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

TRS termination of:
[1] and(tt,T) -> T
[2] isNatIList(IL) -> isNatList(activate(IL))
[3] isNat(n__0) -> tt
[4] isNat(n__s(N)) -> isNat(activate(N))
[5] isNat(n__length(L)) -> isNatList(activate(L))
[6] isNatIList(n__zeros) -> tt
[7] isNatIList(n__cons(N,IL)) ->
 and(isNat(activate(N)),isNatIList(activate(IL)))
[8] isNatList(n__nil) -> tt
[9] isNatList(n__cons(N,L)) -> and(isNat(activate(N)),isNatList(activate(L)))
[10] isNatList(n__take(N,IL)) ->
 and(isNat(activate(N)),isNatIList(activate(IL)))
[11] zeros -> cons(0,n__zeros)
[12] take(0,IL) -> uTake1(isNatIList(IL))
[13] uTake1(tt) -> nil
[14] take(s(M),cons(N,IL)) ->
 uTake2(and(isNat(M),and(isNat(N),isNatIList(activate(IL)))),M,N,activate(IL))
[15] uTake2(tt,M,N,IL) -> cons(activate(N),n__take(activate(M),activate(IL)))
[16] length(cons(N,L)) ->
 uLength(and(isNat(N),isNatList(activate(L))),activate(L))
[17] uLength(tt,L) -> s(length(activate(L)))
[18] 0 -> n__0
[19] s(X) -> n__s(X)
[20] length(X) -> n__length(X)
[21] zeros -> n__zeros
[22] cons(X1,X2) -> n__cons(X1,X2)
[23] nil -> n__nil
[24] take(X1,X2) -> n__take(X1,X2)
[25] activate(n__0) -> 0
[26] activate(n__s(X)) -> s(X)
[27] activate(n__length(X)) -> length(X)
[28] activate(n__zeros) -> zeros
[29] activate(n__cons(X1,X2)) -> cons(X1,X2)
[30] activate(n__nil) -> nil
[31] activate(n__take(X1,X2)) -> take(X1,X2)
[32] activate(X) -> X


Sub problem: 
guided: 

DP termination of:
<Marked_isNatIList(IL) , Marked_isNatList(activate(IL))>
<Marked_isNatIList(IL) , Marked_activate(IL)>
<Marked_isNat(n__s(N)) , Marked_isNat(activate(N))>
<Marked_isNat(n__s(N)) , Marked_activate(N)>
<Marked_isNat(n__length(L)) , Marked_isNatList(activate(L))>
<Marked_isNat(n__length(L)) , Marked_activate(L)>
<Marked_isNatIList(n__cons(N,IL)) , Marked_and(isNat(activate(N)),
                                     isNatIList(activate(IL)))>
<Marked_isNatIList(n__cons(N,IL)) , Marked_isNat(activate(N))>
<Marked_isNatIList(n__cons(N,IL)) , Marked_activate(N)>
<Marked_isNatIList(n__cons(N,IL)) , Marked_isNatIList(activate(IL))>
<Marked_isNatIList(n__cons(N,IL)) , Marked_activate(IL)>
<Marked_isNatList(n__cons(N,L)) , Marked_and(isNat(activate(N)),
                                   isNatList(activate(L)))>
<Marked_isNatList(n__cons(N,L)) , Marked_isNat(activate(N))>
<Marked_isNatList(n__cons(N,L)) , Marked_activate(N)>
<Marked_isNatList(n__cons(N,L)) , Marked_isNatList(activate(L))>
<Marked_isNatList(n__cons(N,L)) , Marked_activate(L)>
<Marked_isNatList(n__take(N,IL)) , Marked_and(isNat(activate(N)),
                                    isNatIList(activate(IL)))>
<Marked_isNatList(n__take(N,IL)) , Marked_isNat(activate(N))>
<Marked_isNatList(n__take(N,IL)) , Marked_activate(N)>
<Marked_isNatList(n__take(N,IL)) , Marked_isNatIList(activate(IL))>
<Marked_isNatList(n__take(N,IL)) , Marked_activate(IL)>
<Marked_zeros , Marked_cons(0,n__zeros)>
<Marked_zeros , Marked_0>
<Marked_take(0,IL) , Marked_uTake1(isNatIList(IL))>
<Marked_take(0,IL) , Marked_isNatIList(IL)>
<Marked_uTake1(tt) , Marked_nil>
<Marked_take(s(M),cons(N,IL)) , Marked_uTake2(and(isNat(M),
                                               and(isNat(N),
                                                isNatIList(activate(IL)))),
                                 M,N,activate(IL))>
<Marked_take(s(M),cons(N,IL)) , Marked_and(isNat(M),
                                 and(isNat(N),isNatIList(activate(IL))))>
<Marked_take(s(M),cons(N,IL)) , Marked_isNat(M)>
<Marked_take(s(M),cons(N,IL)) , Marked_and(isNat(N),isNatIList(activate(IL)))>
<Marked_take(s(M),cons(N,IL)) , Marked_isNat(N)>
<Marked_take(s(M),cons(N,IL)) , Marked_isNatIList(activate(IL))>
<Marked_take(s(M),cons(N,IL)) , Marked_activate(IL)>
<Marked_take(s(M),cons(N,IL)) , Marked_activate(IL)>
<Marked_uTake2(tt,M,N,IL) , Marked_cons(activate(N),
                             n__take(activate(M),activate(IL)))>
<Marked_uTake2(tt,M,N,IL) , Marked_activate(N)>
<Marked_uTake2(tt,M,N,IL) , Marked_activate(M)>
<Marked_uTake2(tt,M,N,IL) , Marked_activate(IL)>
<Marked_length(cons(N,L)) , Marked_uLength(and(isNat(N),isNatList(activate(L))),
                             activate(L))>
<Marked_length(cons(N,L)) , Marked_and(isNat(N),isNatList(activate(L)))>
<Marked_length(cons(N,L)) , Marked_isNat(N)>
<Marked_length(cons(N,L)) , Marked_isNatList(activate(L))>
<Marked_length(cons(N,L)) , Marked_activate(L)>
<Marked_length(cons(N,L)) , Marked_activate(L)>
<Marked_uLength(tt,L) , Marked_s(length(activate(L)))>
<Marked_uLength(tt,L) , Marked_length(activate(L))>
<Marked_uLength(tt,L) , Marked_activate(L)>
<Marked_activate(n__0) , Marked_0>
<Marked_activate(n__s(X)) , Marked_s(X)>
<Marked_activate(n__length(X)) , Marked_length(X)>
<Marked_activate(n__zeros) , Marked_zeros>
<Marked_activate(n__cons(X1,X2)) , Marked_cons(X1,X2)>
<Marked_activate(n__nil) , Marked_nil>
<Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)> 
      --> <Marked_take(s(M),cons(N,IL)) , Marked_activate(IL)>
  <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(s(M),cons(N,IL)) , Marked_activate(IL)>
  <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(s(M),cons(N,IL)) , Marked_isNatIList(activate(IL))>
  <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(s(M),cons(N,IL)) , Marked_isNat(N)>
  <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(s(M),cons(N,IL)) , Marked_isNat(M)>
  <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(s(M),cons(N,IL)) , Marked_uTake2(and(isNat(M),
                                                        and(isNat(N),
                                                         isNatIList(activate(
                                                                    IL)))),
                                          M,N,activate(IL))>
  <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(0,IL) , Marked_isNatIList(IL)>
  <Marked_activate(n__length(X)) , Marked_length(X)> 
     --> <Marked_length(cons(N,L)) , Marked_activate(L)>
  <Marked_activate(n__length(X)) , Marked_length(X)> 
     --> <Marked_length(cons(N,L)) , Marked_activate(L)>
  <Marked_activate(n__length(X)) , Marked_length(X)> 
     --> <Marked_length(cons(N,L)) , Marked_isNatList(activate(L))>
  <Marked_activate(n__length(X)) , Marked_length(X)> 
     --> <Marked_length(cons(N,L)) , Marked_isNat(N)>
  <Marked_activate(n__length(X)) , Marked_length(X)> 
     --> <Marked_length(cons(N,L)) , Marked_uLength(and(isNat(N),
                                                     isNatList(activate(L))),
                                      activate(L))>
  <Marked_uLength(tt,L) , Marked_activate(L)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_uLength(tt,L) , Marked_activate(L)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_uLength(tt,L) , Marked_length(activate(L))> 
     --> <Marked_length(cons(N,L)) , Marked_activate(L)>
  <Marked_uLength(tt,L) , Marked_length(activate(L))> 
     --> <Marked_length(cons(N,L)) , Marked_activate(L)>
  <Marked_uLength(tt,L) , Marked_length(activate(L))> 
     --> <Marked_length(cons(N,L)) , Marked_isNatList(activate(L))>
  <Marked_uLength(tt,L) , Marked_length(activate(L))> 
     --> <Marked_length(cons(N,L)) , Marked_isNat(N)>
  <Marked_uLength(tt,L) , Marked_length(activate(L))> 
     --> <Marked_length(cons(N,L)) , Marked_uLength(and(isNat(N),
                                                     isNatList(activate(L))),
                                      activate(L))>
  <Marked_length(cons(N,L)) , Marked_activate(L)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_length(cons(N,L)) , Marked_activate(L)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_length(cons(N,L)) , Marked_activate(L)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_length(cons(N,L)) , Marked_activate(L)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_length(cons(N,L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__take(N,IL)) , Marked_activate(IL)>
  <Marked_length(cons(N,L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__take(N,IL)) , Marked_isNatIList(activate(IL))>
  <Marked_length(cons(N,L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__take(N,IL)) , Marked_activate(N)>
  <Marked_length(cons(N,L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__take(N,IL)) , Marked_isNat(activate(N))>
  <Marked_length(cons(N,L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__cons(N,L)) , Marked_activate(L)>
  <Marked_length(cons(N,L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__cons(N,L)) , Marked_isNatList(activate(L))>
  <Marked_length(cons(N,L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__cons(N,L)) , Marked_activate(N)>
  <Marked_length(cons(N,L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__cons(N,L)) , Marked_isNat(activate(N))>
  <Marked_length(cons(N,L)) , Marked_isNat(N)> 
     --> <Marked_isNat(n__length(L)) , Marked_activate(L)>
  <Marked_length(cons(N,L)) , Marked_isNat(N)> 
     --> <Marked_isNat(n__length(L)) , Marked_isNatList(activate(L))>
  <Marked_length(cons(N,L)) , Marked_isNat(N)> 
     --> <Marked_isNat(n__s(N)) , Marked_activate(N)>
  <Marked_length(cons(N,L)) , Marked_isNat(N)> 
     --> <Marked_isNat(n__s(N)) , Marked_isNat(activate(N))>
  <Marked_length(cons(N,L)) , Marked_uLength(and(isNat(N),
                                              isNatList(activate(L))),
                               activate(L))> 
     --> <Marked_uLength(tt,L) , Marked_activate(L)>
  <Marked_length(cons(N,L)) , Marked_uLength(and(isNat(N),
                                              isNatList(activate(L))),
                               activate(L))> 
     --> <Marked_uLength(tt,L) , Marked_length(activate(L))>
  <Marked_uTake2(tt,M,N,IL) , Marked_activate(IL)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_uTake2(tt,M,N,IL) , Marked_activate(IL)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_uTake2(tt,M,N,IL) , Marked_activate(M)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_uTake2(tt,M,N,IL) , Marked_activate(M)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_uTake2(tt,M,N,IL) , Marked_activate(N)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_uTake2(tt,M,N,IL) , Marked_activate(N)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_take(s(M),cons(N,IL)) , Marked_activate(IL)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_take(s(M),cons(N,IL)) , Marked_activate(IL)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_take(s(M),cons(N,IL)) , Marked_activate(IL)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_take(s(M),cons(N,IL)) , Marked_activate(IL)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_take(s(M),cons(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_activate(IL)>
  <Marked_take(s(M),cons(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_isNatIList(activate(IL))>
  <Marked_take(s(M),cons(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_activate(N)>
  <Marked_take(s(M),cons(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_isNat(activate(N))>
  <Marked_take(s(M),cons(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(IL) , Marked_activate(IL)>
  <Marked_take(s(M),cons(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(IL) , Marked_isNatList(activate(IL))>
  <Marked_take(s(M),cons(N,IL)) , Marked_isNat(N)> 
     --> <Marked_isNat(n__length(L)) , Marked_activate(L)>
  <Marked_take(s(M),cons(N,IL)) , Marked_isNat(N)> 
     --> <Marked_isNat(n__length(L)) , Marked_isNatList(activate(L))>
  <Marked_take(s(M),cons(N,IL)) , Marked_isNat(N)> 
     --> <Marked_isNat(n__s(N)) , Marked_activate(N)>
  <Marked_take(s(M),cons(N,IL)) , Marked_isNat(N)> 
     --> <Marked_isNat(n__s(N)) , Marked_isNat(activate(N))>
  <Marked_take(s(M),cons(N,IL)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__length(L)) , Marked_activate(L)>
  <Marked_take(s(M),cons(N,IL)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__length(L)) , Marked_isNatList(activate(L))>
  <Marked_take(s(M),cons(N,IL)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__s(N)) , Marked_activate(N)>
  <Marked_take(s(M),cons(N,IL)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__s(N)) , Marked_isNat(activate(N))>
  <Marked_take(s(M),cons(N,IL)) , Marked_uTake2(and(isNat(M),
                                                 and(isNat(N),
                                                  isNatIList(activate(IL)))),
                                   M,N,activate(IL))> 
     --> <Marked_uTake2(tt,M,N,IL) , Marked_activate(IL)>
  <Marked_take(s(M),cons(N,IL)) , Marked_uTake2(and(isNat(M),
                                                 and(isNat(N),
                                                  isNatIList(activate(IL)))),
                                   M,N,activate(IL))> 
     --> <Marked_uTake2(tt,M,N,IL) , Marked_activate(M)>
  <Marked_take(s(M),cons(N,IL)) , Marked_uTake2(and(isNat(M),
                                                 and(isNat(N),
                                                  isNatIList(activate(IL)))),
                                   M,N,activate(IL))> 
     --> <Marked_uTake2(tt,M,N,IL) , Marked_activate(N)>
  <Marked_take(0,IL) , Marked_isNatIList(IL)> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_activate(IL)>
  <Marked_take(0,IL) , Marked_isNatIList(IL)> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_isNatIList(activate(IL))>
  <Marked_take(0,IL) , Marked_isNatIList(IL)> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_activate(N)>
  <Marked_take(0,IL) , Marked_isNatIList(IL)> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_isNat(activate(N))>
  <Marked_take(0,IL) , Marked_isNatIList(IL)> 
     --> <Marked_isNatIList(IL) , Marked_activate(IL)>
  <Marked_take(0,IL) , Marked_isNatIList(IL)> 
     --> <Marked_isNatIList(IL) , Marked_isNatList(activate(IL))>
  <Marked_isNatList(n__take(N,IL)) , Marked_activate(IL)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_isNatList(n__take(N,IL)) , Marked_activate(IL)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_isNatList(n__take(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_activate(IL)>
  <Marked_isNatList(n__take(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_isNatIList(activate(IL))>
  <Marked_isNatList(n__take(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_activate(N)>
  <Marked_isNatList(n__take(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_isNat(activate(N))>
  <Marked_isNatList(n__take(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(IL) , Marked_activate(IL)>
  <Marked_isNatList(n__take(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(IL) , Marked_isNatList(activate(IL))>
  <Marked_isNatList(n__take(N,IL)) , Marked_activate(N)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_isNatList(n__take(N,IL)) , Marked_activate(N)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_isNatList(n__take(N,IL)) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__length(L)) , Marked_activate(L)>
  <Marked_isNatList(n__take(N,IL)) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__length(L)) , Marked_isNatList(activate(L))>
  <Marked_isNatList(n__take(N,IL)) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__s(N)) , Marked_activate(N)>
  <Marked_isNatList(n__take(N,IL)) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__s(N)) , Marked_isNat(activate(N))>
  <Marked_isNatList(n__cons(N,L)) , Marked_activate(L)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_isNatList(n__cons(N,L)) , Marked_activate(L)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_isNatList(n__cons(N,L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__take(N,IL)) , Marked_activate(IL)>
  <Marked_isNatList(n__cons(N,L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__take(N,IL)) , Marked_isNatIList(activate(IL))>
  <Marked_isNatList(n__cons(N,L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__take(N,IL)) , Marked_activate(N)>
  <Marked_isNatList(n__cons(N,L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__take(N,IL)) , Marked_isNat(activate(N))>
  <Marked_isNatList(n__cons(N,L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__cons(N,L)) , Marked_activate(L)>
  <Marked_isNatList(n__cons(N,L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__cons(N,L)) , Marked_isNatList(activate(L))>
  <Marked_isNatList(n__cons(N,L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__cons(N,L)) , Marked_activate(N)>
  <Marked_isNatList(n__cons(N,L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__cons(N,L)) , Marked_isNat(activate(N))>
  <Marked_isNatList(n__cons(N,L)) , Marked_activate(N)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_isNatList(n__cons(N,L)) , Marked_activate(N)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_isNatList(n__cons(N,L)) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__length(L)) , Marked_activate(L)>
  <Marked_isNatList(n__cons(N,L)) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__length(L)) , Marked_isNatList(activate(L))>
  <Marked_isNatList(n__cons(N,L)) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__s(N)) , Marked_activate(N)>
  <Marked_isNatList(n__cons(N,L)) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__s(N)) , Marked_isNat(activate(N))>
  <Marked_isNatIList(n__cons(N,IL)) , Marked_activate(IL)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_isNatIList(n__cons(N,IL)) , Marked_activate(IL)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_isNatIList(n__cons(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_activate(IL)>
  <Marked_isNatIList(n__cons(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_isNatIList(activate(IL))>
  <Marked_isNatIList(n__cons(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_activate(N)>
  <Marked_isNatIList(n__cons(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_isNat(activate(N))>
  <Marked_isNatIList(n__cons(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(IL) , Marked_activate(IL)>
  <Marked_isNatIList(n__cons(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(IL) , Marked_isNatList(activate(IL))>
  <Marked_isNatIList(n__cons(N,IL)) , Marked_activate(N)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_isNatIList(n__cons(N,IL)) , Marked_activate(N)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_isNatIList(n__cons(N,IL)) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__length(L)) , Marked_activate(L)>
  <Marked_isNatIList(n__cons(N,IL)) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__length(L)) , Marked_isNatList(activate(L))>
  <Marked_isNatIList(n__cons(N,IL)) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__s(N)) , Marked_activate(N)>
  <Marked_isNatIList(n__cons(N,IL)) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__s(N)) , Marked_isNat(activate(N))>
  <Marked_isNat(n__length(L)) , Marked_activate(L)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_isNat(n__length(L)) , Marked_activate(L)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_isNat(n__length(L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__take(N,IL)) , Marked_activate(IL)>
  <Marked_isNat(n__length(L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__take(N,IL)) , Marked_isNatIList(activate(IL))>
  <Marked_isNat(n__length(L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__take(N,IL)) , Marked_activate(N)>
  <Marked_isNat(n__length(L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__take(N,IL)) , Marked_isNat(activate(N))>
  <Marked_isNat(n__length(L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__cons(N,L)) , Marked_activate(L)>
  <Marked_isNat(n__length(L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__cons(N,L)) , Marked_isNatList(activate(L))>
  <Marked_isNat(n__length(L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__cons(N,L)) , Marked_activate(N)>
  <Marked_isNat(n__length(L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__cons(N,L)) , Marked_isNat(activate(N))>
  <Marked_isNat(n__s(N)) , Marked_activate(N)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_isNat(n__s(N)) , Marked_activate(N)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_isNat(n__s(N)) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__length(L)) , Marked_activate(L)>
  <Marked_isNat(n__s(N)) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__length(L)) , Marked_isNatList(activate(L))>
  <Marked_isNat(n__s(N)) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__s(N)) , Marked_activate(N)>
  <Marked_isNat(n__s(N)) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__s(N)) , Marked_isNat(activate(N))>
  <Marked_isNatIList(IL) , Marked_activate(IL)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_isNatIList(IL) , Marked_activate(IL)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_isNatIList(IL) , Marked_isNatList(activate(IL))> 
     --> <Marked_isNatList(n__take(N,IL)) , Marked_activate(IL)>
  <Marked_isNatIList(IL) , Marked_isNatList(activate(IL))> 
     --> <Marked_isNatList(n__take(N,IL)) , Marked_isNatIList(activate(IL))>
  <Marked_isNatIList(IL) , Marked_isNatList(activate(IL))> 
     --> <Marked_isNatList(n__take(N,IL)) , Marked_activate(N)>
  <Marked_isNatIList(IL) , Marked_isNatList(activate(IL))> 
     --> <Marked_isNatList(n__take(N,IL)) , Marked_isNat(activate(N))>
  <Marked_isNatIList(IL) , Marked_isNatList(activate(IL))> 
     --> <Marked_isNatList(n__cons(N,L)) , Marked_activate(L)>
  <Marked_isNatIList(IL) , Marked_isNatList(activate(IL))> 
     --> <Marked_isNatList(n__cons(N,L)) , Marked_isNatList(activate(L))>
  <Marked_isNatIList(IL) , Marked_isNatList(activate(IL))> 
     --> <Marked_isNatList(n__cons(N,L)) , Marked_activate(N)>
  <Marked_isNatIList(IL) , Marked_isNatList(activate(IL))> 
     --> <Marked_isNatList(n__cons(N,L)) , Marked_isNat(activate(N))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  and(tt,T) >= T ;
  isNatList(n__cons(N,L)) >= and(isNat(activate(N)),isNatList(activate(L))) ;
  isNatList(n__nil) >= tt ;
  isNatList(n__take(N,IL)) >= and(isNat(activate(N)),isNatIList(activate(IL))) ;
  activate(n__0) >= 0 ;
  activate(n__s(X)) >= s(X) ;
  activate(n__length(X)) >= length(X) ;
  activate(n__zeros) >= zeros ;
  activate(n__cons(X1,X2)) >= cons(X1,X2) ;
  activate(n__nil) >= nil ;
  activate(n__take(X1,X2)) >= take(X1,X2) ;
  activate(X) >= X ;
  isNatIList(n__zeros) >= tt ;
  isNatIList(n__cons(N,IL)) >= and(isNat(activate(N)),isNatIList(activate(IL))) ;
  isNatIList(IL) >= isNatList(activate(IL)) ;
  isNat(n__0) >= tt ;
  isNat(n__s(N)) >= isNat(activate(N)) ;
  isNat(n__length(L)) >= isNatList(activate(L)) ;
  cons(X1,X2) >= n__cons(X1,X2) ;
  0 >= n__0 ;
  zeros >= n__zeros ;
  zeros >= cons(0,n__zeros) ;
  uTake1(tt) >= nil ;
  take(0,IL) >= uTake1(isNatIList(IL)) ;
  take(s(M),cons(N,IL)) >= uTake2(and(isNat(M),
                                   and(isNat(N),isNatIList(activate(IL)))),
                            M,N,activate(IL)) ;
  take(X1,X2) >= n__take(X1,X2) ;
  nil >= n__nil ;
  uTake2(tt,M,N,IL) >= cons(activate(N),n__take(activate(M),activate(IL))) ;
  s(X) >= n__s(X) ;
  uLength(tt,L) >= s(length(activate(L))) ;
  length(cons(N,L)) >= uLength(and(isNat(N),isNatList(activate(L))),
                        activate(L)) ;
  length(X) >= n__length(X) ;
  Marked_activate(n__length(X)) >= Marked_length(X) ;
  Marked_activate(n__take(X1,X2)) >= Marked_take(X1,X2) ;
  Marked_take(0,IL) >= Marked_isNatIList(IL) ;
  Marked_take(s(M),cons(N,IL)) >= Marked_activate(IL) ;
  Marked_take(s(M),cons(N,IL)) >= Marked_isNat(N) ;
  Marked_take(s(M),cons(N,IL)) >= Marked_isNat(M) ;
  Marked_take(s(M),cons(N,IL)) >= Marked_uTake2(and(isNat(M),
                                                 and(isNat(N),
                                                  isNatIList(activate(IL)))),
                                   M,N,activate(IL)) ;
  Marked_take(s(M),cons(N,IL)) >= Marked_isNatIList(activate(IL)) ;
  Marked_length(cons(N,L)) >= Marked_activate(L) ;
  Marked_length(cons(N,L)) >= Marked_uLength(and(isNat(N),
                                              isNatList(activate(L))),
                               activate(L)) ;
  Marked_length(cons(N,L)) >= Marked_isNat(N) ;
  Marked_length(cons(N,L)) >= Marked_isNatList(activate(L)) ;
  Marked_uLength(tt,L) >= Marked_activate(L) ;
  Marked_uLength(tt,L) >= Marked_length(activate(L)) ;
  Marked_isNat(n__s(N)) >= Marked_activate(N) ;
  Marked_isNat(n__s(N)) >= Marked_isNat(activate(N)) ;
  Marked_isNat(n__length(L)) >= Marked_activate(L) ;
  Marked_isNat(n__length(L)) >= Marked_isNatList(activate(L)) ;
  Marked_isNatList(n__cons(N,L)) >= Marked_activate(N) ;
  Marked_isNatList(n__cons(N,L)) >= Marked_activate(L) ;
  Marked_isNatList(n__cons(N,L)) >= Marked_isNat(activate(N)) ;
  Marked_isNatList(n__cons(N,L)) >= Marked_isNatList(activate(L)) ;
  Marked_isNatList(n__take(N,IL)) >= Marked_activate(IL) ;
  Marked_isNatList(n__take(N,IL)) >= Marked_activate(N) ;
  Marked_isNatList(n__take(N,IL)) >= Marked_isNat(activate(N)) ;
  Marked_isNatList(n__take(N,IL)) >= Marked_isNatIList(activate(IL)) ;
  Marked_uTake2(tt,M,N,IL) >= Marked_activate(IL) ;
  Marked_uTake2(tt,M,N,IL) >= Marked_activate(N) ;
  Marked_uTake2(tt,M,N,IL) >= Marked_activate(M) ;
  Marked_isNatIList(n__cons(N,IL)) >= Marked_activate(IL) ;
  Marked_isNatIList(n__cons(N,IL)) >= Marked_activate(N) ;
  Marked_isNatIList(n__cons(N,IL)) >= Marked_isNat(activate(N)) ;
  Marked_isNatIList(n__cons(N,IL)) >= Marked_isNatIList(activate(IL)) ;
  Marked_isNatIList(IL) >= Marked_activate(IL) ;
  Marked_isNatIList(IL) >= Marked_isNatList(activate(IL)) ;
 }
 + Disjunctions:{ 
{
  Marked_activate(n__length(X)) > Marked_length(X) ;
 }
{
  Marked_activate(n__take(X1,X2)) > Marked_take(X1,X2) ;
 }
{
  Marked_take(0,IL) > Marked_isNatIList(IL) ;
 }
{
  Marked_take(s(M),cons(N,IL)) > Marked_activate(IL) ;
 }
{
  Marked_take(s(M),cons(N,IL)) > Marked_isNat(N) ;
 }
{
  Marked_take(s(M),cons(N,IL)) > Marked_isNat(M) ;
 }
{
  Marked_take(s(M),cons(N,IL)) > Marked_uTake2(and(isNat(M),
                                                and(isNat(N),
                                                 isNatIList(activate(IL)))),
                                  M,N,activate(IL)) ;
 }
{
  Marked_take(s(M),cons(N,IL)) > Marked_isNatIList(activate(IL)) ;
 }
{
  Marked_length(cons(N,L)) > Marked_activate(L) ;
 }
{
  Marked_length(cons(N,L)) > Marked_uLength(and(isNat(N),
                                             isNatList(activate(L))),
                              activate(L)) ;
 }
{
  Marked_length(cons(N,L)) > Marked_isNat(N) ;
 }
{
  Marked_length(cons(N,L)) > Marked_isNatList(activate(L)) ;
 }
{
  Marked_uLength(tt,L) > Marked_activate(L) ;
 }
{
  Marked_uLength(tt,L) > Marked_length(activate(L)) ;
 }
{
  Marked_isNat(n__s(N)) > Marked_activate(N) ;
 }
{
  Marked_isNat(n__s(N)) > Marked_isNat(activate(N)) ;
 }
{
  Marked_isNat(n__length(L)) > Marked_activate(L) ;
 }
{
  Marked_isNat(n__length(L)) > Marked_isNatList(activate(L)) ;
 }
{
  Marked_isNatList(n__cons(N,L)) > Marked_activate(N) ;
 }
{
  Marked_isNatList(n__cons(N,L)) > Marked_activate(L) ;
 }
{
  Marked_isNatList(n__cons(N,L)) > Marked_isNat(activate(N)) ;
 }
{
  Marked_isNatList(n__cons(N,L)) > Marked_isNatList(activate(L)) ;
 }
{
  Marked_isNatList(n__take(N,IL)) > Marked_activate(IL) ;
 }
{
  Marked_isNatList(n__take(N,IL)) > Marked_activate(N) ;
 }
{
  Marked_isNatList(n__take(N,IL)) > Marked_isNat(activate(N)) ;
 }
{
  Marked_isNatList(n__take(N,IL)) > Marked_isNatIList(activate(IL)) ;
 }
{
  Marked_uTake2(tt,M,N,IL) > Marked_activate(IL) ;
 }
{
  Marked_uTake2(tt,M,N,IL) > Marked_activate(N) ;
 }
{
  Marked_uTake2(tt,M,N,IL) > Marked_activate(M) ;
 }
{
  Marked_isNatIList(n__cons(N,IL)) > Marked_activate(IL) ;
 }
{
  Marked_isNatIList(n__cons(N,IL)) > Marked_activate(N) ;
 }
{
  Marked_isNatIList(n__cons(N,IL)) > Marked_isNat(activate(N)) ;
 }
{
  Marked_isNatIList(n__cons(N,IL)) > Marked_isNatIList(activate(IL)) ;
 }
{
  Marked_isNatIList(IL) > Marked_activate(IL) ;
 }
{
  Marked_isNatIList(IL) > Marked_isNatList(activate(IL)) ;
 }
 } 
=== 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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: and(tt,T) >= T
constraint: isNatList(n__cons(N,L)) >= and(isNat(activate(N)),
                                        isNatList(activate(L)))
constraint: isNatList(n__nil) >= tt
constraint: isNatList(n__take(N,IL)) >= and(isNat(activate(N)),
                                         isNatIList(activate(IL)))
constraint: activate(n__0) >= 0
constraint: activate(n__s(X)) >= s(X)
constraint: activate(n__length(X)) >= length(X)
constraint: activate(n__zeros) >= zeros
constraint: activate(n__cons(X1,X2)) >= cons(X1,X2)
constraint: activate(n__nil) >= nil
constraint: activate(n__take(X1,X2)) >= take(X1,X2)
constraint: activate(X) >= X
constraint: isNatIList(n__zeros) >= tt
constraint: isNatIList(n__cons(N,IL)) >= and(isNat(activate(N)),
                                          isNatIList(activate(IL)))
constraint: isNatIList(IL) >= isNatList(activate(IL))
constraint: isNat(n__0) >= tt
constraint: isNat(n__s(N)) >= isNat(activate(N))
constraint: isNat(n__length(L)) >= isNatList(activate(L))
constraint: cons(X1,X2) >= n__cons(X1,X2)
constraint: 0 >= n__0
constraint: zeros >= n__zeros
constraint: zeros >= cons(0,n__zeros)
constraint: uTake1(tt) >= nil
constraint: take(0,IL) >= uTake1(isNatIList(IL))
constraint: take(s(M),cons(N,IL)) >= uTake2(and(isNat(M),
                                             and(isNat(N),
                                              isNatIList(activate(IL)))),
                                      M,N,activate(IL))
constraint: take(X1,X2) >= n__take(X1,X2)
constraint: nil >= n__nil
constraint: uTake2(tt,M,N,IL) >= cons(activate(N),
                                  n__take(activate(M),activate(IL)))
constraint: s(X) >= n__s(X)
constraint: uLength(tt,L) >= s(length(activate(L)))
constraint: length(cons(N,L)) >= uLength(and(isNat(N),isNatList(activate(L))),
                                  activate(L))
constraint: length(X) >= n__length(X)
constraint: Marked_activate(n__length(X)) >= Marked_length(X)
constraint: Marked_activate(n__take(X1,X2)) >= Marked_take(X1,X2)
constraint: Marked_take(0,IL) >= Marked_isNatIList(IL)
constraint: Marked_take(s(M),cons(N,IL)) >= Marked_activate(IL)
constraint: Marked_take(s(M),cons(N,IL)) >= Marked_isNat(N)
constraint: Marked_take(s(M),cons(N,IL)) >= Marked_isNat(M)
constraint: Marked_take(s(M),cons(N,IL)) >= Marked_uTake2(and(isNat(M),
                                                           and(isNat(N),
                                                            isNatIList(
                                                             activate(
                                                              IL)))),
                                             M,N,activate(IL))
constraint: Marked_take(s(M),cons(N,IL)) >= Marked_isNatIList(activate(IL))
constraint: Marked_length(cons(N,L)) >= Marked_activate(L)
constraint: Marked_length(cons(N,L)) >= Marked_uLength(and(isNat(N),
                                                        isNatList(activate(L))),
                                         activate(L))
constraint: Marked_length(cons(N,L)) >= Marked_isNat(N)
constraint: Marked_length(cons(N,L)) >= Marked_isNatList(activate(L))
constraint: Marked_uLength(tt,L) >= Marked_activate(L)
constraint: Marked_uLength(tt,L) >= Marked_length(activate(L))
constraint: Marked_isNat(n__s(N)) >= Marked_activate(N)
constraint: Marked_isNat(n__s(N)) >= Marked_isNat(activate(N))
constraint: Marked_isNat(n__length(L)) >= Marked_activate(L)
constraint: Marked_isNat(n__length(L)) >= Marked_isNatList(activate(L))
constraint: Marked_isNatList(n__cons(N,L)) >= Marked_activate(N)
constraint: Marked_isNatList(n__cons(N,L)) >= Marked_activate(L)
constraint: Marked_isNatList(n__cons(N,L)) >= Marked_isNat(activate(N))
constraint: Marked_isNatList(n__cons(N,L)) >= Marked_isNatList(activate(L))
constraint: Marked_isNatList(n__take(N,IL)) >= Marked_activate(IL)
constraint: Marked_isNatList(n__take(N,IL)) >= Marked_activate(N)
constraint: Marked_isNatList(n__take(N,IL)) >= Marked_isNat(activate(N))
constraint: Marked_isNatList(n__take(N,IL)) >= Marked_isNatIList(activate(IL))
constraint: Marked_uTake2(tt,M,N,IL) >= Marked_activate(IL)
constraint: Marked_uTake2(tt,M,N,IL) >= Marked_activate(N)
constraint: Marked_uTake2(tt,M,N,IL) >= Marked_activate(M)
constraint: Marked_isNatIList(n__cons(N,IL)) >= Marked_activate(IL)
constraint: Marked_isNatIList(n__cons(N,IL)) >= Marked_activate(N)
constraint: Marked_isNatIList(n__cons(N,IL)) >= Marked_isNat(activate(N))
constraint: Marked_isNatIList(n__cons(N,IL)) >= Marked_isNatIList(activate(IL))
constraint: Marked_isNatIList(IL) >= Marked_activate(IL)
constraint: Marked_isNatIList(IL) >= Marked_isNatList(activate(IL))
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_uLength(tt,L) , Marked_length(activate(L))> 
      --> <Marked_length(cons(N,L)) , Marked_uLength(and(isNat(N),
                                                      isNatList(activate(L))),
                                       activate(L))>
  <Marked_length(cons(N,L)) , Marked_uLength(and(isNat(N),
                                              isNatList(activate(L))),
                               activate(L))> 
     --> <Marked_uLength(tt,L) , Marked_length(activate(L))>
}

{  <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)> 
      --> <Marked_take(s(M),cons(N,IL)) , Marked_activate(IL)>
  <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(s(M),cons(N,IL)) , Marked_activate(IL)>
  <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(s(M),cons(N,IL)) , Marked_isNatIList(activate(IL))>
  <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(s(M),cons(N,IL)) , Marked_isNat(N)>
  <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(s(M),cons(N,IL)) , Marked_isNat(M)>
  <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(s(M),cons(N,IL)) , Marked_uTake2(and(isNat(M),
                                                        and(isNat(N),
                                                         isNatIList(activate(
                                                                    IL)))),
                                          M,N,activate(IL))>
  <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(0,IL) , Marked_isNatIList(IL)>
  <Marked_uTake2(tt,M,N,IL) , Marked_activate(IL)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_uTake2(tt,M,N,IL) , Marked_activate(M)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_uTake2(tt,M,N,IL) , Marked_activate(N)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_take(s(M),cons(N,IL)) , Marked_activate(IL)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_take(s(M),cons(N,IL)) , Marked_activate(IL)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_take(s(M),cons(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_activate(IL)>
  <Marked_take(s(M),cons(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_isNatIList(activate(IL))>
  <Marked_take(s(M),cons(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_activate(N)>
  <Marked_take(s(M),cons(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_isNat(activate(N))>
  <Marked_take(s(M),cons(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(IL) , Marked_activate(IL)>
  <Marked_take(s(M),cons(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(IL) , Marked_isNatList(activate(IL))>
  <Marked_take(s(M),cons(N,IL)) , Marked_isNat(N)> 
     --> <Marked_isNat(n__s(N)) , Marked_activate(N)>
  <Marked_take(s(M),cons(N,IL)) , Marked_isNat(N)> 
     --> <Marked_isNat(n__s(N)) , Marked_isNat(activate(N))>
  <Marked_take(s(M),cons(N,IL)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__s(N)) , Marked_activate(N)>
  <Marked_take(s(M),cons(N,IL)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__s(N)) , Marked_isNat(activate(N))>
  <Marked_take(s(M),cons(N,IL)) , Marked_uTake2(and(isNat(M),
                                                 and(isNat(N),
                                                  isNatIList(activate(IL)))),
                                   M,N,activate(IL))> 
     --> <Marked_uTake2(tt,M,N,IL) , Marked_activate(IL)>
  <Marked_take(s(M),cons(N,IL)) , Marked_uTake2(and(isNat(M),
                                                 and(isNat(N),
                                                  isNatIList(activate(IL)))),
                                   M,N,activate(IL))> 
     --> <Marked_uTake2(tt,M,N,IL) , Marked_activate(M)>
  <Marked_take(s(M),cons(N,IL)) , Marked_uTake2(and(isNat(M),
                                                 and(isNat(N),
                                                  isNatIList(activate(IL)))),
                                   M,N,activate(IL))> 
     --> <Marked_uTake2(tt,M,N,IL) , Marked_activate(N)>
  <Marked_take(0,IL) , Marked_isNatIList(IL)> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_activate(IL)>
  <Marked_take(0,IL) , Marked_isNatIList(IL)> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_isNatIList(activate(IL))>
  <Marked_take(0,IL) , Marked_isNatIList(IL)> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_activate(N)>
  <Marked_take(0,IL) , Marked_isNatIList(IL)> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_isNat(activate(N))>
  <Marked_take(0,IL) , Marked_isNatIList(IL)> 
     --> <Marked_isNatIList(IL) , Marked_activate(IL)>
  <Marked_take(0,IL) , Marked_isNatIList(IL)> 
     --> <Marked_isNatIList(IL) , Marked_isNatList(activate(IL))>
  <Marked_isNatList(n__take(N,IL)) , Marked_activate(IL)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_isNatList(n__take(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_activate(IL)>
  <Marked_isNatList(n__take(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_isNatIList(activate(IL))>
  <Marked_isNatList(n__take(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_activate(N)>
  <Marked_isNatList(n__take(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_isNat(activate(N))>
  <Marked_isNatList(n__take(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(IL) , Marked_activate(IL)>
  <Marked_isNatList(n__take(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(IL) , Marked_isNatList(activate(IL))>
  <Marked_isNatList(n__take(N,IL)) , Marked_activate(N)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_isNatList(n__take(N,IL)) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__s(N)) , Marked_activate(N)>
  <Marked_isNatList(n__take(N,IL)) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__s(N)) , Marked_isNat(activate(N))>
  <Marked_isNatList(n__cons(N,L)) , Marked_activate(L)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_isNatList(n__cons(N,L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__take(N,IL)) , Marked_activate(IL)>
  <Marked_isNatList(n__cons(N,L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__take(N,IL)) , Marked_isNatIList(activate(IL))>
  <Marked_isNatList(n__cons(N,L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__take(N,IL)) , Marked_activate(N)>
  <Marked_isNatList(n__cons(N,L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__take(N,IL)) , Marked_isNat(activate(N))>
  <Marked_isNatList(n__cons(N,L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__cons(N,L)) , Marked_activate(L)>
  <Marked_isNatList(n__cons(N,L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__cons(N,L)) , Marked_isNatList(activate(L))>
  <Marked_isNatList(n__cons(N,L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__cons(N,L)) , Marked_activate(N)>
  <Marked_isNatList(n__cons(N,L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__cons(N,L)) , Marked_isNat(activate(N))>
  <Marked_isNatList(n__cons(N,L)) , Marked_activate(N)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_isNatList(n__cons(N,L)) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__s(N)) , Marked_activate(N)>
  <Marked_isNatList(n__cons(N,L)) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__s(N)) , Marked_isNat(activate(N))>
  <Marked_isNatIList(n__cons(N,IL)) , Marked_activate(IL)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_isNatIList(n__cons(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_activate(IL)>
  <Marked_isNatIList(n__cons(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_isNatIList(activate(IL))>
  <Marked_isNatIList(n__cons(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_activate(N)>
  <Marked_isNatIList(n__cons(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(n__cons(N,IL)) , Marked_isNat(activate(N))>
  <Marked_isNatIList(n__cons(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(IL) , Marked_activate(IL)>
  <Marked_isNatIList(n__cons(N,IL)) , Marked_isNatIList(activate(IL))> 
     --> <Marked_isNatIList(IL) , Marked_isNatList(activate(IL))>
  <Marked_isNatIList(n__cons(N,IL)) , Marked_activate(N)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_isNatIList(n__cons(N,IL)) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__s(N)) , Marked_activate(N)>
  <Marked_isNatIList(n__cons(N,IL)) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__s(N)) , Marked_isNat(activate(N))>
  <Marked_isNat(n__s(N)) , Marked_activate(N)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_isNat(n__s(N)) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__s(N)) , Marked_activate(N)>
  <Marked_isNat(n__s(N)) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__s(N)) , Marked_isNat(activate(N))>
  <Marked_isNatIList(IL) , Marked_activate(IL)> 
     --> <Marked_activate(n__take(X1,X2)) , Marked_take(X1,X2)>
  <Marked_isNatIList(IL) , Marked_isNatList(activate(IL))> 
     --> <Marked_isNatList(n__take(N,IL)) , Marked_activate(IL)>
  <Marked_isNatIList(IL) , Marked_isNatList(activate(IL))> 
     --> <Marked_isNatList(n__take(N,IL)) , Marked_isNatIList(activate(IL))>
  <Marked_isNatIList(IL) , Marked_isNatList(activate(IL))> 
     --> <Marked_isNatList(n__take(N,IL)) , Marked_activate(N)>
  <Marked_isNatIList(IL) , Marked_isNatList(activate(IL))> 
     --> <Marked_isNatList(n__take(N,IL)) , Marked_isNat(activate(N))>
  <Marked_isNatIList(IL) , Marked_isNatList(activate(IL))> 
     --> <Marked_isNatList(n__cons(N,L)) , Marked_activate(L)>
  <Marked_isNatIList(IL) , Marked_isNatList(activate(IL))> 
     --> <Marked_isNatList(n__cons(N,L)) , Marked_isNatList(activate(L))>
  <Marked_isNatIList(IL) , Marked_isNatList(activate(IL))> 
     --> <Marked_isNatList(n__cons(N,L)) , Marked_activate(N)>
  <Marked_isNatIList(IL) , Marked_isNatList(activate(IL))> 
     --> <Marked_isNatList(n__cons(N,L)) , Marked_isNat(activate(N))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  and(tt,T) >= T ;
  isNatList(n__cons(N,L)) >= and(isNat(activate(N)),isNatList(activate(L))) ;
  isNatList(n__nil) >= tt ;
  isNatList(n__take(N,IL)) >= and(isNat(activate(N)),isNatIList(activate(IL))) ;
  activate(n__0) >= 0 ;
  activate(n__s(X)) >= s(X) ;
  activate(n__length(X)) >= length(X) ;
  activate(n__zeros) >= zeros ;
  activate(n__cons(X1,X2)) >= cons(X1,X2) ;
  activate(n__nil) >= nil ;
  activate(n__take(X1,X2)) >= take(X1,X2) ;
  activate(X) >= X ;
  isNatIList(n__zeros) >= tt ;
  isNatIList(n__cons(N,IL)) >= and(isNat(activate(N)),isNatIList(activate(IL))) ;
  isNatIList(IL) >= isNatList(activate(IL)) ;
  isNat(n__0) >= tt ;
  isNat(n__s(N)) >= isNat(activate(N)) ;
  isNat(n__length(L)) >= isNatList(activate(L)) ;
  cons(X1,X2) >= n__cons(X1,X2) ;
  0 >= n__0 ;
  zeros >= n__zeros ;
  zeros >= cons(0,n__zeros) ;
  uTake1(tt) >= nil ;
  take(0,IL) >= uTake1(isNatIList(IL)) ;
  take(s(M),cons(N,IL)) >= uTake2(and(isNat(M),
                                   and(isNat(N),isNatIList(activate(IL)))),
                            M,N,activate(IL)) ;
  take(X1,X2) >= n__take(X1,X2) ;
  nil >= n__nil ;
  uTake2(tt,M,N,IL) >= cons(activate(N),n__take(activate(M),activate(IL))) ;
  s(X) >= n__s(X) ;
  uLength(tt,L) >= s(length(activate(L))) ;
  length(cons(N,L)) >= uLength(and(isNat(N),isNatList(activate(L))),
                        activate(L)) ;
  length(X) >= n__length(X) ;
  Marked_length(cons(N,L)) >= Marked_uLength(and(isNat(N),
                                              isNatList(activate(L))),
                               activate(L)) ;
  Marked_uLength(tt,L) >= Marked_length(activate(L)) ;
 }
 + Disjunctions:{ 
{
  Marked_length(cons(N,L)) > Marked_uLength(and(isNat(N),
                                             isNatList(activate(L))),
                              activate(L)) ;
 }
{
  Marked_uLength(tt,L) > Marked_length(activate(L)) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
Time out for these parameters.
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: and(tt,T) >= T
constraint: isNatList(n__cons(N,L)) >= and(isNat(activate(N)),
                                        isNatList(activate(L)))
constraint: isNatList(n__nil) >= tt
constraint: isNatList(n__take(N,IL)) >= and(isNat(activate(N)),
                                         isNatIList(activate(IL)))
constraint: activate(n__0) >= 0
constraint: activate(n__s(X)) >= s(X)
constraint: activate(n__length(X)) >= length(X)
constraint: activate(n__zeros) >= zeros
constraint: activate(n__cons(X1,X2)) >= cons(X1,X2)
constraint: activate(n__nil) >= nil
constraint: activate(n__take(X1,X2)) >= take(X1,X2)
constraint: activate(X) >= X
constraint: isNatIList(n__zeros) >= tt
constraint: isNatIList(n__cons(N,IL)) >= and(isNat(activate(N)),
                                          isNatIList(activate(IL)))
constraint: isNatIList(IL) >= isNatList(activate(IL))
constraint: isNat(n__0) >= tt
constraint: isNat(n__s(N)) >= isNat(activate(N))
constraint: isNat(n__length(L)) >= isNatList(activate(L))
constraint: cons(X1,X2) >= n__cons(X1,X2)
constraint: 0 >= n__0
constraint: zeros >= n__zeros
constraint: zeros >= cons(0,n__zeros)
constraint: uTake1(tt) >= nil
constraint: take(0,IL) >= uTake1(isNatIList(IL))
constraint: take(s(M),cons(N,IL)) >= uTake2(and(isNat(M),
                                             and(isNat(N),
                                              isNatIList(activate(IL)))),
                                      M,N,activate(IL))
constraint: take(X1,X2) >= n__take(X1,X2)
constraint: nil >= n__nil
constraint: uTake2(tt,M,N,IL) >= cons(activate(N),
                                  n__take(activate(M),activate(IL)))
constraint: s(X) >= n__s(X)
constraint: uLength(tt,L) >= s(length(activate(L)))
constraint: length(cons(N,L)) >= uLength(and(isNat(N),isNatList(activate(L))),
                                  activate(L))
constraint: length(X) >= n__length(X)
constraint: Marked_length(cons(N,L)) >= Marked_uLength(and(isNat(N),
                                                        isNatList(activate(L))),
                                         activate(L))
constraint: Marked_uLength(tt,L) >= Marked_length(activate(L))
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  and(tt,T) >= T ;
  isNatList(n__cons(N,L)) >= and(isNat(activate(N)),isNatList(activate(L))) ;
  isNatList(n__nil) >= tt ;
  isNatList(n__take(N,IL)) >= and(isNat(activate(N)),isNatIList(activate(IL))) ;
  activate(n__0) >= 0 ;
  activate(n__s(X)) >= s(X) ;
  activate(n__length(X)) >= length(X) ;
  activate(n__zeros) >= zeros ;
  activate(n__cons(X1,X2)) >= cons(X1,X2) ;
  activate(n__nil) >= nil ;
  activate(n__take(X1,X2)) >= take(X1,X2) ;
  activate(X) >= X ;
  isNatIList(n__zeros) >= tt ;
  isNatIList(n__cons(N,IL)) >= and(isNat(activate(N)),isNatIList(activate(IL))) ;
  isNatIList(IL) >= isNatList(activate(IL)) ;
  isNat(n__0) >= tt ;
  isNat(n__s(N)) >= isNat(activate(N)) ;
  isNat(n__length(L)) >= isNatList(activate(L)) ;
  cons(X1,X2) >= n__cons(X1,X2) ;
  0 >= n__0 ;
  zeros >= n__zeros ;
  zeros >= cons(0,n__zeros) ;
  uTake1(tt) >= nil ;
  take(0,IL) >= uTake1(isNatIList(IL)) ;
  take(s(M),cons(N,IL)) >= uTake2(and(isNat(M),
                                   and(isNat(N),isNatIList(activate(IL)))),
                            M,N,activate(IL)) ;
  take(X1,X2) >= n__take(X1,X2) ;
  nil >= n__nil ;
  uTake2(tt,M,N,IL) >= cons(activate(N),n__take(activate(M),activate(IL))) ;
  s(X) >= n__s(X) ;
  uLength(tt,L) >= s(length(activate(L))) ;
  length(cons(N,L)) >= uLength(and(isNat(N),isNatList(activate(L))),
                        activate(L)) ;
  length(X) >= n__length(X) ;
  Marked_activate(n__take(X1,X2)) >= Marked_take(X1,X2) ;
  Marked_take(0,IL) >= Marked_isNatIList(IL) ;
  Marked_take(s(M),cons(N,IL)) >= Marked_activate(IL) ;
  Marked_take(s(M),cons(N,IL)) >= Marked_isNat(N) ;
  Marked_take(s(M),cons(N,IL)) >= Marked_isNat(M) ;
  Marked_take(s(M),cons(N,IL)) >= Marked_uTake2(and(isNat(M),
                                                 and(isNat(N),
                                                  isNatIList(activate(IL)))),
                                   M,N,activate(IL)) ;
  Marked_take(s(M),cons(N,IL)) >= Marked_isNatIList(activate(IL)) ;
  Marked_isNat(n__s(N)) >= Marked_activate(N) ;
  Marked_isNat(n__s(N)) >= Marked_isNat(activate(N)) ;
  Marked_isNatList(n__cons(N,L)) >= Marked_activate(N) ;
  Marked_isNatList(n__cons(N,L)) >= Marked_activate(L) ;
  Marked_isNatList(n__cons(N,L)) >= Marked_isNat(activate(N)) ;
  Marked_isNatList(n__cons(N,L)) >= Marked_isNatList(activate(L)) ;
  Marked_isNatList(n__take(N,IL)) >= Marked_activate(IL) ;
  Marked_isNatList(n__take(N,IL)) >= Marked_activate(N) ;
  Marked_isNatList(n__take(N,IL)) >= Marked_isNat(activate(N)) ;
  Marked_isNatList(n__take(N,IL)) >= Marked_isNatIList(activate(IL)) ;
  Marked_uTake2(tt,M,N,IL) >= Marked_activate(IL) ;
  Marked_uTake2(tt,M,N,IL) >= Marked_activate(N) ;
  Marked_uTake2(tt,M,N,IL) >= Marked_activate(M) ;
  Marked_isNatIList(n__cons(N,IL)) >= Marked_activate(IL) ;
  Marked_isNatIList(n__cons(N,IL)) >= Marked_activate(N) ;
  Marked_isNatIList(n__cons(N,IL)) >= Marked_isNat(activate(N)) ;
  Marked_isNatIList(n__cons(N,IL)) >= Marked_isNatIList(activate(IL)) ;
  Marked_isNatIList(IL) >= Marked_activate(IL) ;
  Marked_isNatIList(IL) >= Marked_isNatList(activate(IL)) ;
 }
 + Disjunctions:{ 
{
  Marked_activate(n__take(X1,X2)) > Marked_take(X1,X2) ;
 }
{
  Marked_take(0,IL) > Marked_isNatIList(IL) ;
 }
{
  Marked_take(s(M),cons(N,IL)) > Marked_activate(IL) ;
 }
{
  Marked_take(s(M),cons(N,IL)) > Marked_isNat(N) ;
 }
{
  Marked_take(s(M),cons(N,IL)) > Marked_isNat(M) ;
 }
{
  Marked_take(s(M),cons(N,IL)) > Marked_uTake2(and(isNat(M),
                                                and(isNat(N),
                                                 isNatIList(activate(IL)))),
                                  M,N,activate(IL)) ;
 }
{
  Marked_take(s(M),cons(N,IL)) > Marked_isNatIList(activate(IL)) ;
 }
{
  Marked_isNat(n__s(N)) > Marked_activate(N) ;
 }
{
  Marked_isNat(n__s(N)) > Marked_isNat(activate(N)) ;
 }
{
  Marked_isNatList(n__cons(N,L)) > Marked_activate(N) ;
 }
{
  Marked_isNatList(n__cons(N,L)) > Marked_activate(L) ;
 }
{
  Marked_isNatList(n__cons(N,L)) > Marked_isNat(activate(N)) ;
 }
{
  Marked_isNatList(n__cons(N,L)) > Marked_isNatList(activate(L)) ;
 }
{
  Marked_isNatList(n__take(N,IL)) > Marked_activate(IL) ;
 }
{
  Marked_isNatList(n__take(N,IL)) > Marked_activate(N) ;
 }
{
  Marked_isNatList(n__take(N,IL)) > Marked_isNat(activate(N)) ;
 }
{
  Marked_isNatList(n__take(N,IL)) > Marked_isNatIList(activate(IL)) ;
 }
{
  Marked_uTake2(tt,M,N,IL) > Marked_activate(IL) ;
 }
{
  Marked_uTake2(tt,M,N,IL) > Marked_activate(N) ;
 }
{
  Marked_uTake2(tt,M,N,IL) > Marked_activate(M) ;
 }
{
  Marked_isNatIList(n__cons(N,IL)) > Marked_activate(IL) ;
 }
{
  Marked_isNatIList(n__cons(N,IL)) > Marked_activate(N) ;
 }
{
  Marked_isNatIList(n__cons(N,IL)) > Marked_isNat(activate(N)) ;
 }
{
  Marked_isNatIList(n__cons(N,IL)) > Marked_isNatIList(activate(IL)) ;
 }
{
  Marked_isNatIList(IL) > Marked_activate(IL) ;
 }
{
  Marked_isNatIList(IL) > Marked_isNatList(activate(IL)) ;
 }
 } 
=== 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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: and(tt,T) >= T
constraint: isNatList(n__cons(N,L)) >= and(isNat(activate(N)),
                                        isNatList(activate(L)))
constraint: isNatList(n__nil) >= tt
constraint: isNatList(n__take(N,IL)) >= and(isNat(activate(N)),
                                         isNatIList(activate(IL)))
constraint: activate(n__0) >= 0
constraint: activate(n__s(X)) >= s(X)
constraint: activate(n__length(X)) >= length(X)
constraint: activate(n__zeros) >= zeros
constraint: activate(n__cons(X1,X2)) >= cons(X1,X2)
constraint: activate(n__nil) >= nil
constraint: activate(n__take(X1,X2)) >= take(X1,X2)
constraint: activate(X) >= X
constraint: isNatIList(n__zeros) >= tt
constraint: isNatIList(n__cons(N,IL)) >= and(isNat(activate(N)),
                                          isNatIList(activate(IL)))
constraint: isNatIList(IL) >= isNatList(activate(IL))
constraint: isNat(n__0) >= tt
constraint: isNat(n__s(N)) >= isNat(activate(N))
constraint: isNat(n__length(L)) >= isNatList(activate(L))
constraint: cons(X1,X2) >= n__cons(X1,X2)
constraint: 0 >= n__0
constraint: zeros >= n__zeros
constraint: zeros >= cons(0,n__zeros)
constraint: uTake1(tt) >= nil
constraint: take(0,IL) >= uTake1(isNatIList(IL))
constraint: take(s(M),cons(N,IL)) >= uTake2(and(isNat(M),
                                             and(isNat(N),
                                              isNatIList(activate(IL)))),
                                      M,N,activate(IL))
constraint: take(X1,X2) >= n__take(X1,X2)
constraint: nil >= n__nil
constraint: uTake2(tt,M,N,IL) >= cons(activate(N),
                                  n__take(activate(M),activate(IL)))
constraint: s(X) >= n__s(X)
constraint: uLength(tt,L) >= s(length(activate(L)))
constraint: length(cons(N,L)) >= uLength(and(isNat(N),isNatList(activate(L))),
                                  activate(L))
constraint: length(X) >= n__length(X)
constraint: Marked_activate(n__take(X1,X2)) >= Marked_take(X1,X2)
constraint: Marked_take(0,IL) >= Marked_isNatIList(IL)
constraint: Marked_take(s(M),cons(N,IL)) >= Marked_activate(IL)
constraint: Marked_take(s(M),cons(N,IL)) >= Marked_isNat(N)
constraint: Marked_take(s(M),cons(N,IL)) >= Marked_isNat(M)
constraint: Marked_take(s(M),cons(N,IL)) >= Marked_uTake2(and(isNat(M),
                                                           and(isNat(N),
                                                            isNatIList(
                                                             activate(
                                                              IL)))),
                                             M,N,activate(IL))
constraint: Marked_take(s(M),cons(N,IL)) >= Marked_isNatIList(activate(IL))
constraint: Marked_isNat(n__s(N)) >= Marked_activate(N)
constraint: Marked_isNat(n__s(N)) >= Marked_isNat(activate(N))
constraint: Marked_isNatList(n__cons(N,L)) >= Marked_activate(N)
constraint: Marked_isNatList(n__cons(N,L)) >= Marked_activate(L)
constraint: Marked_isNatList(n__cons(N,L)) >= Marked_isNat(activate(N))
constraint: Marked_isNatList(n__cons(N,L)) >= Marked_isNatList(activate(L))
constraint: Marked_isNatList(n__take(N,IL)) >= Marked_activate(IL)
constraint: Marked_isNatList(n__take(N,IL)) >= Marked_activate(N)
constraint: Marked_isNatList(n__take(N,IL)) >= Marked_isNat(activate(N))
constraint: Marked_isNatList(n__take(N,IL)) >= Marked_isNatIList(activate(IL))
constraint: Marked_uTake2(tt,M,N,IL) >= Marked_activate(IL)
constraint: Marked_uTake2(tt,M,N,IL) >= Marked_activate(N)
constraint: Marked_uTake2(tt,M,N,IL) >= Marked_activate(M)
constraint: Marked_isNatIList(n__cons(N,IL)) >= Marked_activate(IL)
constraint: Marked_isNatIList(n__cons(N,IL)) >= Marked_activate(N)
constraint: Marked_isNatIList(n__cons(N,IL)) >= Marked_isNat(activate(N))
constraint: Marked_isNatIList(n__cons(N,IL)) >= Marked_isNatIList(activate(IL))
constraint: Marked_isNatIList(IL) >= Marked_activate(IL)
constraint: Marked_isNatIList(IL) >= Marked_isNatList(activate(IL))
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_isNatIList(n__cons(N,IL)) , Marked_isNatIList(activate(IL))> 
      --> <Marked_isNatIList(n__cons(N,IL)) , Marked_isNatIList(activate(IL))>
}

{  <Marked_isNatList(n__cons(N,L)) , Marked_isNatList(activate(L))> 
      --> <Marked_isNatList(n__cons(N,L)) , Marked_isNatList(activate(L))>
}

{  <Marked_isNat(n__s(N)) , Marked_isNat(activate(N))> 
      --> <Marked_isNat(n__s(N)) , Marked_isNat(activate(N))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  and(tt,T) >= T ;
  isNatList(n__cons(N,L)) >= and(isNat(activate(N)),isNatList(activate(L))) ;
  isNatList(n__nil) >= tt ;
  isNatList(n__take(N,IL)) >= and(isNat(activate(N)),isNatIList(activate(IL))) ;
  activate(n__0) >= 0 ;
  activate(n__s(X)) >= s(X) ;
  activate(n__length(X)) >= length(X) ;
  activate(n__zeros) >= zeros ;
  activate(n__cons(X1,X2)) >= cons(X1,X2) ;
  activate(n__nil) >= nil ;
  activate(n__take(X1,X2)) >= take(X1,X2) ;
  activate(X) >= X ;
  isNatIList(n__zeros) >= tt ;
  isNatIList(n__cons(N,IL)) >= and(isNat(activate(N)),isNatIList(activate(IL))) ;
  isNatIList(IL) >= isNatList(activate(IL)) ;
  isNat(n__0) >= tt ;
  isNat(n__s(N)) >= isNat(activate(N)) ;
  isNat(n__length(L)) >= isNatList(activate(L)) ;
  cons(X1,X2) >= n__cons(X1,X2) ;
  0 >= n__0 ;
  zeros >= n__zeros ;
  zeros >= cons(0,n__zeros) ;
  uTake1(tt) >= nil ;
  take(0,IL) >= uTake1(isNatIList(IL)) ;
  take(s(M),cons(N,IL)) >= uTake2(and(isNat(M),
                                   and(isNat(N),isNatIList(activate(IL)))),
                            M,N,activate(IL)) ;
  take(X1,X2) >= n__take(X1,X2) ;
  nil >= n__nil ;
  uTake2(tt,M,N,IL) >= cons(activate(N),n__take(activate(M),activate(IL))) ;
  s(X) >= n__s(X) ;
  uLength(tt,L) >= s(length(activate(L))) ;
  length(cons(N,L)) >= uLength(and(isNat(N),isNatList(activate(L))),
                        activate(L)) ;
  length(X) >= n__length(X) ;
  Marked_isNatIList(n__cons(N,IL)) >= Marked_isNatIList(activate(IL)) ;
 }
 + Disjunctions:{ 
{
  Marked_isNatIList(n__cons(N,IL)) > Marked_isNatIList(activate(IL)) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
Time out for these parameters.
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (Simple graph)
Found the following constraints:
{
  and(tt,T) >= T ;
  isNatList(n__cons(N,L)) >= and(isNat(activate(N)),isNatList(activate(L))) ;
  isNatList(n__nil) >= tt ;
  isNatList(n__take(N,IL)) >= and(isNat(activate(N)),isNatIList(activate(IL))) ;
  activate(n__0) >= 0 ;
  activate(n__s(X)) >= s(X) ;
  activate(n__length(X)) >= length(X) ;
  activate(n__zeros) >= zeros ;
  activate(n__cons(X1,X2)) >= cons(X1,X2) ;
  activate(n__nil) >= nil ;
  activate(n__take(X1,X2)) >= take(X1,X2) ;
  activate(X) >= X ;
  isNatIList(n__zeros) >= tt ;
  isNatIList(n__cons(N,IL)) >= and(isNat(activate(N)),isNatIList(activate(IL))) ;
  isNatIList(IL) >= isNatList(activate(IL)) ;
  isNat(n__0) >= tt ;
  isNat(n__s(N)) >= isNat(activate(N)) ;
  isNat(n__length(L)) >= isNatList(activate(L)) ;
  cons(X1,X2) >= n__cons(X1,X2) ;
  0 >= n__0 ;
  zeros >= n__zeros ;
  zeros >= cons(0,n__zeros) ;
  uTake1(tt) >= nil ;
  take(0,IL) >= uTake1(isNatIList(IL)) ;
  take(s(M),cons(N,IL)) >= uTake2(and(isNat(M),
                                   and(isNat(N),isNatIList(activate(IL)))),
                            M,N,activate(IL)) ;
  take(X1,X2) >= n__take(X1,X2) ;
  nil >= n__nil ;
  uTake2(tt,M,N,IL) >= cons(activate(N),n__take(activate(M),activate(IL))) ;
  s(X) >= n__s(X) ;
  uLength(tt,L) >= s(length(activate(L))) ;
  length(cons(N,L)) >= uLength(and(isNat(N),isNatList(activate(L))),
                        activate(L)) ;
  length(X) >= n__length(X) ;
  Marked_isNatIList(n__cons(N,IL)) > Marked_isNatIList(activate(IL)) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  and(tt,T) >= T ;
  isNatList(n__cons(N,L)) >= and(isNat(activate(N)),isNatList(activate(L))) ;
  isNatList(n__nil) >= tt ;
  isNatList(n__take(N,IL)) >= and(isNat(activate(N)),isNatIList(activate(IL))) ;
  activate(n__0) >= 0 ;
  activate(n__s(X)) >= s(X) ;
  activate(n__length(X)) >= length(X) ;
  activate(n__zeros) >= zeros ;
  activate(n__cons(X1,X2)) >= cons(X1,X2) ;
  activate(n__nil) >= nil ;
  activate(n__take(X1,X2)) >= take(X1,X2) ;
  activate(X) >= X ;
  isNatIList(n__zeros) >= tt ;
  isNatIList(n__cons(N,IL)) >= and(isNat(activate(N)),isNatIList(activate(IL))) ;
  isNatIList(IL) >= isNatList(activate(IL)) ;
  isNat(n__0) >= tt ;
  isNat(n__s(N)) >= isNat(activate(N)) ;
  isNat(n__length(L)) >= isNatList(activate(L)) ;
  cons(X1,X2) >= n__cons(X1,X2) ;
  0 >= n__0 ;
  zeros >= n__zeros ;
  zeros >= cons(0,n__zeros) ;
  uTake1(tt) >= nil ;
  take(0,IL) >= uTake1(isNatIList(IL)) ;
  take(s(M),cons(N,IL)) >= uTake2(and(isNat(M),
                                   and(isNat(N),isNatIList(activate(IL)))),
                            M,N,activate(IL)) ;
  take(X1,X2) >= n__take(X1,X2) ;
  nil >= n__nil ;
  uTake2(tt,M,N,IL) >= cons(activate(N),n__take(activate(M),activate(IL))) ;
  s(X) >= n__s(X) ;
  uLength(tt,L) >= s(length(activate(L))) ;
  length(cons(N,L)) >= uLength(and(isNat(N),isNatList(activate(L))),
                        activate(L)) ;
  length(X) >= n__length(X) ;
  Marked_isNatIList(n__cons(N,IL)) > Marked_isNatIList(activate(IL)) ;
 }
 + Disjunctions:{ 
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
Time out for these parameters.
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== 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 95.434751 seconds (real time)
Cime Exit Status: 0