- : 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(U12(tt,L))
[3] active(U12(tt,L)) -> mark(s(length(L)))
[4] active(U21(tt,IL,M,N)) -> mark(U22(tt,IL,M,N))
[5] active(U22(tt,IL,M,N)) -> mark(U23(tt,IL,M,N))
[6] active(U23(tt,IL,M,N)) -> mark(cons(N,take(M,IL)))
[7] active(length(nil)) -> mark(0)
[8] active(length(cons(N,L))) -> mark(U11(tt,L))
[9] active(take(0,IL)) -> mark(nil)
[10] active(take(s(M),cons(N,IL))) -> mark(U21(tt,IL,M,N))
[11] active(cons(X1,X2)) -> cons(active(X1),X2)
[12] active(U11(X1,X2)) -> U11(active(X1),X2)
[13] active(U12(X1,X2)) -> U12(active(X1),X2)
[14] active(s(X)) -> s(active(X))
[15] active(length(X)) -> length(active(X))
[16] active(U21(X1,X2,X3,X4)) -> U21(active(X1),X2,X3,X4)
[17] active(U22(X1,X2,X3,X4)) -> U22(active(X1),X2,X3,X4)
[18] active(U23(X1,X2,X3,X4)) -> U23(active(X1),X2,X3,X4)
[19] active(take(X1,X2)) -> take(active(X1),X2)
[20] active(take(X1,X2)) -> take(X1,active(X2))
[21] cons(mark(X1),X2) -> mark(cons(X1,X2))
[22] U11(mark(X1),X2) -> mark(U11(X1,X2))
[23] U12(mark(X1),X2) -> mark(U12(X1,X2))
[24] s(mark(X)) -> mark(s(X))
[25] length(mark(X)) -> mark(length(X))
[26] U21(mark(X1),X2,X3,X4) -> mark(U21(X1,X2,X3,X4))
[27] U22(mark(X1),X2,X3,X4) -> mark(U22(X1,X2,X3,X4))
[28] U23(mark(X1),X2,X3,X4) -> mark(U23(X1,X2,X3,X4))
[29] take(mark(X1),X2) -> mark(take(X1,X2))
[30] take(X1,mark(X2)) -> mark(take(X1,X2))
[31] proper(zeros) -> ok(zeros)
[32] proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
[33] proper(0) -> ok(0)
[34] proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
[35] proper(tt) -> ok(tt)
[36] proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
[37] proper(s(X)) -> s(proper(X))
[38] proper(length(X)) -> length(proper(X))
[39] proper(U21(X1,X2,X3,X4)) ->
 U21(proper(X1),proper(X2),proper(X3),proper(X4))
[40] proper(U22(X1,X2,X3,X4)) ->
 U22(proper(X1),proper(X2),proper(X3),proper(X4))
[41] proper(U23(X1,X2,X3,X4)) ->
 U23(proper(X1),proper(X2),proper(X3),proper(X4))
[42] proper(take(X1,X2)) -> take(proper(X1),proper(X2))
[43] proper(nil) -> ok(nil)
[44] cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
[45] U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
[46] U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
[47] s(ok(X)) -> ok(s(X))
[48] length(ok(X)) -> ok(length(X))
[49] U21(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U21(X1,X2,X3,X4))
[50] U22(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U22(X1,X2,X3,X4))
[51] U23(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U23(X1,X2,X3,X4))
[52] take(ok(X1),ok(X2)) -> ok(take(X1,X2))
[53] top(mark(X)) -> top(proper(X))
[54] 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_U12(tt,L)>
<Marked_active(U12(tt,L)) , Marked_s(length(L))>
<Marked_active(U12(tt,L)) , Marked_length(L)>
<Marked_active(U21(tt,IL,M,N)) , Marked_U22(tt,IL,M,N)>
<Marked_active(U22(tt,IL,M,N)) , Marked_U23(tt,IL,M,N)>
<Marked_active(U23(tt,IL,M,N)) , Marked_cons(N,take(M,IL))>
<Marked_active(U23(tt,IL,M,N)) , Marked_take(M,IL)>
<Marked_active(length(cons(N,L))) , Marked_U11(tt,L)>
<Marked_active(take(s(M),cons(N,IL))) , Marked_U21(tt,IL,M,N)>
<Marked_active(cons(X1,X2)) , Marked_cons(active(X1),X2)>
<Marked_active(cons(X1,X2)) , Marked_active(X1)>
<Marked_active(U11(X1,X2)) , Marked_U11(active(X1),X2)>
<Marked_active(U11(X1,X2)) , Marked_active(X1)>
<Marked_active(U12(X1,X2)) , Marked_U12(active(X1),X2)>
<Marked_active(U12(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(X1,X2,X3,X4)) , Marked_U21(active(X1),X2,X3,X4)>
<Marked_active(U21(X1,X2,X3,X4)) , Marked_active(X1)>
<Marked_active(U22(X1,X2,X3,X4)) , Marked_U22(active(X1),X2,X3,X4)>
<Marked_active(U22(X1,X2,X3,X4)) , Marked_active(X1)>
<Marked_active(U23(X1,X2,X3,X4)) , Marked_U23(active(X1),X2,X3,X4)>
<Marked_active(U23(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_cons(mark(X1),X2) , Marked_cons(X1,X2)>
<Marked_U11(mark(X1),X2) , Marked_U11(X1,X2)>
<Marked_U12(mark(X1),X2) , Marked_U12(X1,X2)>
<Marked_s(mark(X)) , Marked_s(X)>
<Marked_length(mark(X)) , Marked_length(X)>
<Marked_U21(mark(X1),X2,X3,X4) , Marked_U21(X1,X2,X3,X4)>
<Marked_U22(mark(X1),X2,X3,X4) , Marked_U22(X1,X2,X3,X4)>
<Marked_U23(mark(X1),X2,X3,X4) , Marked_U23(X1,X2,X3,X4)>
<Marked_take(mark(X1),X2) , Marked_take(X1,X2)>
<Marked_take(X1,mark(X2)) , Marked_take(X1,X2)>
<Marked_proper(cons(X1,X2)) , Marked_cons(proper(X1),proper(X2))>
<Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
<Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U11(X1,X2)) , Marked_U11(proper(X1),proper(X2))>
<Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U12(X1,X2)) , Marked_U12(proper(X1),proper(X2))>
<Marked_proper(U12(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U12(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(X1,X2,X3,X4)) , Marked_U21(proper(X1),proper(X2),proper(X3),
                                    proper(X4))>
<Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)>
<Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)>
<Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)>
<Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)>
<Marked_proper(U22(X1,X2,X3,X4)) , Marked_U22(proper(X1),proper(X2),proper(X3),
                                    proper(X4))>
<Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)>
<Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)>
<Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)>
<Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)>
<Marked_proper(U23(X1,X2,X3,X4)) , Marked_U23(proper(X1),proper(X2),proper(X3),
                                    proper(X4))>
<Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)>
<Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)>
<Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)>
<Marked_proper(U23(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_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)>
<Marked_U11(ok(X1),ok(X2)) , Marked_U11(X1,X2)>
<Marked_U12(ok(X1),ok(X2)) , Marked_U12(X1,X2)>
<Marked_s(ok(X)) , Marked_s(X)>
<Marked_length(ok(X)) , Marked_length(X)>
<Marked_U21(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U21(X1,X2,X3,X4)>
<Marked_U22(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U22(X1,X2,X3,X4)>
<Marked_U23(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U23(X1,X2,X3,X4)>
<Marked_take(ok(X1),ok(X2)) , Marked_take(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 12 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(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(U23(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , 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(U12(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X1)>
  <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(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(U23(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , 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(U12(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X1)>
  <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(U23(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(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(U23(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , 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(U12(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X1)>
  <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(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(U23(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , 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(U12(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X1)>
  <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(U12(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(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(U23(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X1)>
  <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(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(U23(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X1)>
  <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(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(U23(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , 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(U12(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X1)>
  <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(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(U23(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U23(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3,X4)) , 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(U12(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2)) , Marked_proper(X1)>
  <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(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(U23(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U22(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U21(X1,X2,X3,X4)) , 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(U12(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(X2)> 
     --> <Marked_active(cons(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(U23(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3,X4)) , 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(U12(X1,X2)) , Marked_active(X1)>
  <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(U23(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U23(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U23(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U23(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U23(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U23(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U23(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(U23(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U23(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2)) , Marked_active(X1)>
  <Marked_active(U23(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2)) , Marked_active(X1)>
  <Marked_active(U23(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U22(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U23(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(U22(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U22(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U21(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U23(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(cons(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(U23(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(U22(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2,X3,X4)) , 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(U12(X1,X2)) , Marked_active(X1)>
  <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(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(U23(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U22(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2,X3,X4)) , 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(U12(X1,X2)) , Marked_active(X1)>
  <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(U12(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(U12(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U23(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(U12(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U12(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(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(U23(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2)) , Marked_active(X1)>
  <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(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(U23(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3,X4)) , 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(U12(X1,X2)) , Marked_active(X1)>
  <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_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)> 
      --> <Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)>
  <Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)> 
     --> <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
  <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)> 
     --> <Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)>
  <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)> 
     --> <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
}

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

{  <Marked_U12(ok(X1),ok(X2)) , Marked_U12(X1,X2)> 
      --> <Marked_U12(ok(X1),ok(X2)) , Marked_U12(X1,X2)>
  <Marked_U12(ok(X1),ok(X2)) , Marked_U12(X1,X2)> 
     --> <Marked_U12(mark(X1),X2) , Marked_U12(X1,X2)>
  <Marked_U12(mark(X1),X2) , Marked_U12(X1,X2)> 
     --> <Marked_U12(ok(X1),ok(X2)) , Marked_U12(X1,X2)>
  <Marked_U12(mark(X1),X2) , Marked_U12(X1,X2)> 
     --> <Marked_U12(mark(X1),X2) , Marked_U12(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(X1),ok(X2),ok(X3),ok(X4)) , Marked_U21(X1,X2,X3,X4)> 
      --> <Marked_U21(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U21(X1,X2,X3,X4)>
  <Marked_U21(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U21(X1,X2,X3,X4)> 
     --> <Marked_U21(mark(X1),X2,X3,X4) , Marked_U21(X1,X2,X3,X4)>
  <Marked_U21(mark(X1),X2,X3,X4) , Marked_U21(X1,X2,X3,X4)> 
     --> <Marked_U21(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U21(X1,X2,X3,X4)>
  <Marked_U21(mark(X1),X2,X3,X4) , Marked_U21(X1,X2,X3,X4)> 
     --> <Marked_U21(mark(X1),X2,X3,X4) , Marked_U21(X1,X2,X3,X4)>
}

{  <Marked_U22(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U22(X1,X2,X3,X4)> 
      --> <Marked_U22(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U22(X1,X2,X3,X4)>
  <Marked_U22(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U22(X1,X2,X3,X4)> 
     --> <Marked_U22(mark(X1),X2,X3,X4) , Marked_U22(X1,X2,X3,X4)>
  <Marked_U22(mark(X1),X2,X3,X4) , Marked_U22(X1,X2,X3,X4)> 
     --> <Marked_U22(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U22(X1,X2,X3,X4)>
  <Marked_U22(mark(X1),X2,X3,X4) , Marked_U22(X1,X2,X3,X4)> 
     --> <Marked_U22(mark(X1),X2,X3,X4) , Marked_U22(X1,X2,X3,X4)>
}

{  <Marked_U23(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U23(X1,X2,X3,X4)> 
      --> <Marked_U23(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U23(X1,X2,X3,X4)>
  <Marked_U23(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U23(X1,X2,X3,X4)> 
     --> <Marked_U23(mark(X1),X2,X3,X4) , Marked_U23(X1,X2,X3,X4)>
  <Marked_U23(mark(X1),X2,X3,X4) , Marked_U23(X1,X2,X3,X4)> 
     --> <Marked_U23(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_U23(X1,X2,X3,X4)>
  <Marked_U23(mark(X1),X2,X3,X4) , Marked_U23(X1,X2,X3,X4)> 
     --> <Marked_U23(mark(X1),X2,X3,X4) , Marked_U23(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)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  cons(mark(X1),X2) >= mark(cons(X1,X2)) ;
  cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ;
  active(cons(X1,X2)) >= cons(active(X1),X2) ;
  active(zeros) >= mark(cons(0,zeros)) ;
  active(U12(tt,L)) >= mark(s(length(L))) ;
  active(U12(X1,X2)) >= U12(active(X1),X2) ;
  active(U11(tt,L)) >= mark(U12(tt,L)) ;
  active(U11(X1,X2)) >= U11(active(X1),X2) ;
  active(s(X)) >= s(active(X)) ;
  active(length(cons(N,L))) >= mark(U11(tt,L)) ;
  active(length(nil)) >= mark(0) ;
  active(length(X)) >= length(active(X)) ;
  active(U22(tt,IL,M,N)) >= mark(U23(tt,IL,M,N)) ;
  active(U22(X1,X2,X3,X4)) >= U22(active(X1),X2,X3,X4) ;
  active(U21(tt,IL,M,N)) >= mark(U22(tt,IL,M,N)) ;
  active(U21(X1,X2,X3,X4)) >= U21(active(X1),X2,X3,X4) ;
  active(U23(tt,IL,M,N)) >= mark(cons(N,take(M,IL))) ;
  active(U23(X1,X2,X3,X4)) >= U23(active(X1),X2,X3,X4) ;
  active(take(0,IL)) >= mark(nil) ;
  active(take(s(M),cons(N,IL))) >= mark(U21(tt,IL,M,N)) ;
  active(take(X1,X2)) >= take(active(X1),X2) ;
  active(take(X1,X2)) >= take(X1,active(X2)) ;
  U12(mark(X1),X2) >= mark(U12(X1,X2)) ;
  U12(ok(X1),ok(X2)) >= ok(U12(X1,X2)) ;
  U11(mark(X1),X2) >= mark(U11(X1,X2)) ;
  U11(ok(X1),ok(X2)) >= ok(U11(X1,X2)) ;
  s(mark(X)) >= mark(s(X)) ;
  s(ok(X)) >= ok(s(X)) ;
  length(mark(X)) >= mark(length(X)) ;
  length(ok(X)) >= ok(length(X)) ;
  U22(mark(X1),X2,X3,X4) >= mark(U22(X1,X2,X3,X4)) ;
  U22(ok(X1),ok(X2),ok(X3),ok(X4)) >= ok(U22(X1,X2,X3,X4)) ;
  U21(mark(X1),X2,X3,X4) >= mark(U21(X1,X2,X3,X4)) ;
  U21(ok(X1),ok(X2),ok(X3),ok(X4)) >= ok(U21(X1,X2,X3,X4)) ;
  U23(mark(X1),X2,X3,X4) >= mark(U23(X1,X2,X3,X4)) ;
  U23(ok(X1),ok(X2),ok(X3),ok(X4)) >= ok(U23(X1,X2,X3,X4)) ;
  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)) ;
  proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ;
  proper(0) >= ok(0) ;
  proper(zeros) >= ok(zeros) ;
  proper(U12(X1,X2)) >= U12(proper(X1),proper(X2)) ;
  proper(tt) >= ok(tt) ;
  proper(U11(X1,X2)) >= U11(proper(X1),proper(X2)) ;
  proper(s(X)) >= s(proper(X)) ;
  proper(length(X)) >= length(proper(X)) ;
  proper(U22(X1,X2,X3,X4)) >= U22(proper(X1),proper(X2),proper(X3),proper(X4)) ;
  proper(U21(X1,X2,X3,X4)) >= U21(proper(X1),proper(X2),proper(X3),proper(X4)) ;
  proper(U23(X1,X2,X3,X4)) >= U23(proper(X1),proper(X2),proper(X3),proper(X4)) ;
  proper(take(X1,X2)) >= take(proper(X1),proper(X2)) ;
  proper(nil) >= ok(nil) ;
  top(mark(X)) >= top(proper(X)) ;
  top(ok(X)) >= top(active(X)) ;
  Marked_top(mark(X)) >= Marked_top(proper(X)) ;
  Marked_top(ok(X)) >= Marked_top(active(X)) ;
 }
 + Disjunctions:{ 
{
  Marked_top(mark(X)) > Marked_top(proper(X)) ;
 }
{
  Marked_top(ok(X)) > Marked_top(active(X)) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== 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 (ID_CRIT)
NOT SOLVED
No proof found
Cime worked for 68.251862 seconds (real time)
Cime Exit Status: 0