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

TRS termination of:
[1] active(and(tt,T)) -> mark(T)
[2] active(isNatIList(IL)) -> mark(isNatList(IL))
[3] active(isNat(0)) -> mark(tt)
[4] active(isNat(s(N))) -> mark(isNat(N))
[5] active(isNat(length(L))) -> mark(isNatList(L))
[6] active(isNatIList(zeros)) -> mark(tt)
[7] active(isNatIList(cons(N,IL))) -> mark(and(isNat(N),isNatIList(IL)))
[8] active(isNatList(nil)) -> mark(tt)
[9] active(isNatList(cons(N,L))) -> mark(and(isNat(N),isNatList(L)))
[10] active(isNatList(take(N,IL))) -> mark(and(isNat(N),isNatIList(IL)))
[11] active(zeros) -> mark(cons(0,zeros))
[12] active(take(0,IL)) -> mark(uTake1(isNatIList(IL)))
[13] active(uTake1(tt)) -> mark(nil)
[14] active(take(s(M),cons(N,IL))) ->
 mark(uTake2(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL))
[15] active(uTake2(tt,M,N,IL)) -> mark(cons(N,take(M,IL)))
[16] active(length(cons(N,L))) -> mark(uLength(and(isNat(N),isNatList(L)),L))
[17] active(uLength(tt,L)) -> mark(s(length(L)))
[18] active(and(X1,X2)) -> and(active(X1),X2)
[19] active(and(X1,X2)) -> and(X1,active(X2))
[20] active(s(X)) -> s(active(X))
[21] active(length(X)) -> length(active(X))
[22] active(cons(X1,X2)) -> cons(active(X1),X2)
[23] active(take(X1,X2)) -> take(active(X1),X2)
[24] active(take(X1,X2)) -> take(X1,active(X2))
[25] active(uTake1(X)) -> uTake1(active(X))
[26] active(uTake2(X1,X2,X3,X4)) -> uTake2(active(X1),X2,X3,X4)
[27] active(uLength(X1,X2)) -> uLength(active(X1),X2)
[28] and(mark(X1),X2) -> mark(and(X1,X2))
[29] and(X1,mark(X2)) -> mark(and(X1,X2))
[30] s(mark(X)) -> mark(s(X))
[31] length(mark(X)) -> mark(length(X))
[32] cons(mark(X1),X2) -> mark(cons(X1,X2))
[33] take(mark(X1),X2) -> mark(take(X1,X2))
[34] take(X1,mark(X2)) -> mark(take(X1,X2))
[35] uTake1(mark(X)) -> mark(uTake1(X))
[36] uTake2(mark(X1),X2,X3,X4) -> mark(uTake2(X1,X2,X3,X4))
[37] uLength(mark(X1),X2) -> mark(uLength(X1,X2))
[38] proper(and(X1,X2)) -> and(proper(X1),proper(X2))
[39] proper(tt) -> ok(tt)
[40] proper(isNatIList(X)) -> isNatIList(proper(X))
[41] proper(isNatList(X)) -> isNatList(proper(X))
[42] proper(isNat(X)) -> isNat(proper(X))
[43] proper(0) -> ok(0)
[44] proper(s(X)) -> s(proper(X))
[45] proper(length(X)) -> length(proper(X))
[46] proper(zeros) -> ok(zeros)
[47] proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
[48] proper(nil) -> ok(nil)
[49] proper(take(X1,X2)) -> take(proper(X1),proper(X2))
[50] proper(uTake1(X)) -> uTake1(proper(X))
[51] proper(uTake2(X1,X2,X3,X4)) ->
 uTake2(proper(X1),proper(X2),proper(X3),proper(X4))
[52] proper(uLength(X1,X2)) -> uLength(proper(X1),proper(X2))
[53] and(ok(X1),ok(X2)) -> ok(and(X1,X2))
[54] isNatIList(ok(X)) -> ok(isNatIList(X))
[55] isNatList(ok(X)) -> ok(isNatList(X))
[56] isNat(ok(X)) -> ok(isNat(X))
[57] s(ok(X)) -> ok(s(X))
[58] length(ok(X)) -> ok(length(X))
[59] cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
[60] take(ok(X1),ok(X2)) -> ok(take(X1,X2))
[61] uTake1(ok(X)) -> ok(uTake1(X))
[62] uTake2(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(uTake2(X1,X2,X3,X4))
[63] uLength(ok(X1),ok(X2)) -> ok(uLength(X1,X2))
[64] top(mark(X)) -> top(proper(X))
[65] top(ok(X)) -> top(active(X))


Sub problem: 
guided: 

DP termination of:
<Marked_active(isNatIList(IL)) , Marked_isNatList(IL)>
<Marked_active(isNat(s(N))) , Marked_isNat(N)>
<Marked_active(isNat(length(L))) , Marked_isNatList(L)>
<Marked_active(isNatIList(cons(N,IL))) , Marked_and(isNat(N),isNatIList(IL))>
<Marked_active(isNatIList(cons(N,IL))) , Marked_isNat(N)>
<Marked_active(isNatIList(cons(N,IL))) , Marked_isNatIList(IL)>
<Marked_active(isNatList(cons(N,L))) , Marked_and(isNat(N),isNatList(L))>
<Marked_active(isNatList(cons(N,L))) , Marked_isNat(N)>
<Marked_active(isNatList(cons(N,L))) , Marked_isNatList(L)>
<Marked_active(isNatList(take(N,IL))) , Marked_and(isNat(N),isNatIList(IL))>
<Marked_active(isNatList(take(N,IL))) , Marked_isNat(N)>
<Marked_active(isNatList(take(N,IL))) , Marked_isNatIList(IL)>
<Marked_active(zeros) , Marked_cons(0,zeros)>
<Marked_active(take(0,IL)) , Marked_uTake1(isNatIList(IL))>
<Marked_active(take(0,IL)) , Marked_isNatIList(IL)>
<Marked_active(take(s(M),cons(N,IL))) , Marked_uTake2(and(isNat(M),
                                                       and(isNat(N),
                                                        isNatIList(IL))),
                                         M,N,IL)>
<Marked_active(take(s(M),cons(N,IL))) , Marked_and(isNat(M),
                                         and(isNat(N),isNatIList(IL)))>
<Marked_active(take(s(M),cons(N,IL))) , Marked_isNat(M)>
<Marked_active(take(s(M),cons(N,IL))) , Marked_and(isNat(N),isNatIList(IL))>
<Marked_active(take(s(M),cons(N,IL))) , Marked_isNat(N)>
<Marked_active(take(s(M),cons(N,IL))) , Marked_isNatIList(IL)>
<Marked_active(uTake2(tt,M,N,IL)) , Marked_cons(N,take(M,IL))>
<Marked_active(uTake2(tt,M,N,IL)) , Marked_take(M,IL)>
<Marked_active(length(cons(N,L))) , Marked_uLength(and(isNat(N),isNatList(L)),
                                     L)>
<Marked_active(length(cons(N,L))) , Marked_and(isNat(N),isNatList(L))>
<Marked_active(length(cons(N,L))) , Marked_isNat(N)>
<Marked_active(length(cons(N,L))) , Marked_isNatList(L)>
<Marked_active(uLength(tt,L)) , Marked_s(length(L))>
<Marked_active(uLength(tt,L)) , Marked_length(L)>
<Marked_active(and(X1,X2)) , Marked_and(active(X1),X2)>
<Marked_active(and(X1,X2)) , Marked_active(X1)>
<Marked_active(and(X1,X2)) , Marked_and(X1,active(X2))>
<Marked_active(and(X1,X2)) , Marked_active(X2)>
<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(cons(X1,X2)) , Marked_cons(active(X1),X2)>
<Marked_active(cons(X1,X2)) , Marked_active(X1)>
<Marked_active(take(X1,X2)) , Marked_take(active(X1),X2)>
<Marked_active(take(X1,X2)) , Marked_active(X1)>
<Marked_active(take(X1,X2)) , Marked_take(X1,active(X2))>
<Marked_active(take(X1,X2)) , Marked_active(X2)>
<Marked_active(uTake1(X)) , Marked_uTake1(active(X))>
<Marked_active(uTake1(X)) , Marked_active(X)>
<Marked_active(uTake2(X1,X2,X3,X4)) , Marked_uTake2(active(X1),X2,X3,X4)>
<Marked_active(uTake2(X1,X2,X3,X4)) , Marked_active(X1)>
<Marked_active(uLength(X1,X2)) , Marked_uLength(active(X1),X2)>
<Marked_active(uLength(X1,X2)) , Marked_active(X1)>
<Marked_and(mark(X1),X2) , Marked_and(X1,X2)>
<Marked_and(X1,mark(X2)) , Marked_and(X1,X2)>
<Marked_s(mark(X)) , Marked_s(X)>
<Marked_length(mark(X)) , Marked_length(X)>
<Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
<Marked_take(mark(X1),X2) , Marked_take(X1,X2)>
<Marked_take(X1,mark(X2)) , Marked_take(X1,X2)>
<Marked_uTake1(mark(X)) , Marked_uTake1(X)>
<Marked_uTake2(mark(X1),X2,X3,X4) , Marked_uTake2(X1,X2,X3,X4)>
<Marked_uLength(mark(X1),X2) , Marked_uLength(X1,X2)>
<Marked_proper(and(X1,X2)) , Marked_and(proper(X1),proper(X2))>
<Marked_proper(and(X1,X2)) , Marked_proper(X1)>
<Marked_proper(and(X1,X2)) , Marked_proper(X2)>
<Marked_proper(isNatIList(X)) , Marked_isNatIList(proper(X))>
<Marked_proper(isNatIList(X)) , Marked_proper(X)>
<Marked_proper(isNatList(X)) , Marked_isNatList(proper(X))>
<Marked_proper(isNatList(X)) , Marked_proper(X)>
<Marked_proper(isNat(X)) , Marked_isNat(proper(X))>
<Marked_proper(isNat(X)) , Marked_proper(X)>
<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(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(take(X1,X2)) , Marked_take(proper(X1),proper(X2))>
<Marked_proper(take(X1,X2)) , Marked_proper(X1)>
<Marked_proper(take(X1,X2)) , Marked_proper(X2)>
<Marked_proper(uTake1(X)) , Marked_uTake1(proper(X))>
<Marked_proper(uTake1(X)) , Marked_proper(X)>
<Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_uTake2(proper(X1),proper(X2),
                                       proper(X3),proper(X4))>
<Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)>
<Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)>
<Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)>
<Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)>
<Marked_proper(uLength(X1,X2)) , Marked_uLength(proper(X1),proper(X2))>
<Marked_proper(uLength(X1,X2)) , Marked_proper(X1)>
<Marked_proper(uLength(X1,X2)) , Marked_proper(X2)>
<Marked_and(ok(X1),ok(X2)) , Marked_and(X1,X2)>
<Marked_isNatIList(ok(X)) , Marked_isNatIList(X)>
<Marked_isNatList(ok(X)) , Marked_isNatList(X)>
<Marked_isNat(ok(X)) , Marked_isNat(X)>
<Marked_s(ok(X)) , Marked_s(X)>
<Marked_length(ok(X)) , Marked_length(X)>
<Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)>
<Marked_take(ok(X1),ok(X2)) , Marked_take(X1,X2)>
<Marked_uTake1(ok(X)) , Marked_uTake1(X)>
<Marked_uTake2(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_uTake2(X1,X2,X3,X4)>
<Marked_uLength(ok(X1),ok(X2)) , Marked_uLength(X1,X2)>
<Marked_top(mark(X)) , Marked_top(proper(X))>
<Marked_top(mark(X)) , Marked_proper(X)>
<Marked_top(ok(X)) , Marked_top(active(X))>
<Marked_top(ok(X)) , Marked_active(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 14 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(uLength(X1,X2)) , Marked_proper(X2)> 
      --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(uTake1(X)) , Marked_proper(X)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(uTake1(X)) , Marked_proper(X)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(uTake1(X)) , Marked_proper(X)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(uTake1(X)) , Marked_proper(X)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(uTake1(X)) , Marked_proper(X)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(uTake1(X)) , Marked_proper(X)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(uTake1(X)) , Marked_proper(X)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(uTake1(X)) , Marked_proper(X)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(uTake1(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(uTake1(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(uTake1(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(uTake1(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(uTake1(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake1(X)) , Marked_proper(X)>
  <Marked_proper(uTake1(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(uTake1(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(uTake1(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(uTake1(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(uTake1(X)) , Marked_proper(X)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(uTake1(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(uTake1(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(uTake1(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(uTake1(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(uTake1(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(uTake1(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(uTake1(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(uTake1(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(uTake1(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(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(isNat(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(X2)> 
     --> <Marked_proper(isNatIList(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(X1)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(uTake1(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(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(isNat(X)) , Marked_proper(X)>
  <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(isNatIList(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(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake1(X)) , Marked_proper(X)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(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(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(isNat(X)) , Marked_proper(X)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(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(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake1(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(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(isNat(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(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(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake1(X)) , Marked_proper(X)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(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(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(isNat(X)) , Marked_proper(X)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(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(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake1(X)) , Marked_proper(X)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(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(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(isNat(X)) , Marked_proper(X)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(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(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(uTake1(X)) , Marked_proper(X)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(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(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(isNat(X)) , Marked_proper(X)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(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(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(uTake1(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(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(isNat(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(X2)> 
     --> <Marked_proper(isNatIList(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(X1)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(uLength(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(uTake2(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(uTake1(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(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(isNat(X)) , Marked_proper(X)>
  <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(isNatIList(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_active(uLength(X1,X2)) , Marked_active(X1)> 
      --> <Marked_active(uLength(X1,X2)) , Marked_active(X1)>
  <Marked_active(uLength(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(uTake2(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(uLength(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(uTake1(X)) , Marked_active(X)>
  <Marked_active(uLength(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(uLength(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(uLength(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(uLength(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(uLength(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(uLength(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X2)>
  <Marked_active(uLength(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(uTake2(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(uLength(X1,X2)) , Marked_active(X1)>
  <Marked_active(uTake2(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(uTake2(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(uTake2(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(uTake1(X)) , Marked_active(X)>
  <Marked_active(uTake2(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(uTake2(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(uTake2(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(uTake2(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(uTake2(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(uTake2(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X2)>
  <Marked_active(uTake2(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(uTake1(X)) , Marked_active(X)> 
     --> <Marked_active(uLength(X1,X2)) , Marked_active(X1)>
  <Marked_active(uTake1(X)) , Marked_active(X)> 
     --> <Marked_active(uTake2(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(uTake1(X)) , Marked_active(X)> 
     --> <Marked_active(uTake1(X)) , Marked_active(X)>
  <Marked_active(uTake1(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(uTake1(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(uTake1(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(uTake1(X)) , Marked_active(X)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(uTake1(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(uTake1(X)) , Marked_active(X)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X2)>
  <Marked_active(uTake1(X)) , Marked_active(X)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(uLength(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(uTake2(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(uTake1(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(uLength(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(uTake2(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(uTake1(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(uLength(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(uTake2(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(uTake1(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(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(and(X1,X2)) , Marked_active(X2)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(uLength(X1,X2)) , Marked_active(X1)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(uTake2(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(uTake1(X)) , Marked_active(X)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(cons(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(and(X1,X2)) , Marked_active(X2)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(uLength(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(uTake2(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(uTake1(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(cons(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(and(X1,X2)) , Marked_active(X2)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(uLength(X1,X2)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(uTake2(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(uTake1(X)) , Marked_active(X)>
  <Marked_active(and(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(and(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(and(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(and(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X2)>
  <Marked_active(and(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(uLength(X1,X2)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(uTake2(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(uTake1(X)) , Marked_active(X)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(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(and(X1,X2)) , Marked_active(X2)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
}

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

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

{  <Marked_isNatList(ok(X)) , Marked_isNatList(X)> 
      --> <Marked_isNatList(ok(X)) , Marked_isNatList(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(X1,mark(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(X1,mark(X2)) , Marked_and(X1,X2)> 
     --> <Marked_and(ok(X1),ok(X2)) , Marked_and(X1,X2)>
  <Marked_and(X1,mark(X2)) , Marked_and(X1,X2)> 
     --> <Marked_and(X1,mark(X2)) , Marked_and(X1,X2)>
  <Marked_and(X1,mark(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(X1,mark(X2)) , Marked_and(X1,X2)>
  <Marked_and(mark(X1),X2) , Marked_and(X1,X2)> 
     --> <Marked_and(mark(X1),X2) , Marked_and(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_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_take(ok(X1),ok(X2)) , Marked_take(X1,X2)> 
      --> <Marked_take(ok(X1),ok(X2)) , Marked_take(X1,X2)>
  <Marked_take(ok(X1),ok(X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(X1,mark(X2)) , Marked_take(X1,X2)>
  <Marked_take(ok(X1),ok(X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(mark(X1),X2) , Marked_take(X1,X2)>
  <Marked_take(X1,mark(X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(ok(X1),ok(X2)) , Marked_take(X1,X2)>
  <Marked_take(X1,mark(X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(X1,mark(X2)) , Marked_take(X1,X2)>
  <Marked_take(X1,mark(X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(mark(X1),X2) , Marked_take(X1,X2)>
  <Marked_take(mark(X1),X2) , Marked_take(X1,X2)> 
     --> <Marked_take(ok(X1),ok(X2)) , Marked_take(X1,X2)>
  <Marked_take(mark(X1),X2) , Marked_take(X1,X2)> 
     --> <Marked_take(X1,mark(X2)) , Marked_take(X1,X2)>
  <Marked_take(mark(X1),X2) , Marked_take(X1,X2)> 
     --> <Marked_take(mark(X1),X2) , Marked_take(X1,X2)>
}

{  <Marked_uTake1(ok(X)) , Marked_uTake1(X)> 
      --> <Marked_uTake1(ok(X)) , Marked_uTake1(X)>
  <Marked_uTake1(ok(X)) , Marked_uTake1(X)> 
     --> <Marked_uTake1(mark(X)) , Marked_uTake1(X)>
  <Marked_uTake1(mark(X)) , Marked_uTake1(X)> 
     --> <Marked_uTake1(ok(X)) , Marked_uTake1(X)>
  <Marked_uTake1(mark(X)) , Marked_uTake1(X)> 
     --> <Marked_uTake1(mark(X)) , Marked_uTake1(X)>
}

{  <Marked_uTake2(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_uTake2(X1,X2,X3,X4)> 
      --> <Marked_uTake2(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_uTake2(
                                                         X1,X2,X3,X4)>
  <Marked_uTake2(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_uTake2(X1,X2,X3,X4)> 
     --> <Marked_uTake2(mark(X1),X2,X3,X4) , Marked_uTake2(X1,X2,X3,X4)>
  <Marked_uTake2(mark(X1),X2,X3,X4) , Marked_uTake2(X1,X2,X3,X4)> 
     --> <Marked_uTake2(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_uTake2(
                                                        X1,X2,X3,X4)>
  <Marked_uTake2(mark(X1),X2,X3,X4) , Marked_uTake2(X1,X2,X3,X4)> 
     --> <Marked_uTake2(mark(X1),X2,X3,X4) , Marked_uTake2(X1,X2,X3,X4)>
}

{  <Marked_uLength(ok(X1),ok(X2)) , Marked_uLength(X1,X2)> 
      --> <Marked_uLength(ok(X1),ok(X2)) , Marked_uLength(X1,X2)>
  <Marked_uLength(ok(X1),ok(X2)) , Marked_uLength(X1,X2)> 
     --> <Marked_uLength(mark(X1),X2) , Marked_uLength(X1,X2)>
  <Marked_uLength(mark(X1),X2) , Marked_uLength(X1,X2)> 
     --> <Marked_uLength(ok(X1),ok(X2)) , Marked_uLength(X1,X2)>
  <Marked_uLength(mark(X1),X2) , Marked_uLength(X1,X2)> 
     --> <Marked_uLength(mark(X1),X2) , Marked_uLength(X1,X2)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  active(and(tt,T)) >= mark(T) ;
  active(and(X1,X2)) >= and(active(X1),X2) ;
  active(and(X1,X2)) >= and(X1,active(X2)) ;
  active(isNatList(cons(N,L))) >= mark(and(isNat(N),isNatList(L))) ;
  active(isNatList(nil)) >= mark(tt) ;
  active(isNatList(take(N,IL))) >= mark(and(isNat(N),isNatIList(IL))) ;
  active(isNatIList(zeros)) >= mark(tt) ;
  active(isNatIList(cons(N,IL))) >= mark(and(isNat(N),isNatIList(IL))) ;
  active(isNatIList(IL)) >= mark(isNatList(IL)) ;
  active(isNat(0)) >= mark(tt) ;
  active(isNat(s(N))) >= mark(isNat(N)) ;
  active(isNat(length(L))) >= mark(isNatList(L)) ;
  active(s(X)) >= s(active(X)) ;
  active(length(cons(N,L))) >= mark(uLength(and(isNat(N),isNatList(L)),L)) ;
  active(length(X)) >= length(active(X)) ;
  active(zeros) >= mark(cons(0,zeros)) ;
  active(cons(X1,X2)) >= cons(active(X1),X2) ;
  active(take(0,IL)) >= mark(uTake1(isNatIList(IL))) ;
  active(take(s(M),cons(N,IL))) >= mark(uTake2(and(isNat(M),
                                                and(isNat(N),isNatIList(IL))),
                                         M,N,IL)) ;
  active(take(X1,X2)) >= take(active(X1),X2) ;
  active(take(X1,X2)) >= take(X1,active(X2)) ;
  active(uTake1(tt)) >= mark(nil) ;
  active(uTake1(X)) >= uTake1(active(X)) ;
  active(uTake2(tt,M,N,IL)) >= mark(cons(N,take(M,IL))) ;
  active(uTake2(X1,X2,X3,X4)) >= uTake2(active(X1),X2,X3,X4) ;
  active(uLength(tt,L)) >= mark(s(length(L))) ;
  active(uLength(X1,X2)) >= uLength(active(X1),X2) ;
  and(mark(X1),X2) >= mark(and(X1,X2)) ;
  and(ok(X1),ok(X2)) >= ok(and(X1,X2)) ;
  and(X1,mark(X2)) >= mark(and(X1,X2)) ;
  isNatList(ok(X)) >= ok(isNatList(X)) ;
  isNatIList(ok(X)) >= ok(isNatIList(X)) ;
  isNat(ok(X)) >= ok(isNat(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)) ;
  cons(mark(X1),X2) >= mark(cons(X1,X2)) ;
  cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ;
  take(mark(X1),X2) >= mark(take(X1,X2)) ;
  take(ok(X1),ok(X2)) >= ok(take(X1,X2)) ;
  take(X1,mark(X2)) >= mark(take(X1,X2)) ;
  uTake1(mark(X)) >= mark(uTake1(X)) ;
  uTake1(ok(X)) >= ok(uTake1(X)) ;
  uTake2(mark(X1),X2,X3,X4) >= mark(uTake2(X1,X2,X3,X4)) ;
  uTake2(ok(X1),ok(X2),ok(X3),ok(X4)) >= ok(uTake2(X1,X2,X3,X4)) ;
  uLength(mark(X1),X2) >= mark(uLength(X1,X2)) ;
  uLength(ok(X1),ok(X2)) >= ok(uLength(X1,X2)) ;
  proper(and(X1,X2)) >= and(proper(X1),proper(X2)) ;
  proper(tt) >= ok(tt) ;
  proper(isNatList(X)) >= isNatList(proper(X)) ;
  proper(isNatIList(X)) >= isNatIList(proper(X)) ;
  proper(isNat(X)) >= isNat(proper(X)) ;
  proper(0) >= ok(0) ;
  proper(s(X)) >= s(proper(X)) ;
  proper(length(X)) >= length(proper(X)) ;
  proper(zeros) >= ok(zeros) ;
  proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ;
  proper(nil) >= ok(nil) ;
  proper(take(X1,X2)) >= take(proper(X1),proper(X2)) ;
  proper(uTake1(X)) >= uTake1(proper(X)) ;
  proper(uTake2(X1,X2,X3,X4)) >= uTake2(proper(X1),proper(X2),proper(X3),
                                  proper(X4)) ;
  proper(uLength(X1,X2)) >= uLength(proper(X1),proper(X2)) ;
  top(mark(X)) >= top(proper(X)) ;
  top(ok(X)) >= top(active(X)) ;
  Marked_top(mark(X)) >= Marked_top(proper(X)) ;
  Marked_top(ok(X)) >= Marked_top(active(X)) ;
 }
 + Disjunctions:{ 
{
  Marked_top(mark(X)) > Marked_top(proper(X)) ;
 }
{
  Marked_top(ok(X)) > Marked_top(active(X)) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== 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:
{
  active(and(tt,T)) >= mark(T) ;
  active(and(X1,X2)) >= and(active(X1),X2) ;
  active(and(X1,X2)) >= and(X1,active(X2)) ;
  active(isNatList(cons(N,L))) >= mark(and(isNat(N),isNatList(L))) ;
  active(isNatList(nil)) >= mark(tt) ;
  active(isNatList(take(N,IL))) >= mark(and(isNat(N),isNatIList(IL))) ;
  active(isNatIList(zeros)) >= mark(tt) ;
  active(isNatIList(cons(N,IL))) >= mark(and(isNat(N),isNatIList(IL))) ;
  active(isNatIList(IL)) >= mark(isNatList(IL)) ;
  active(isNat(0)) >= mark(tt) ;
  active(isNat(s(N))) >= mark(isNat(N)) ;
  active(isNat(length(L))) >= mark(isNatList(L)) ;
  active(s(X)) >= s(active(X)) ;
  active(length(cons(N,L))) >= mark(uLength(and(isNat(N),isNatList(L)),L)) ;
  active(length(X)) >= length(active(X)) ;
  active(zeros) >= mark(cons(0,zeros)) ;
  active(cons(X1,X2)) >= cons(active(X1),X2) ;
  active(take(0,IL)) >= mark(uTake1(isNatIList(IL))) ;
  active(take(s(M),cons(N,IL))) >= mark(uTake2(and(isNat(M),
                                                and(isNat(N),isNatIList(IL))),
                                         M,N,IL)) ;
  active(take(X1,X2)) >= take(active(X1),X2) ;
  active(take(X1,X2)) >= take(X1,active(X2)) ;
  active(uTake1(tt)) >= mark(nil) ;
  active(uTake1(X)) >= uTake1(active(X)) ;
  active(uTake2(tt,M,N,IL)) >= mark(cons(N,take(M,IL))) ;
  active(uTake2(X1,X2,X3,X4)) >= uTake2(active(X1),X2,X3,X4) ;
  active(uLength(tt,L)) >= mark(s(length(L))) ;
  active(uLength(X1,X2)) >= uLength(active(X1),X2) ;
  and(mark(X1),X2) >= mark(and(X1,X2)) ;
  and(ok(X1),ok(X2)) >= ok(and(X1,X2)) ;
  and(X1,mark(X2)) >= mark(and(X1,X2)) ;
  isNatList(ok(X)) >= ok(isNatList(X)) ;
  isNatIList(ok(X)) >= ok(isNatIList(X)) ;
  isNat(ok(X)) >= ok(isNat(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)) ;
  cons(mark(X1),X2) >= mark(cons(X1,X2)) ;
  cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ;
  take(mark(X1),X2) >= mark(take(X1,X2)) ;
  take(ok(X1),ok(X2)) >= ok(take(X1,X2)) ;
  take(X1,mark(X2)) >= mark(take(X1,X2)) ;
  uTake1(mark(X)) >= mark(uTake1(X)) ;
  uTake1(ok(X)) >= ok(uTake1(X)) ;
  uTake2(mark(X1),X2,X3,X4) >= mark(uTake2(X1,X2,X3,X4)) ;
  uTake2(ok(X1),ok(X2),ok(X3),ok(X4)) >= ok(uTake2(X1,X2,X3,X4)) ;
  uLength(mark(X1),X2) >= mark(uLength(X1,X2)) ;
  uLength(ok(X1),ok(X2)) >= ok(uLength(X1,X2)) ;
  proper(and(X1,X2)) >= and(proper(X1),proper(X2)) ;
  proper(tt) >= ok(tt) ;
  proper(isNatList(X)) >= isNatList(proper(X)) ;
  proper(isNatIList(X)) >= isNatIList(proper(X)) ;
  proper(isNat(X)) >= isNat(proper(X)) ;
  proper(0) >= ok(0) ;
  proper(s(X)) >= s(proper(X)) ;
  proper(length(X)) >= length(proper(X)) ;
  proper(zeros) >= ok(zeros) ;
  proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ;
  proper(nil) >= ok(nil) ;
  proper(take(X1,X2)) >= take(proper(X1),proper(X2)) ;
  proper(uTake1(X)) >= uTake1(proper(X)) ;
  proper(uTake2(X1,X2,X3,X4)) >= uTake2(proper(X1),proper(X2),proper(X3),
                                  proper(X4)) ;
  proper(uLength(X1,X2)) >= uLength(proper(X1),proper(X2)) ;
  top(mark(X)) >= top(proper(X)) ;
  top(ok(X)) >= top(active(X)) ;
  Marked_top(mark(X)) > Marked_top(proper(X)) ;
  Marked_top(ok(X)) > Marked_top(active(X)) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  active(and(tt,T)) >= mark(T) ;
  active(and(X1,X2)) >= and(active(X1),X2) ;
  active(and(X1,X2)) >= and(X1,active(X2)) ;
  active(isNatList(cons(N,L))) >= mark(and(isNat(N),isNatList(L))) ;
  active(isNatList(nil)) >= mark(tt) ;
  active(isNatList(take(N,IL))) >= mark(and(isNat(N),isNatIList(IL))) ;
  active(isNatIList(zeros)) >= mark(tt) ;
  active(isNatIList(cons(N,IL))) >= mark(and(isNat(N),isNatIList(IL))) ;
  active(isNatIList(IL)) >= mark(isNatList(IL)) ;
  active(isNat(0)) >= mark(tt) ;
  active(isNat(s(N))) >= mark(isNat(N)) ;
  active(isNat(length(L))) >= mark(isNatList(L)) ;
  active(s(X)) >= s(active(X)) ;
  active(length(cons(N,L))) >= mark(uLength(and(isNat(N),isNatList(L)),L)) ;
  active(length(X)) >= length(active(X)) ;
  active(zeros) >= mark(cons(0,zeros)) ;
  active(cons(X1,X2)) >= cons(active(X1),X2) ;
  active(take(0,IL)) >= mark(uTake1(isNatIList(IL))) ;
  active(take(s(M),cons(N,IL))) >= mark(uTake2(and(isNat(M),
                                                and(isNat(N),isNatIList(IL))),
                                         M,N,IL)) ;
  active(take(X1,X2)) >= take(active(X1),X2) ;
  active(take(X1,X2)) >= take(X1,active(X2)) ;
  active(uTake1(tt)) >= mark(nil) ;
  active(uTake1(X)) >= uTake1(active(X)) ;
  active(uTake2(tt,M,N,IL)) >= mark(cons(N,take(M,IL))) ;
  active(uTake2(X1,X2,X3,X4)) >= uTake2(active(X1),X2,X3,X4) ;
  active(uLength(tt,L)) >= mark(s(length(L))) ;
  active(uLength(X1,X2)) >= uLength(active(X1),X2) ;
  and(mark(X1),X2) >= mark(and(X1,X2)) ;
  and(ok(X1),ok(X2)) >= ok(and(X1,X2)) ;
  and(X1,mark(X2)) >= mark(and(X1,X2)) ;
  isNatList(ok(X)) >= ok(isNatList(X)) ;
  isNatIList(ok(X)) >= ok(isNatIList(X)) ;
  isNat(ok(X)) >= ok(isNat(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)) ;
  cons(mark(X1),X2) >= mark(cons(X1,X2)) ;
  cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ;
  take(mark(X1),X2) >= mark(take(X1,X2)) ;
  take(ok(X1),ok(X2)) >= ok(take(X1,X2)) ;
  take(X1,mark(X2)) >= mark(take(X1,X2)) ;
  uTake1(mark(X)) >= mark(uTake1(X)) ;
  uTake1(ok(X)) >= ok(uTake1(X)) ;
  uTake2(mark(X1),X2,X3,X4) >= mark(uTake2(X1,X2,X3,X4)) ;
  uTake2(ok(X1),ok(X2),ok(X3),ok(X4)) >= ok(uTake2(X1,X2,X3,X4)) ;
  uLength(mark(X1),X2) >= mark(uLength(X1,X2)) ;
  uLength(ok(X1),ok(X2)) >= ok(uLength(X1,X2)) ;
  proper(and(X1,X2)) >= and(proper(X1),proper(X2)) ;
  proper(tt) >= ok(tt) ;
  proper(isNatList(X)) >= isNatList(proper(X)) ;
  proper(isNatIList(X)) >= isNatIList(proper(X)) ;
  proper(isNat(X)) >= isNat(proper(X)) ;
  proper(0) >= ok(0) ;
  proper(s(X)) >= s(proper(X)) ;
  proper(length(X)) >= length(proper(X)) ;
  proper(zeros) >= ok(zeros) ;
  proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ;
  proper(nil) >= ok(nil) ;
  proper(take(X1,X2)) >= take(proper(X1),proper(X2)) ;
  proper(uTake1(X)) >= uTake1(proper(X)) ;
  proper(uTake2(X1,X2,X3,X4)) >= uTake2(proper(X1),proper(X2),proper(X3),
                                  proper(X4)) ;
  proper(uLength(X1,X2)) >= uLength(proper(X1),proper(X2)) ;
  top(mark(X)) >= top(proper(X)) ;
  top(ok(X)) >= top(active(X)) ;
  Marked_top(mark(X)) > Marked_top(proper(X)) ;
  Marked_top(ok(X)) > Marked_top(active(X)) ;
 }
 + Disjunctions:{ 
 } 
=== 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 ===
No solution found for these parameters.(20842 bt (30577) [818])
=== 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 138.680502 seconds (real time)
Cime Exit Status: 0