKind(V1),
                                               isNatIListKind(V2))) ;
  active(isNatIListKind(zeros)) >= mark(tt) ;
  active(isNatIListKind(nil)) >= mark(tt) ;
  active(isNatKind(0)) >= mark(tt) ;
  active(isNatKind(s(V1))) >= mark(isNatKind(V1)) ;
  active(isNatKind(length(V1))) >= mark(isNatIListKind(V1)) ;
  U12(mark(X)) >= mark(U12(X)) ;
  U12(ok(X)) >= ok(U12(X)) ;
  isNatList(ok(X)) >= ok(isNatList(X)) ;
  U11(mark(X1),X2) >= mark(U11(X1,X2)) ;
  U11(ok(X1),ok(X2)) >= ok(U11(X1,X2)) ;
  U22(mark(X)) >= mark(U22(X)) ;
  U22(ok(X)) >= ok(U22(X)) ;
  isNat(ok(X)) >= ok(isNat(X)) ;
  U21(mark(X1),X2) >= mark(U21(X1,X2)) ;
  U21(ok(X1),ok(X2)) >= ok(U21(X1,X2)) ;
  U32(mark(X)) >= mark(U32(X)) ;
  U32(ok(X)) >= ok(U32(X)) ;
  U31(mark(X1),X2) >= mark(U31(X1,X2)) ;
  U31(ok(X1),ok(X2)) >= ok(U31(X1,X2)) ;
  U42(mark(X1),X2) >= mark(U42(X1,X2)) ;
  U42(ok(X1),ok(X2)) >= ok(U42(X1,X2)) ;
  U41(mark(X1),X2,X3) >= mark(U41(X1,X2,X3)) ;
  U41(ok(X1),ok(X2),ok(X3)) >= ok(U41(X1,X2,X3)) ;
  U43(mark(X)) >= mark(U43(X)) ;
  U43(ok(X)) >= ok(U43(X)) ;
  isNatIList(ok(X)) >= ok(isNatIList(X)) ;
  U52(mark(X1),X2) >= mark(U52(X1,X2)) ;
  U52(ok(X1),ok(X2)) >= ok(U52(X1,X2)) ;
  U51(mark(X1),X2,X3) >= mark(U51(X1,X2,X3)) ;
  U51(ok(X1),ok(X2),ok(X3)) >= ok(U51(X1,X2,X3)) ;
  U53(mark(X)) >= mark(U53(X)) ;
  U53(ok(X)) >= ok(U53(X)) ;
  s(mark(X)) >= mark(s(X)) ;
  s(ok(X)) >= ok(s(X)) ;
  length(mark(X)) >= mark(length(X)) ;
  length(ok(X)) >= ok(length(X)) ;
  U61(mark(X1),X2) >= mark(U61(X1,X2)) ;
  U61(ok(X1),ok(X2)) >= ok(U61(X1,X2)) ;
  and(mark(X1),X2) >= mark(and(X1,X2)) ;
  and(ok(X1),ok(X2)) >= ok(and(X1,X2)) ;
  isNatIListKind(ok(X)) >= ok(isNatIListKind(X)) ;
  isNatKind(ok(X)) >= ok(isNatKind(X)) ;
  proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ;
  proper(0) >= ok(0) ;
  proper(zeros) >= ok(zeros) ;
  proper(U12(X)) >= U12(proper(X)) ;
  proper(isNatList(X)) >= isNatList(proper(X)) ;
  proper(U11(X1,X2)) >= U11(proper(X1),proper(X2)) ;
  proper(tt) >= ok(tt) ;
  proper(U22(X)) >= U22(proper(X)) ;
  proper(isNat(X)) >= isNat(proper(X)) ;
  proper(U21(X1,X2)) >= U21(proper(X1),proper(X2)) ;
  proper(U32(X)) >= U32(proper(X)) ;
  proper(U31(X1,X2)) >= U31(proper(X1),proper(X2)) ;
  proper(U42(X1,X2)) >= U42(proper(X1),proper(X2)) ;
  proper(U41(X1,X2,X3)) >= U41(proper(X1),proper(X2),proper(X3)) ;
  proper(U43(X)) >= U43(proper(X)) ;
  proper(isNatIList(X)) >= isNatIList(proper(X)) ;
  proper(U52(X1,X2)) >= U52(proper(X1),proper(X2)) ;
  proper(U51(X1,X2,X3)) >= U51(proper(X1),proper(X2),proper(X3)) ;
  proper(U53(X)) >= U53(proper(X)) ;
  proper(s(X)) >= s(proper(X)) ;
  proper(length(X)) >= length(proper(X)) ;
  proper(U61(X1,X2)) >= U61(proper(X1),proper(X2)) ;
  proper(and(X1,X2)) >= and(proper(X1),proper(X2)) ;
  proper(isNatIListKind(X)) >= isNatIListKind(proper(X)) ;
  proper(isNatKind(X)) >= isNatKind(proper(X)) ;
  proper(nil) >= ok(nil) ;
  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 (Simple graph)
Found the following constraints:
{
  cons(mark(X1),X2) >= mark(cons(X1,X2)) ;
  cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ;
  active(cons(X1,X2)) >= cons(active(X1),X2) ;
  active(zeros) >= mark(cons(0,zeros)) ;
  active(U12(tt)) >= mark(tt) ;
  active(U12(X)) >= U12(active(X)) ;
  active(isNatList(cons(V1,V2))) >= mark(U51(and(isNatKind(V1),
                                              isNatIListKind(V2)),V1,
                                          V2)) ;
  active(isNatList(nil)) >= mark(tt) ;
  active(U11(tt,V1)) >= mark(U12(isNatList(V1))) ;
  active(U11(X1,X2)) >= U11(active(X1),X2) ;
  active(U22(tt)) >= mark(tt) ;
  active(U22(X)) >= U22(active(X)) ;
  active(isNat(0)) >= mark(tt) ;
  active(isNat(s(V1))) >= mark(U21(isNatKind(V1),V1)) ;
  active(isNat(length(V1))) >= mark(U11(isNatIListKind(V1),V1)) ;
  active(U21(tt,V1)) >= mark(U22(isNat(V1))) ;
  active(U21(X1,X2)) >= U21(active(X1),X2) ;
  active(U32(tt)) >= mark(tt) ;
  active(U32(X)) >= U32(active(X)) ;
  active(U31(tt,V)) >= mark(U32(isNatList(V))) ;
  active(U31(X1,X2)) >= U31(active(X1),X2) ;
  active(U42(tt,V2)) >= mark(U43(isNatIList(V2))) ;
  active(U42(X1,X2)) >= U42(active(X1),X2) ;
  active(U41(tt,V1,V2)) >= mark(U42(isNat(V1),V2)) ;
  active(U41(X1,X2,X3)) >= U41(active(X1),X2,X3) ;
  active(U43(tt)) >= mark(tt) ;
  active(U43(X)) >= U43(active(X)) ;
  active(isNatIList(cons(V1,V2))) >= mark(U41(and(isNatKind(V1),
                                               isNatIListKind(V2)),V1,
                                           V2)) ;
  active(isNatIList(zeros)) >= mark(tt) ;
  active(isNatIList(V)) >= mark(U31(isNatIListKind(V),V)) ;
  active(U52(tt,V2)) >= mark(U53(isNatList(V2))) ;
  active(U52(X1,X2)) >= U52(active(X1),X2) ;
  active(U51(tt,V1,V2)) >= mark(U52(isNat(V1),V2)) ;
  active(U51(X1,X2,X3)) >= U51(active(X1),X2,X3) ;
  active(U53(tt)) >= mark(tt) ;
  active(U53(X)) >= U53(active(X)) ;
  active(s(X)) >= s(active(X)) ;
  active(length(cons(N,L))) >= mark(U61(and(and(isNatList(L),isNatIListKind(L)),
                                         and(isNat(N),isNatKind(N))),
                                     L)) ;
  active(length(nil)) >= mark(0) ;
  active(length(X)) >= length(active(X)) ;
  active(U61(tt,L)) >= mark(s(length(L))) ;
  active(U61(X1,X2)) >= U61(active(X1),X2) ;
  active(and(tt,X)) >= mark(X) ;
  active(and(X1,X2)) >= and(active(X1),X2) ;
  active(isNatIListKind(cons(V1,V2))) >= mark(and(isNatKind(V1),
                                               isNatIListKind(V2))) ;
  active(isNatIListKind(zeros)) >= mark(tt) ;
  active(isNatIListKind(nil)) >= mark(tt) ;
  active(isNatKind(0)) >= mark(tt) ;
  active(isNatKind(s(V1))) >= mark(isNatKind(V1)) ;
  active(isNatKind(length(V1))) >= mark(isNatIListKind(V1)) ;
  U12(mark(X)) >= mark(U12(X)) ;
  U12(ok(X)) >= ok(U12(X)) ;
  isNatList(ok(X)) >= ok(isNatList(X)) ;
  U11(mark(X1),X2) >= mark(U11(X1,X2)) ;
  U11(ok(X1),ok(X2)) >= ok(U11(X1,X2)) ;
  U22(mark(X)) >= mark(U22(X)) ;
  U22(ok(X)) >= ok(U22(X)) ;
  isNat(ok(X)) >= ok(isNat(X)) ;
  U21(mark(X1),X2) >= mark(U21(X1,X2)) ;
  U21(ok(X1),ok(X2)) >= ok(U21(X1,X2)) ;
  U32(mark(X)) >= mark(U32(X)) ;
  U32(ok(X)) >= ok(U32(X)) ;
  U31(mark(X1),X2) >= mark(U31(X1,X2)) ;
  U31(ok(X1),ok(X2)) >= ok(U31(X1,X2)) ;
  U42(mark(X1),X2) >= mark(U42(X1,X2)) ;
  U42(ok(X1),ok(X2)) >= ok(U42(X1,X2)) ;
  U41(mark(X1),X2,X3) >= mark(U41(X1,X2,X3)) ;
  U41(ok(X1),ok(X2),ok(X3)) >= ok(U41(X1,X2,X3)) ;
  U43(mark(X)) >= mark(U43(X)) ;
  U43(ok(X)) >= ok(U43(X)) ;
  isNatIList(ok(X)) >= ok(isNatIList(X)) ;
  U52(mark(X1),X2) >= mark(U52(X1,X2)) ;
  U52(ok(X1),ok(X2)) >= ok(U52(X1,X2)) ;
  U51(mark(X1),X2,X3) >= mark(U51(X1,X2,X3)) ;
  U51(ok(X1),ok(X2),ok(X3)) >= ok(U51(X1,X2,X3)) ;
  U53(mark(X)) >= mark(U53(X)) ;
  U53(ok(X)) >= ok(U53(X)) ;
  s(mark(X)) >= mark(s(X)) ;
  s(ok(X)) >= ok(s(X)) ;
  length(mark(X)) >= mark(length(X)) ;
  length(ok(X)) >= ok(length(X)) ;
  U61(mark(X1),X2) >= mark(U61(X1,X2)) ;
  U61(ok(X1),ok(X2)) >= ok(U61(X1,X2)) ;
  and(mark(X1),X2) >= mark(and(X1,X2)) ;
  and(ok(X1),ok(X2)) >= ok(and(X1,X2)) ;
  isNatIListKind(ok(X)) >= ok(isNatIListKind(X)) ;
  isNatKind(ok(X)) >= ok(isNatKind(X)) ;
  proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ;
  proper(0) >= ok(0) ;
  proper(zeros) >= ok(zeros) ;
  proper(U12(X)) >= U12(proper(X)) ;
  proper(isNatList(X)) >= isNatList(proper(X)) ;
  proper(U11(X1,X2)) >= U11(proper(X1),proper(X2)) ;
  proper(tt) >= ok(tt) ;
  proper(U22(X)) >= U22(proper(X)) ;
  proper(isNat(X)) >= isNat(proper(X)) ;
  proper(U21(X1,X2)) >= U21(proper(X1),proper(X2)) ;
  proper(U32(X)) >= U32(proper(X)) ;
  proper(U31(X1,X2)) >= U31(proper(X1),proper(X2)) ;
  proper(U42(X1,X2)) >= U42(proper(X1),proper(X2)) ;
  proper(U41(X1,X2,X3)) >= U41(proper(X1),proper(X2),proper(X3)) ;
  proper(U43(X)) >= U43(proper(X)) ;
  proper(isNatIList(X)) >= isNatIList(proper(X)) ;
  proper(U52(X1,X2)) >= U52(proper(X1),proper(X2)) ;
  proper(U51(X1,X2,X3)) >= U51(proper(X1),proper(X2),proper(X3)) ;
  proper(U53(X)) >= U53(proper(X)) ;
  proper(s(X)) >= s(proper(X)) ;
  proper(length(X)) >= length(proper(X)) ;
  proper(U61(X1,X2)) >= U61(proper(X1),proper(X2)) ;
  proper(and(X1,X2)) >= and(proper(X1),proper(X2)) ;
  proper(isNatIListKind(X)) >= isNatIListKind(proper(X)) ;
  proper(isNatKind(X)) >= isNatKind(proper(X)) ;
  proper(nil) >= ok(nil) ;
  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)) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  cons(mark(X1),X2) >= mark(cons(X1,X2)) ;
  cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ;
  active(cons(X1,X2)) >= cons(active(X1),X2) ;
  active(zeros) >= mark(cons(0,zeros)) ;
  active(U12(tt)) >= mark(tt) ;
  active(U12(X)) >= U12(active(X)) ;
  active(isNatList(cons(V1,V2))) >= mark(U51(and(isNatKind(V1),
                                              isNatIListKind(V2)),V1,
                                          V2)) ;
  active(isNatList(nil)) >= mark(tt) ;
  active(U11(tt,V1)) >= mark(U12(isNatList(V1))) ;
  active(U11(X1,X2)) >= U11(active(X1),X2) ;
  active(U22(tt)) >= mark(tt) ;
  active(U22(X)) >= U22(active(X)) ;
  active(isNat(0)) >= mark(tt) ;
  active(isNat(s(V1))) >= mark(U21(isNatKind(V1),V1)) ;
  active(isNat(length(V1))) >= mark(U11(isNatIListKind(V1),V1)) ;
  active(U21(tt,V1)) >= mark(U22(isNat(V1))) ;
  active(U21(X1,X2)) >= U21(active(X1),X2) ;
  active(U32(tt)) >= mark(tt) ;
  active(U32(X)) >= U32(active(X)) ;
  active(U31(tt,V)) >= mark(U32(isNatList(V))) ;
  active(U31(X1,X2)) >= U31(active(X1),X2) ;
  active(U42(tt,V2)) >= mark(U43(isNatIList(V2))) ;
  active(U42(X1,X2)) >= U42(active(X1),X2) ;
  active(U41(tt,V1,V2)) >= mark(U42(isNat(V1),V2)) ;
  active(U41(X1,X2,X3)) >= U41(active(X1),X2,X3) ;
  active(U43(tt)) >= mark(tt) ;
  active(U43(X)) >= U43(active(X)) ;
  active(isNatIList(cons(V1,V2))) >= mark(U41(and(isNatKind(V1),
                                               isNatIListKind(V2)),V1,
                                           V2)) ;
  active(isNatIList(zeros)) >= mark(tt) ;
  active(isNatIList(V)) >= mark(U31(isNatIListKind(V),V)) ;
  active(U52(tt,V2)) >= mark(U53(isNatList(V2))) ;
  active(U52(X1,X2)) >= U52(active(X1),X2) ;
  active(U51(tt,V1,V2)) >= mark(U52(isNat(V1),V2)) ;
  active(U51(X1,X2,X3)) >= U51(active(X1),X2,X3) ;
  active(U53(tt)) >= mark(tt) ;
  active(U53(X)) >= U53(active(X)) ;
  active(s(X)) >= s(active(X)) ;
  active(length(cons(N,L))) >= mark(U61(and(and(isNatList(L),isNatIListKind(L)),
                                         and(isNat(N),isNatKind(N))),
                                     L)) ;
  active(length(nil)) >= mark(0) ;
  active(length(X)) >= length(active(X)) ;
  active(U61(tt,L)) >= mark(s(length(L))) ;
  active(U61(X1,X2)) >= U61(active(X1),X2) ;
  active(and(tt,X)) >= mark(X) ;
  active(and(X1,X2)) >= and(active(X1),X2) ;
  active(isNatIListKind(cons(V1,V2))) >= mark(and(isNatKind(V1),
                                               isNatIListKind(V2))) ;
  active(isNatIListKind(zeros)) >= mark(tt) ;
  active(isNatIListKind(nil)) >= mark(tt) ;
  active(isNatKind(0)) >= mark(tt) ;
  active(isNatKind(s(V1))) >= mark(isNatKind(V1)) ;
  active(isNatKind(length(V1))) >= mark(isNatIListKind(V1)) ;
  U12(mark(X)) >= mark(U12(X)) ;
  U12(ok(X)) >= ok(U12(X)) ;
  isNatList(ok(X)) >= ok(isNatList(X)) ;
  U11(mark(X1),X2) >= mark(U11(X1,X2)) ;
  U11(ok(X1),ok(X2)) >= ok(U11(X1,X2)) ;
  U22(mark(X)) >= mark(U22(X)) ;
  U22(ok(X)) >= ok(U22(X)) ;
  isNat(ok(X)) >= ok(isNat(X)) ;
  U21(mark(X1),X2) >= mark(U21(X1,X2)) ;
  U21(ok(X1),ok(X2)) >= ok(U21(X1,X2)) ;
  U32(mark(X)) >= mark(U32(X)) ;
  U32(ok(X)) >= ok(U32(X)) ;
  U31(mark(X1),X2) >= mark(U31(X1,X2)) ;
  U31(ok(X1),ok(X2)) >= ok(U31(X1,X2)) ;
  U42(mark(X1),X2) >= mark(U42(X1,X2)) ;
  U42(ok(X1),ok(X2)) >= ok(U42(X1,X2)) ;
  U41(mark(X1),X2,X3) >= mark(U41(X1,X2,X3)) ;
  U41(ok(X1),ok(X2),ok(X3)) >= ok(U41(X1,X2,X3)) ;
  U43(mark(X)) >= mark(U43(X)) ;
  U43(ok(X)) >= ok(U43(X)) ;
  isNatIList(ok(X)) >= ok(isNatIList(X)) ;
  U52(mark(X1),X2) >= mark(U52(X1,X2)) ;
  U52(ok(X1),ok(X2)) >= ok(U52(X1,X2)) ;
  U51(mark(X1),X2,X3) >= mark(U51(X1,X2,X3)) ;
  U51(ok(X1),ok(X2),ok(X3)) >= ok(U51(X1,X2,X3)) ;
  U53(mark(X)) >= mark(U53(X)) ;
  U53(ok(X)) >= ok(U53(X)) ;
  s(mark(X)) >= mark(s(X)) ;
  s(ok(X)) >= ok(s(X)) ;
  length(mark(X)) >= mark(length(X)) ;
  length(ok(X)) >= ok(length(X)) ;
  U61(mark(X1),X2) >= mark(U61(X1,X2)) ;
  U61(ok(X1),ok(X2)) >= ok(U61(X1,X2)) ;
  and(mark(X1),X2) >= mark(and(X1,X2)) ;
  and(ok(X1),ok(X2)) >= ok(and(X1,X2)) ;
  isNatIListKind(ok(X)) >= ok(isNatIListKind(X)) ;
  isNatKind(ok(X)) >= ok(isNatKind(X)) ;
  proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ;
  proper(0) >= ok(0) ;
  proper(zeros) >= ok(zeros) ;
  proper(U12(X)) >= U12(proper(X)) ;
  proper(isNatList(X)) >= isNatList(proper(X)) ;
  proper(U11(X1,X2)) >= U11(proper(X1),proper(X2)) ;
  proper(tt) >= ok(tt) ;
  proper(U22(X)) >= U22(proper(X)) ;
  proper(isNat(X)) >= isNat(proper(X)) ;
  proper(U21(X1,X2)) >= U21(proper(X1),proper(X2)) ;
  proper(U32(X)) >= U32(proper(X)) ;
  proper(U31(X1,X2)) >= U31(proper(X1),proper(X2)) ;
  proper(U42(X1,X2)) >= U42(proper(X1),proper(X2)) ;
  proper(U41(X1,X2,X3)) >= U41(proper(X1),proper(X2),proper(X3)) ;
  proper(U43(X)) >= U43(proper(X)) ;
  proper(isNatIList(X)) >= isNatIList(proper(X)) ;
  proper(U52(X1,X2)) >= U52(proper(X1),proper(X2)) ;
  proper(U51(X1,X2,X3)) >= U51(proper(X1),proper(X2),proper(X3)) ;
  proper(U53(X)) >= U53(proper(X)) ;
  proper(s(X)) >= s(proper(X)) ;
  proper(length(X)) >= length(proper(X)) ;
  proper(U61(X1,X2)) >= U61(proper(X1),proper(X2)) ;
  proper(and(X1,X2)) >= and(proper(X1),proper(X2)) ;
  proper(isNatIListKind(X)) >= isNatIListKind(proper(X)) ;
  proper(isNatKind(X)) >= isNatKind(proper(X)) ;
  proper(nil) >= ok(nil) ;
  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:{ 
 } 
=== 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 178.245273 seconds (real time)
Cime Exit Status: 0