- : 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,L)) -> mark(s(length(L)))
[3] active(U21(tt)) -> mark(nil)
[4] active(U31(tt,IL,M,N)) -> mark(cons(N,take(M,IL)))
[5] active(and(tt,X)) -> mark(X)
[6] active(isNat(0)) -> mark(tt)
[7] active(isNat(length(V1))) -> mark(isNatList(V1))
[8] active(isNat(s(V1))) -> mark(isNat(V1))
[9] active(isNatIList(V)) -> mark(isNatList(V))
[10] active(isNatIList(zeros)) -> mark(tt)
[11] active(isNatIList(cons(V1,V2))) -> mark(and(isNat(V1),isNatIList(V2)))
[12] active(isNatList(nil)) -> mark(tt)
[13] active(isNatList(cons(V1,V2))) -> mark(and(isNat(V1),isNatList(V2)))
[14] active(isNatList(take(V1,V2))) -> mark(and(isNat(V1),isNatIList(V2)))
[15] active(length(nil)) -> mark(0)
[16] active(length(cons(N,L))) -> mark(U11(and(isNatList(L),isNat(N)),L))
[17] active(take(0,IL)) -> mark(U21(isNatIList(IL)))
[18] active(take(s(M),cons(N,IL))) ->
 mark(U31(and(isNatIList(IL),and(isNat(M),isNat(N))),IL,M,N))
[19] active(cons(X1,X2)) -> cons(active(X1),X2)
[20] active(U11(X1,X2)) -> U11(active(X1),X2)
[21] active(s(X)) -> s(active(X))
[22] active(length(X)) -> length(active(X))
[23] active(U21(X)) -> U21(active(X))
[24] active(U31(X1,X2,X3,X4)) -> U31(active(X1),X2,X3,X4)
[25] active(take(X1,X2)) -> take(active(X1),X2)
[26] active(take(X1,X2)) -> take(X1,active(X2))
[27] active(and(X1,X2)) -> and(active(X1),X2)
[28] cons(mark(X1),X2) -> mark(cons(X1,X2))
[29] U11(mark(X1),X2) -> mark(U11(X1,X2))
[30] s(mark(X)) -> mark(s(X))
[31] length(mark(X)) -> mark(length(X))
[32] U21(mark(X)) -> mark(U21(X))
[33] U31(mark(X1),X2,X3,X4) -> mark(U31(X1,X2,X3,X4))
[34] take(mark(X1),X2) -> mark(take(X1,X2))
[35] take(X1,mark(X2)) -> mark(take(X1,X2))
[36] and(mark(X1),X2) -> mark(and(X1,X2))
[37] proper(zeros) -> ok(zeros)
[38] proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
[39] proper(0) -> ok(0)
[40] proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
[41] proper(tt) -> ok(tt)
[42] proper(s(X)) -> s(proper(X))
[43] proper(length(X)) -> length(proper(X))
[44] proper(U21(X)) -> U21(proper(X))
[45] proper(nil) -> ok(nil)
[46] proper(U31(X1,X2,X3,X4)) ->
 U31(proper(X1),proper(X2),proper(X3),proper(X4))
[47] proper(take(X1,X2)) -> take(proper(X1),proper(X2))
[48] proper(and(X1,X2)) -> and(proper(X1),proper(X2))
[49] proper(isNat(X)) -> isNat(proper(X))
[50] proper(isNatList(X)) -> isNatList(proper(X))
[51] proper(isNatIList(X)) -> isNatIList(proper(X))
[52] cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
[53] U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
[54] s(ok(X)) -> ok(s(X))
[55] length(ok(X)) -> ok(length(X))
[56] U21(ok(X)) -> ok(U21(X))
[57] U31(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U31(X1,X2,X3,X4))
[58] take(ok(X1),ok(X2)) -> ok(take(X1,X2))
[59] and(ok(X1),ok(X2)) -> ok(and(X1,X2))
[60] isNat(ok(X)) -> ok(isNat(X))
[61] isNatList(ok(X)) -> ok(isNatList(X))
[62] isNatIList(ok(X)) -> ok(isNatIList(X))
[63] top(mark(X)) -> top(proper(X))
[64] top(ok(X)) -> top(active(X))


Sub problem: 
guided: 

DP termination of:
<Marked_active(zeros) , Marked_cons(0,zeros)>
<Marked_active(U11(tt,L)) , Marked_s(length(L))>
<Marked_active(U11(tt,L)) , Marked_length(L)>
<Marked_active(U31(tt,IL,M,N)) , Marked_cons(N,take(M,IL))>
<Marked_active(U31(tt,IL,M,N)) , Marked_take(M,IL)>
<Marked_active(isNat(length(V1))) , Marked_isNatList(V1)>
<Marked_active(isNat(s(V1))) , Marked_isNat(V1)>
<Marked_active(isNatIList(V)) , Marked_isNatList(V)>
<Marked_active(isNatIList(cons(V1,V2))) , Marked_and(isNat(V1),isNatIList(V2))>
<Marked_active(isNatIList(cons(V1,V2))) , Marked_isNat(V1)>
<Marked_active(isNatIList(cons(V1,V2))) , Marked_isNatIList(V2)>
<Marked_active(isNatList(cons(V1,V2))) , Marked_and(isNat(V1),isNatList(V2))>
<Marked_active(isNatList(cons(V1,V2))) , Marked_isNat(V1)>
<Marked_active(isNatList(cons(V1,V2))) , Marked_isNatList(V2)>
<Marked_active(isNatList(take(V1,V2))) , Marked_and(isNat(V1),isNatIList(V2))>
<Marked_active(isNatList(take(V1,V2))) , Marked_isNat(V1)>
<Marked_active(isNatList(take(V1,V2))) , Marked_isNatIList(V2)>
<Marked_active(length(cons(N,L))) , Marked_U11(and(isNatList(L),isNat(N)),L)>
<Marked_active(length(cons(N,L))) , Marked_and(isNatList(L),isNat(N))>
<Marked_active(length(cons(N,L))) , Marked_isNatList(L)>
<Marked_active(length(cons(N,L))) , Marked_isNat(N)>
<Marked_active(take(0,IL)) , Marked_U21(isNatIList(IL))>
<Marked_active(take(0,IL)) , Marked_isNatIList(IL)>
<Marked_active(take(s(M),cons(N,IL))) , Marked_U31(and(isNatIList(IL),
                                                    and(isNat(M),isNat(N))),
                                         IL,M,N)>
<Marked_active(take(s(M),cons(N,IL))) , Marked_and(isNatIList(IL),
                                         and(isNat(M),isNat(N)))>
<Marked_active(take(s(M),cons(N,IL))) , Marked_isNatIList(IL)>
<Marked_active(take(s(M),cons(N,IL))) , Marked_and(isNat(M),isNat(N))>
<Marked_active(take(s(M),cons(N,IL))) , Marked_isNat(M)>
<Marked_active(take(s(M),cons(N,IL))) , Marked_isNat(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(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(U21(X)) , Marked_U21(active(X))>
<Marked_active(U21(X)) , Marked_active(X)>
<Marked_active(U31(X1,X2,X3,X4)) , Marked_U31(active(X1),X2,X3,X4)>
<Marked_active(U31(X1,X2,X3,X4)) , 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(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_s(mark(X)) , Marked_s(X)>
<Marked_length(mark(X)) , Marked_length(X)>
<Marked_U21(mark(X)) , Marked_U21(X)>
<Marked_U31(mark(X1),X2,X3,X4) , Marked_U31(X1,X2,X3,X4)>
<Marked_take(mark(X1),X2) , Marked_take(X1,X2)>
<Marked_take(X1,mark(X2)) , Marked_take(X1,X2)>
<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(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(U21(X)) , Marked_U21(proper(X))>
<Marked_proper(U21(X)) , Marked_proper(X)>
<Marked_proper(U31(X1,X2,X3,X4)) , Marked_U31(proper(X1),proper(X2),proper(X3),
                                    proper(X4))>
<Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)>
<Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)>
<Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)>
<Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X4)>
<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(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(isNat(X)) , Marked_isNat(proper(X))>
<Marked_proper(isNat(X)) , Marked_proper(X)>
<Marked_proper(isNatList(X)) , Marked_isNatList(proper(X))>
<Marked_proper(isNatList(X)) , Marked_proper(X)>
<Marked_proper(isNatIList(X)) , Marked_isNatIList(proper(X))>
<Marked_proper(isNatIList(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_s(ok(X)) , Marked_s(X)>
<Marked_length(ok(X)) , Marked_length(X)>
<Marked_U21(ok(X)) , Marked_U21(X)>
<Marked_U31(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U31(X1,X2,X3,X4)>
<Marked_take(ok(X1),ok(X2)) , Marked_take(X1,X2)>
<Marked_and(ok(X1),ok(X2)) , Marked_and(X1,X2)>
<Marked_isNat(ok(X)) , Marked_isNat(X)>
<Marked_isNatList(ok(X)) , Marked_isNatList(X)>
<Marked_isNatIList(ok(X)) , Marked_isNatIList(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 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(isNatIList(X)) , Marked_proper(X)> 
      --> <Marked_proper(isNatIList(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(isNat(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(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(U31(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <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(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(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(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(isNat(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(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(U31(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <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(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(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(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(isNat(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(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(U31(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <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(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(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatIList(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(isNat(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(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(U31(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(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(X2)> 
     --> <Marked_proper(s(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(isNatIList(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(isNat(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(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(U31(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <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(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(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatIList(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(isNat(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(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(U31(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(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(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(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(X1)> 
     --> <Marked_proper(isNatIList(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(isNat(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(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(U31(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <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(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(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(U31(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , 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(isNatList(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(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(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(U31(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <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(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(isNatIList(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(isNat(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(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(U31(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <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(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(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatIList(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(X2)> 
     --> <Marked_proper(isNat(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(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(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(X2)> 
     --> <Marked_proper(s(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(isNatIList(X)) , Marked_proper(X)>
  <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(isNat(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(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <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(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(isNatIList(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(isNat(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(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(U31(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(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(X2)> 
     --> <Marked_proper(s(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(isNatIList(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(isNat(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(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(U31(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <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(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(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(U31(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X)) , Marked_active(X)>
  <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(U11(X1,X2)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(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(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(U31(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U21(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(X2)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U11(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(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X)) , Marked_active(X)>
  <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(U11(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U31(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U21(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U31(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X)) , Marked_active(X)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U21(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U21(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X)) , Marked_active(X)>
  <Marked_active(U21(X)) , Marked_active(X)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(U21(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U21(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X)) , Marked_active(X)> 
     --> <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(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(U31(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X)) , Marked_active(X)>
  <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(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(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(U31(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X)) , Marked_active(X)>
  <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(U11(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(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(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U11(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X)) , Marked_active(X)>
  <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(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(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(U31(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X)) , Marked_active(X)>
  <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(U11(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
}

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

{  <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_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_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_U21(ok(X)) , Marked_U21(X)> --> <Marked_U21(ok(X)) , Marked_U21(X)>
  <Marked_U21(ok(X)) , Marked_U21(X)> --> <Marked_U21(mark(X)) , Marked_U21(X)>
  <Marked_U21(mark(X)) , Marked_U21(X)> --> <Marked_U21(ok(X)) , Marked_U21(X)>
  <Marked_U21(mark(X)) , Marked_U21(X)> 
     --> <Marked_U21(mark(X)) , Marked_U21(X)>
}

{  <Marked_U31(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U31(X1,X2,X3,X4)> 
      --> <Marked_U31(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U31(X1,X2,X3,X4)>
  <Marked_U31(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U31(X1,X2,X3,X4)> 
     --> <Marked_U31(mark(X1),X2,X3,X4) , Marked_U31(X1,X2,X3,X4)>
  <Marked_U31(mark(X1),X2,X3,X4) , Marked_U31(X1,X2,X3,X4)> 
     --> <Marked_U31(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U31(X1,X2,X3,X4)>
  <Marked_U31(mark(X1),X2,X3,X4) , Marked_U31(X1,X2,X3,X4)> 
     --> <Marked_U31(mark(X1),X2,X3,X4) , Marked_U31(X1,X2,X3,X4)>
}

{  <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_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(s(X)) >= s(active(X)) ;
  active(length(cons(N,L))) >= mark(U11(and(isNatList(L),isNat(N)),L)) ;
  active(length(nil)) >= mark(0) ;
  active(length(X)) >= length(active(X)) ;
  active(U11(tt,L)) >= mark(s(length(L))) ;
  active(U11(X1,X2)) >= U11(active(X1),X2) ;
  active(U21(tt)) >= mark(nil) ;
  active(U21(X)) >= U21(active(X)) ;
  active(take(0,IL)) >= mark(U21(isNatIList(IL))) ;
  active(take(s(M),cons(N,IL))) >= mark(U31(and(isNatIList(IL),
                                             and(isNat(M),isNat(N))),
                                         IL,M,N)) ;
  active(take(X1,X2)) >= take(active(X1),X2) ;
  active(take(X1,X2)) >= take(X1,active(X2)) ;
  active(U31(tt,IL,M,N)) >= mark(cons(N,take(M,IL))) ;
  active(U31(X1,X2,X3,X4)) >= U31(active(X1),X2,X3,X4) ;
  active(and(tt,X)) >= mark(X) ;
  active(and(X1,X2)) >= and(active(X1),X2) ;
  active(isNat(0)) >= mark(tt) ;
  active(isNat(s(V1))) >= mark(isNat(V1)) ;
  active(isNat(length(V1))) >= mark(isNatList(V1)) ;
  active(isNatList(cons(V1,V2))) >= mark(and(isNat(V1),isNatList(V2))) ;
  active(isNatList(nil)) >= mark(tt) ;
  active(isNatList(take(V1,V2))) >= mark(and(isNat(V1),isNatIList(V2))) ;
  active(isNatIList(cons(V1,V2))) >= mark(and(isNat(V1),isNatIList(V2))) ;
  active(isNatIList(zeros)) >= mark(tt) ;
  active(isNatIList(V)) >= mark(isNatList(V)) ;
  s(mark(X)) >= mark(s(X)) ;
  s(ok(X)) >= ok(s(X)) ;
  length(mark(X)) >= mark(length(X)) ;
  length(ok(X)) >= ok(length(X)) ;
  U11(mark(X1),X2) >= mark(U11(X1,X2)) ;
  U11(ok(X1),ok(X2)) >= ok(U11(X1,X2)) ;
  U21(mark(X)) >= mark(U21(X)) ;
  U21(ok(X)) >= ok(U21(X)) ;
  take(mark(X1),X2) >= mark(take(X1,X2)) ;
  take(ok(X1),ok(X2)) >= ok(take(X1,X2)) ;
  take(X1,mark(X2)) >= mark(take(X1,X2)) ;
  U31(mark(X1),X2,X3,X4) >= mark(U31(X1,X2,X3,X4)) ;
  U31(ok(X1),ok(X2),ok(X3),ok(X4)) >= ok(U31(X1,X2,X3,X4)) ;
  and(mark(X1),X2) >= mark(and(X1,X2)) ;
  and(ok(X1),ok(X2)) >= ok(and(X1,X2)) ;
  isNat(ok(X)) >= ok(isNat(X)) ;
  isNatList(ok(X)) >= ok(isNatList(X)) ;
  isNatIList(ok(X)) >= ok(isNatIList(X)) ;
  proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ;
  proper(0) >= ok(0) ;
  proper(zeros) >= ok(zeros) ;
  proper(s(X)) >= s(proper(X)) ;
  proper(length(X)) >= length(proper(X)) ;
  proper(U11(X1,X2)) >= U11(proper(X1),proper(X2)) ;
  proper(tt) >= ok(tt) ;
  proper(nil) >= ok(nil) ;
  proper(U21(X)) >= U21(proper(X)) ;
  proper(take(X1,X2)) >= take(proper(X1),proper(X2)) ;
  proper(U31(X1,X2,X3,X4)) >= U31(proper(X1),proper(X2),proper(X3),proper(X4)) ;
  proper(and(X1,X2)) >= and(proper(X1),proper(X2)) ;
  proper(isNat(X)) >= isNat(proper(X)) ;
  proper(isNatList(X)) >= isNatList(proper(X)) ;
  proper(isNatIList(X)) >= isNatIList(proper(X)) ;
  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:
{
  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(s(X)) >= s(active(X)) ;
  active(length(cons(N,L))) >= mark(U11(and(isNatList(L),isNat(N)),L)) ;
  active(length(nil)) >= mark(0) ;
  active(length(X)) >= length(active(X)) ;
  active(U11(tt,L)) >= mark(s(length(L))) ;
  active(U11(X1,X2)) >= U11(active(X1),X2) ;
  active(U21(tt)) >= mark(nil) ;
  active(U21(X)) >= U21(active(X)) ;
  active(take(0,IL)) >= mark(U21(isNatIList(IL))) ;
  active(take(s(M),cons(N,IL))) >= mark(U31(and(isNatIList(IL),
                                             and(isNat(M),isNat(N))),
                                         IL,M,N)) ;
  active(take(X1,X2)) >= take(active(X1),X2) ;
  active(take(X1,X2)) >= take(X1,active(X2)) ;
  active(U31(tt,IL,M,N)) >= mark(cons(N,take(M,IL))) ;
  active(U31(X1,X2,X3,X4)) >= U31(active(X1),X2,X3,X4) ;
  active(and(tt,X)) >= mark(X) ;
  active(and(X1,X2)) >= and(active(X1),X2) ;
  active(isNat(0)) >= mark(tt) ;
  active(isNat(s(V1))) >= mark(isNat(V1)) ;
  active(isNat(length(V1))) >= mark(isNatList(V1)) ;
  active(isNatList(cons(V1,V2))) >= mark(and(isNat(V1),isNatList(V2))) ;
  active(isNatList(nil)) >= mark(tt) ;
  active(isNatList(take(V1,V2))) >= mark(and(isNat(V1),isNatIList(V2))) ;
  active(isNatIList(cons(V1,V2))) >= mark(and(isNat(V1),isNatIList(V2))) ;
  active(isNatIList(zeros)) >= mark(tt) ;
  active(isNatIList(V)) >= mark(isNatList(V)) ;
  s(mark(X)) >= mark(s(X)) ;
  s(ok(X)) >= ok(s(X)) ;
  length(mark(X)) >= mark(length(X)) ;
  length(ok(X)) >= ok(length(X)) ;
  U11(mark(X1),X2) >= mark(U11(X1,X2)) ;
  U11(ok(X1),ok(X2)) >= ok(U11(X1,X2)) ;
  U21(mark(X)) >= mark(U21(X)) ;
  U21(ok(X)) >= ok(U21(X)) ;
  take(mark(X1),X2) >= mark(take(X1,X2)) ;
  take(ok(X1),ok(X2)) >= ok(take(X1,X2)) ;
  take(X1,mark(X2)) >= mark(take(X1,X2)) ;
  U31(mark(X1),X2,X3,X4) >= mark(U31(X1,X2,X3,X4)) ;
  U31(ok(X1),ok(X2),ok(X3),ok(X4)) >= ok(U31(X1,X2,X3,X4)) ;
  and(mark(X1),X2) >= mark(and(X1,X2)) ;
  and(ok(X1),ok(X2)) >= ok(and(X1,X2)) ;
  isNat(ok(X)) >= ok(isNat(X)) ;
  isNatList(ok(X)) >= ok(isNatList(X)) ;
  isNatIList(ok(X)) >= ok(isNatIList(X)) ;
  proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ;
  proper(0) >= ok(0) ;
  proper(zeros) >= ok(zeros) ;
  proper(s(X)) >= s(proper(X)) ;
  proper(length(X)) >= length(proper(X)) ;
  proper(U11(X1,X2)) >= U11(proper(X1),proper(X2)) ;
  proper(tt) >= ok(tt) ;
  proper(nil) >= ok(nil) ;
  proper(U21(X)) >= U21(proper(X)) ;
  proper(take(X1,X2)) >= take(proper(X1),proper(X2)) ;
  proper(U31(X1,X2,X3,X4)) >= U31(proper(X1),proper(X2),proper(X3),proper(X4)) ;
  proper(and(X1,X2)) >= and(proper(X1),proper(X2)) ;
  proper(isNat(X)) >= isNat(proper(X)) ;
  proper(isNatList(X)) >= isNatList(proper(X)) ;
  proper(isNatIList(X)) >= isNatIList(proper(X)) ;
  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(s(X)) >= s(active(X)) ;
  active(length(cons(N,L))) >= mark(U11(and(isNatList(L),isNat(N)),L)) ;
  active(length(nil)) >= mark(0) ;
  active(length(X)) >= length(active(X)) ;
  active(U11(tt,L)) >= mark(s(length(L))) ;
  active(U11(X1,X2)) >= U11(active(X1),X2) ;
  active(U21(tt)) >= mark(nil) ;
  active(U21(X)) >= U21(active(X)) ;
  active(take(0,IL)) >= mark(U21(isNatIList(IL))) ;
  active(take(s(M),cons(N,IL))) >= mark(U31(and(isNatIList(IL),
                                             and(isNat(M),isNat(N))),
                                         IL,M,N)) ;
  active(take(X1,X2)) >= take(active(X1),X2) ;
  active(take(X1,X2)) >= take(X1,active(X2)) ;
  active(U31(tt,IL,M,N)) >= mark(cons(N,take(M,IL))) ;
  active(U31(X1,X2,X3,X4)) >= U31(active(X1),X2,X3,X4) ;
  active(and(tt,X)) >= mark(X) ;
  active(and(X1,X2)) >= and(active(X1),X2) ;
  active(isNat(0)) >= mark(tt) ;
  active(isNat(s(V1))) >= mark(isNat(V1)) ;
  active(isNat(length(V1))) >= mark(isNatList(V1)) ;
  active(isNatList(cons(V1,V2))) >= mark(and(isNat(V1),isNatList(V2))) ;
  active(isNatList(nil)) >= mark(tt) ;
  active(isNatList(take(V1,V2))) >= mark(and(isNat(V1),isNatIList(V2))) ;
  active(isNatIList(cons(V1,V2))) >= mark(and(isNat(V1),isNatIList(V2))) ;
  active(isNatIList(zeros)) >= mark(tt) ;
  active(isNatIList(V)) >= mark(isNatList(V)) ;
  s(mark(X)) >= mark(s(X)) ;
  s(ok(X)) >= ok(s(X)) ;
  length(mark(X)) >= mark(length(X)) ;
  length(ok(X)) >= ok(length(X)) ;
  U11(mark(X1),X2) >= mark(U11(X1,X2)) ;
  U11(ok(X1),ok(X2)) >= ok(U11(X1,X2)) ;
  U21(mark(X)) >= mark(U21(X)) ;
  U21(ok(X)) >= ok(U21(X)) ;
  take(mark(X1),X2) >= mark(take(X1,X2)) ;
  take(ok(X1),ok(X2)) >= ok(take(X1,X2)) ;
  take(X1,mark(X2)) >= mark(take(X1,X2)) ;
  U31(mark(X1),X2,X3,X4) >= mark(U31(X1,X2,X3,X4)) ;
  U31(ok(X1),ok(X2),ok(X3),ok(X4)) >= ok(U31(X1,X2,X3,X4)) ;
  and(mark(X1),X2) >= mark(and(X1,X2)) ;
  and(ok(X1),ok(X2)) >= ok(and(X1,X2)) ;
  isNat(ok(X)) >= ok(isNat(X)) ;
  isNatList(ok(X)) >= ok(isNatList(X)) ;
  isNatIList(ok(X)) >= ok(isNatIList(X)) ;
  proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ;
  proper(0) >= ok(0) ;
  proper(zeros) >= ok(zeros) ;
  proper(s(X)) >= s(proper(X)) ;
  proper(length(X)) >= length(proper(X)) ;
  proper(U11(X1,X2)) >= U11(proper(X1),proper(X2)) ;
  proper(tt) >= ok(tt) ;
  proper(nil) >= ok(nil) ;
  proper(U21(X)) >= U21(proper(X)) ;
  proper(take(X1,X2)) >= take(proper(X1),proper(X2)) ;
  proper(U31(X1,X2,X3,X4)) >= U31(proper(X1),proper(X2),proper(X3),proper(X4)) ;
  proper(and(X1,X2)) >= and(proper(X1),proper(X2)) ;
  proper(isNat(X)) >= isNat(proper(X)) ;
  proper(isNatList(X)) >= isNatList(proper(X)) ;
  proper(isNatIList(X)) >= isNatIList(proper(X)) ;
  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.(10229 bt (13999) [130])
=== 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 134.129443 seconds (real time)
Cime Exit Status: 0