MAYBE

Problem:
 a__and(tt(),T) -> mark(T)
 a__isNatIList(IL) -> a__isNatList(IL)
 a__isNat(0()) -> tt()
 a__isNat(s(N)) -> a__isNat(N)
 a__isNat(length(L)) -> a__isNatList(L)
 a__isNatIList(zeros()) -> tt()
 a__isNatIList(cons(N,IL)) -> a__and(a__isNat(N),a__isNatIList(IL))
 a__isNatList(nil()) -> tt()
 a__isNatList(cons(N,L)) -> a__and(a__isNat(N),a__isNatList(L))
 a__isNatList(take(N,IL)) -> a__and(a__isNat(N),a__isNatIList(IL))
 a__zeros() -> cons(0(),zeros())
 a__take(0(),IL) -> a__uTake1(a__isNatIList(IL))
 a__uTake1(tt()) -> nil()
 a__take(s(M),cons(N,IL)) ->
 a__uTake2(a__and(a__isNat(M),a__and(a__isNat(N),a__isNatIList(IL))),M,N,IL)
 a__uTake2(tt(),M,N,IL) -> cons(mark(N),take(M,IL))
 a__length(cons(N,L)) -> a__uLength(a__and(a__isNat(N),a__isNatList(L)),L)
 a__uLength(tt(),L) -> s(a__length(mark(L)))
 mark(and(X1,X2)) -> a__and(mark(X1),mark(X2))
 mark(isNatIList(X)) -> a__isNatIList(X)
 mark(isNatList(X)) -> a__isNatList(X)
 mark(isNat(X)) -> a__isNat(X)
 mark(length(X)) -> a__length(mark(X))
 mark(zeros()) -> a__zeros()
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(uTake1(X)) -> a__uTake1(mark(X))
 mark(uTake2(X1,X2,X3,X4)) -> a__uTake2(mark(X1),X2,X3,X4)
 mark(uLength(X1,X2)) -> a__uLength(mark(X1),X2)
 mark(tt()) -> tt()
 mark(0()) -> 0()
 mark(s(X)) -> s(mark(X))
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(nil()) -> nil()
 a__and(X1,X2) -> and(X1,X2)
 a__isNatIList(X) -> isNatIList(X)
 a__isNatList(X) -> isNatList(X)
 a__isNat(X) -> isNat(X)
 a__length(X) -> length(X)
 a__zeros() -> zeros()
 a__take(X1,X2) -> take(X1,X2)
 a__uTake1(X) -> uTake1(X)
 a__uTake2(X1,X2,X3,X4) -> uTake2(X1,X2,X3,X4)
 a__uLength(X1,X2) -> uLength(X1,X2)

Proof:
 DP Processor:
  DPs:
   a__and#(tt(),T) -> mark#(T)
   a__isNatIList#(IL) -> a__isNatList#(IL)
   a__isNat#(s(N)) -> a__isNat#(N)
   a__isNat#(length(L)) -> a__isNatList#(L)
   a__isNatIList#(cons(N,IL)) -> a__isNatIList#(IL)
   a__isNatIList#(cons(N,IL)) -> a__isNat#(N)
   a__isNatIList#(cons(N,IL)) -> a__and#(a__isNat(N),a__isNatIList(IL))
   a__isNatList#(cons(N,L)) -> a__isNatList#(L)
   a__isNatList#(cons(N,L)) -> a__isNat#(N)
   a__isNatList#(cons(N,L)) -> a__and#(a__isNat(N),a__isNatList(L))
   a__isNatList#(take(N,IL)) -> a__isNatIList#(IL)
   a__isNatList#(take(N,IL)) -> a__isNat#(N)
   a__isNatList#(take(N,IL)) -> a__and#(a__isNat(N),a__isNatIList(IL))
   a__take#(0(),IL) -> a__isNatIList#(IL)
   a__take#(0(),IL) -> a__uTake1#(a__isNatIList(IL))
   a__take#(s(M),cons(N,IL)) -> a__isNatIList#(IL)
   a__take#(s(M),cons(N,IL)) -> a__isNat#(N)
   a__take#(s(M),cons(N,IL)) -> a__and#(a__isNat(N),a__isNatIList(IL))
   a__take#(s(M),cons(N,IL)) -> a__isNat#(M)
   a__take#(s(M),cons(N,IL)) -> a__and#(a__isNat(M),a__and(a__isNat(N),a__isNatIList(IL)))
   a__take#(s(M),cons(N,IL)) ->
   a__uTake2#(a__and(a__isNat(M),a__and(a__isNat(N),a__isNatIList(IL))),M,N,IL)
   a__uTake2#(tt(),M,N,IL) -> mark#(N)
   a__length#(cons(N,L)) -> a__isNatList#(L)
   a__length#(cons(N,L)) -> a__isNat#(N)
   a__length#(cons(N,L)) -> a__and#(a__isNat(N),a__isNatList(L))
   a__length#(cons(N,L)) -> a__uLength#(a__and(a__isNat(N),a__isNatList(L)),L)
   a__uLength#(tt(),L) -> mark#(L)
   a__uLength#(tt(),L) -> a__length#(mark(L))
   mark#(and(X1,X2)) -> mark#(X2)
   mark#(and(X1,X2)) -> mark#(X1)
   mark#(and(X1,X2)) -> a__and#(mark(X1),mark(X2))
   mark#(isNatIList(X)) -> a__isNatIList#(X)
   mark#(isNatList(X)) -> a__isNatList#(X)
   mark#(isNat(X)) -> a__isNat#(X)
   mark#(length(X)) -> mark#(X)
   mark#(length(X)) -> a__length#(mark(X))
   mark#(zeros()) -> a__zeros#()
   mark#(take(X1,X2)) -> mark#(X2)
   mark#(take(X1,X2)) -> mark#(X1)
   mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
   mark#(uTake1(X)) -> mark#(X)
   mark#(uTake1(X)) -> a__uTake1#(mark(X))
   mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1)
   mark#(uTake2(X1,X2,X3,X4)) -> a__uTake2#(mark(X1),X2,X3,X4)
   mark#(uLength(X1,X2)) -> mark#(X1)
   mark#(uLength(X1,X2)) -> a__uLength#(mark(X1),X2)
   mark#(s(X)) -> mark#(X)
   mark#(cons(X1,X2)) -> mark#(X1)
  TRS:
   a__and(tt(),T) -> mark(T)
   a__isNatIList(IL) -> a__isNatList(IL)
   a__isNat(0()) -> tt()
   a__isNat(s(N)) -> a__isNat(N)
   a__isNat(length(L)) -> a__isNatList(L)
   a__isNatIList(zeros()) -> tt()
   a__isNatIList(cons(N,IL)) -> a__and(a__isNat(N),a__isNatIList(IL))
   a__isNatList(nil()) -> tt()
   a__isNatList(cons(N,L)) -> a__and(a__isNat(N),a__isNatList(L))
   a__isNatList(take(N,IL)) -> a__and(a__isNat(N),a__isNatIList(IL))
   a__zeros() -> cons(0(),zeros())
   a__take(0(),IL) -> a__uTake1(a__isNatIList(IL))
   a__uTake1(tt()) -> nil()
   a__take(s(M),cons(N,IL)) ->
   a__uTake2(a__and(a__isNat(M),a__and(a__isNat(N),a__isNatIList(IL))),M,N,IL)
   a__uTake2(tt(),M,N,IL) -> cons(mark(N),take(M,IL))
   a__length(cons(N,L)) -> a__uLength(a__and(a__isNat(N),a__isNatList(L)),L)
   a__uLength(tt(),L) -> s(a__length(mark(L)))
   mark(and(X1,X2)) -> a__and(mark(X1),mark(X2))
   mark(isNatIList(X)) -> a__isNatIList(X)
   mark(isNatList(X)) -> a__isNatList(X)
   mark(isNat(X)) -> a__isNat(X)
   mark(length(X)) -> a__length(mark(X))
   mark(zeros()) -> a__zeros()
   mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
   mark(uTake1(X)) -> a__uTake1(mark(X))
   mark(uTake2(X1,X2,X3,X4)) -> a__uTake2(mark(X1),X2,X3,X4)
   mark(uLength(X1,X2)) -> a__uLength(mark(X1),X2)
   mark(tt()) -> tt()
   mark(0()) -> 0()
   mark(s(X)) -> s(mark(X))
   mark(cons(X1,X2)) -> cons(mark(X1),X2)
   mark(nil()) -> nil()
   a__and(X1,X2) -> and(X1,X2)
   a__isNatIList(X) -> isNatIList(X)
   a__isNatList(X) -> isNatList(X)
   a__isNat(X) -> isNat(X)
   a__length(X) -> length(X)
   a__zeros() -> zeros()
   a__take(X1,X2) -> take(X1,X2)
   a__uTake1(X) -> uTake1(X)
   a__uTake2(X1,X2,X3,X4) -> uTake2(X1,X2,X3,X4)
   a__uLength(X1,X2) -> uLength(X1,X2)
  EDG Processor:
   DPs:
    a__and#(tt(),T) -> mark#(T)
    a__isNatIList#(IL) -> a__isNatList#(IL)
    a__isNat#(s(N)) -> a__isNat#(N)
    a__isNat#(length(L)) -> a__isNatList#(L)
    a__isNatIList#(cons(N,IL)) -> a__isNatIList#(IL)
    a__isNatIList#(cons(N,IL)) -> a__isNat#(N)
    a__isNatIList#(cons(N,IL)) -> a__and#(a__isNat(N),a__isNatIList(IL))
    a__isNatList#(cons(N,L)) -> a__isNatList#(L)
    a__isNatList#(cons(N,L)) -> a__isNat#(N)
    a__isNatList#(cons(N,L)) -> a__and#(a__isNat(N),a__isNatList(L))
    a__isNatList#(take(N,IL)) -> a__isNatIList#(IL)
    a__isNatList#(take(N,IL)) -> a__isNat#(N)
    a__isNatList#(take(N,IL)) -> a__and#(a__isNat(N),a__isNatIList(IL))
    a__take#(0(),IL) -> a__isNatIList#(IL)
    a__take#(0(),IL) -> a__uTake1#(a__isNatIList(IL))
    a__take#(s(M),cons(N,IL)) -> a__isNatIList#(IL)
    a__take#(s(M),cons(N,IL)) -> a__isNat#(N)
    a__take#(s(M),cons(N,IL)) -> a__and#(a__isNat(N),a__isNatIList(IL))
    a__take#(s(M),cons(N,IL)) -> a__isNat#(M)
    a__take#(s(M),cons(N,IL)) -> a__and#(a__isNat(M),a__and(a__isNat(N),a__isNatIList(IL)))
    a__take#(s(M),cons(N,IL)) ->
    a__uTake2#(a__and(a__isNat(M),a__and(a__isNat(N),a__isNatIList(IL))),M,N,IL)
    a__uTake2#(tt(),M,N,IL) -> mark#(N)
    a__length#(cons(N,L)) -> a__isNatList#(L)
    a__length#(cons(N,L)) -> a__isNat#(N)
    a__length#(cons(N,L)) -> a__and#(a__isNat(N),a__isNatList(L))
    a__length#(cons(N,L)) -> a__uLength#(a__and(a__isNat(N),a__isNatList(L)),L)
    a__uLength#(tt(),L) -> mark#(L)
    a__uLength#(tt(),L) -> a__length#(mark(L))
    mark#(and(X1,X2)) -> mark#(X2)
    mark#(and(X1,X2)) -> mark#(X1)
    mark#(and(X1,X2)) -> a__and#(mark(X1),mark(X2))
    mark#(isNatIList(X)) -> a__isNatIList#(X)
    mark#(isNatList(X)) -> a__isNatList#(X)
    mark#(isNat(X)) -> a__isNat#(X)
    mark#(length(X)) -> mark#(X)
    mark#(length(X)) -> a__length#(mark(X))
    mark#(zeros()) -> a__zeros#()
    mark#(take(X1,X2)) -> mark#(X2)
    mark#(take(X1,X2)) -> mark#(X1)
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    mark#(uTake1(X)) -> mark#(X)
    mark#(uTake1(X)) -> a__uTake1#(mark(X))
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1)
    mark#(uTake2(X1,X2,X3,X4)) -> a__uTake2#(mark(X1),X2,X3,X4)
    mark#(uLength(X1,X2)) -> mark#(X1)
    mark#(uLength(X1,X2)) -> a__uLength#(mark(X1),X2)
    mark#(s(X)) -> mark#(X)
    mark#(cons(X1,X2)) -> mark#(X1)
   TRS:
    a__and(tt(),T) -> mark(T)
    a__isNatIList(IL) -> a__isNatList(IL)
    a__isNat(0()) -> tt()
    a__isNat(s(N)) -> a__isNat(N)
    a__isNat(length(L)) -> a__isNatList(L)
    a__isNatIList(zeros()) -> tt()
    a__isNatIList(cons(N,IL)) -> a__and(a__isNat(N),a__isNatIList(IL))
    a__isNatList(nil()) -> tt()
    a__isNatList(cons(N,L)) -> a__and(a__isNat(N),a__isNatList(L))
    a__isNatList(take(N,IL)) -> a__and(a__isNat(N),a__isNatIList(IL))
    a__zeros() -> cons(0(),zeros())
    a__take(0(),IL) -> a__uTake1(a__isNatIList(IL))
    a__uTake1(tt()) -> nil()
    a__take(s(M),cons(N,IL)) ->
    a__uTake2(a__and(a__isNat(M),a__and(a__isNat(N),a__isNatIList(IL))),M,N,IL)
    a__uTake2(tt(),M,N,IL) -> cons(mark(N),take(M,IL))
    a__length(cons(N,L)) -> a__uLength(a__and(a__isNat(N),a__isNatList(L)),L)
    a__uLength(tt(),L) -> s(a__length(mark(L)))
    mark(and(X1,X2)) -> a__and(mark(X1),mark(X2))
    mark(isNatIList(X)) -> a__isNatIList(X)
    mark(isNatList(X)) -> a__isNatList(X)
    mark(isNat(X)) -> a__isNat(X)
    mark(length(X)) -> a__length(mark(X))
    mark(zeros()) -> a__zeros()
    mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
    mark(uTake1(X)) -> a__uTake1(mark(X))
    mark(uTake2(X1,X2,X3,X4)) -> a__uTake2(mark(X1),X2,X3,X4)
    mark(uLength(X1,X2)) -> a__uLength(mark(X1),X2)
    mark(tt()) -> tt()
    mark(0()) -> 0()
    mark(s(X)) -> s(mark(X))
    mark(cons(X1,X2)) -> cons(mark(X1),X2)
    mark(nil()) -> nil()
    a__and(X1,X2) -> and(X1,X2)
    a__isNatIList(X) -> isNatIList(X)
    a__isNatList(X) -> isNatList(X)
    a__isNat(X) -> isNat(X)
    a__length(X) -> length(X)
    a__zeros() -> zeros()
    a__take(X1,X2) -> take(X1,X2)
    a__uTake1(X) -> uTake1(X)
    a__uTake2(X1,X2,X3,X4) -> uTake2(X1,X2,X3,X4)
    a__uLength(X1,X2) -> uLength(X1,X2)
   graph:
    a__uLength#(tt(),L) -> a__length#(mark(L)) ->
    a__length#(cons(N,L)) -> a__isNatList#(L)
    a__uLength#(tt(),L) -> a__length#(mark(L)) ->
    a__length#(cons(N,L)) -> a__isNat#(N)
    a__uLength#(tt(),L) -> a__length#(mark(L)) ->
    a__length#(cons(N,L)) -> a__and#(a__isNat(N),a__isNatList(L))
    a__uLength#(tt(),L) -> a__length#(mark(L)) ->
    a__length#(cons(N,L)) -> a__uLength#(a__and(a__isNat(N),a__isNatList(L)),L)
    a__uLength#(tt(),L) -> mark#(L) ->
    mark#(and(X1,X2)) -> mark#(X2)
    a__uLength#(tt(),L) -> mark#(L) ->
    mark#(and(X1,X2)) -> mark#(X1)
    a__uLength#(tt(),L) -> mark#(L) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),mark(X2))
    a__uLength#(tt(),L) -> mark#(L) ->
    mark#(isNatIList(X)) -> a__isNatIList#(X)
    a__uLength#(tt(),L) -> mark#(L) ->
    mark#(isNatList(X)) -> a__isNatList#(X)
    a__uLength#(tt(),L) -> mark#(L) ->
    mark#(isNat(X)) -> a__isNat#(X)
    a__uLength#(tt(),L) -> mark#(L) -> mark#(length(X)) -> mark#(X)
    a__uLength#(tt(),L) -> mark#(L) ->
    mark#(length(X)) -> a__length#(mark(X))
    a__uLength#(tt(),L) -> mark#(L) -> mark#(zeros()) -> a__zeros#()
    a__uLength#(tt(),L) -> mark#(L) ->
    mark#(take(X1,X2)) -> mark#(X2)
    a__uLength#(tt(),L) -> mark#(L) ->
    mark#(take(X1,X2)) -> mark#(X1)
    a__uLength#(tt(),L) -> mark#(L) ->
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    a__uLength#(tt(),L) -> mark#(L) -> mark#(uTake1(X)) -> mark#(X)
    a__uLength#(tt(),L) -> mark#(L) ->
    mark#(uTake1(X)) -> a__uTake1#(mark(X))
    a__uLength#(tt(),L) -> mark#(L) ->
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1)
    a__uLength#(tt(),L) -> mark#(L) ->
    mark#(uTake2(X1,X2,X3,X4)) -> a__uTake2#(mark(X1),X2,X3,X4)
    a__uLength#(tt(),L) -> mark#(L) ->
    mark#(uLength(X1,X2)) -> mark#(X1)
    a__uLength#(tt(),L) -> mark#(L) ->
    mark#(uLength(X1,X2)) -> a__uLength#(mark(X1),X2)
    a__uLength#(tt(),L) -> mark#(L) -> mark#(s(X)) -> mark#(X)
    a__uLength#(tt(),L) -> mark#(L) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    a__length#(cons(N,L)) -> a__uLength#(a__and(a__isNat(N),a__isNatList(L)),L) ->
    a__uLength#(tt(),L) -> mark#(L)
    a__length#(cons(N,L)) -> a__uLength#(a__and(a__isNat(N),a__isNatList(L)),L) ->
    a__uLength#(tt(),L) -> a__length#(mark(L))
    a__length#(cons(N,L)) -> a__isNat#(N) ->
    a__isNat#(s(N)) -> a__isNat#(N)
    a__length#(cons(N,L)) -> a__isNat#(N) ->
    a__isNat#(length(L)) -> a__isNatList#(L)
    a__length#(cons(N,L)) -> a__isNatList#(L) ->
    a__isNatList#(cons(N,L)) -> a__isNatList#(L)
    a__length#(cons(N,L)) -> a__isNatList#(L) ->
    a__isNatList#(cons(N,L)) -> a__isNat#(N)
    a__length#(cons(N,L)) -> a__isNatList#(L) ->
    a__isNatList#(cons(N,L)) -> a__and#(a__isNat(N),a__isNatList(L))
    a__length#(cons(N,L)) -> a__isNatList#(L) ->
    a__isNatList#(take(N,IL)) -> a__isNatIList#(IL)
    a__length#(cons(N,L)) -> a__isNatList#(L) ->
    a__isNatList#(take(N,IL)) -> a__isNat#(N)
    a__length#(cons(N,L)) -> a__isNatList#(L) ->
    a__isNatList#(take(N,IL)) -> a__and#(a__isNat(N),a__isNatIList(IL))
    a__length#(cons(N,L)) -> a__and#(a__isNat(N),a__isNatList(L)) ->
    a__and#(tt(),T) -> mark#(T)
    a__uTake2#(tt(),M,N,IL) -> mark#(N) ->
    mark#(and(X1,X2)) -> mark#(X2)
    a__uTake2#(tt(),M,N,IL) -> mark#(N) ->
    mark#(and(X1,X2)) -> mark#(X1)
    a__uTake2#(tt(),M,N,IL) -> mark#(N) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),mark(X2))
    a__uTake2#(tt(),M,N,IL) -> mark#(N) ->
    mark#(isNatIList(X)) -> a__isNatIList#(X)
    a__uTake2#(tt(),M,N,IL) -> mark#(N) ->
    mark#(isNatList(X)) -> a__isNatList#(X)
    a__uTake2#(tt(),M,N,IL) -> mark#(N) ->
    mark#(isNat(X)) -> a__isNat#(X)
    a__uTake2#(tt(),M,N,IL) -> mark#(N) ->
    mark#(length(X)) -> mark#(X)
    a__uTake2#(tt(),M,N,IL) -> mark#(N) ->
    mark#(length(X)) -> a__length#(mark(X))
    a__uTake2#(tt(),M,N,IL) -> mark#(N) ->
    mark#(zeros()) -> a__zeros#()
    a__uTake2#(tt(),M,N,IL) -> mark#(N) ->
    mark#(take(X1,X2)) -> mark#(X2)
    a__uTake2#(tt(),M,N,IL) -> mark#(N) ->
    mark#(take(X1,X2)) -> mark#(X1)
    a__uTake2#(tt(),M,N,IL) -> mark#(N) ->
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    a__uTake2#(tt(),M,N,IL) -> mark#(N) ->
    mark#(uTake1(X)) -> mark#(X)
    a__uTake2#(tt(),M,N,IL) -> mark#(N) ->
    mark#(uTake1(X)) -> a__uTake1#(mark(X))
    a__uTake2#(tt(),M,N,IL) -> mark#(N) ->
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1)
    a__uTake2#(tt(),M,N,IL) -> mark#(N) ->
    mark#(uTake2(X1,X2,X3,X4)) -> a__uTake2#(mark(X1),X2,X3,X4)
    a__uTake2#(tt(),M,N,IL) -> mark#(N) ->
    mark#(uLength(X1,X2)) -> mark#(X1)
    a__uTake2#(tt(),M,N,IL) -> mark#(N) ->
    mark#(uLength(X1,X2)) -> a__uLength#(mark(X1),X2)
    a__uTake2#(tt(),M,N,IL) -> mark#(N) ->
    mark#(s(X)) -> mark#(X)
    a__uTake2#(tt(),M,N,IL) -> mark#(N) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    a__take#(s(M),cons(N,IL)) ->
    a__uTake2#(a__and(a__isNat(M),a__and(a__isNat(N),a__isNatIList(IL))),M,N,IL) ->
    a__uTake2#(tt(),M,N,IL) -> mark#(N)
    a__take#(s(M),cons(N,IL)) -> a__isNat#(M) ->
    a__isNat#(s(N)) -> a__isNat#(N)
    a__take#(s(M),cons(N,IL)) -> a__isNat#(M) ->
    a__isNat#(length(L)) -> a__isNatList#(L)
    a__take#(s(M),cons(N,IL)) -> a__isNat#(N) ->
    a__isNat#(s(N)) -> a__isNat#(N)
    a__take#(s(M),cons(N,IL)) -> a__isNat#(N) ->
    a__isNat#(length(L)) -> a__isNatList#(L)
    a__take#(s(M),cons(N,IL)) -> a__isNatIList#(IL) ->
    a__isNatIList#(IL) -> a__isNatList#(IL)
    a__take#(s(M),cons(N,IL)) -> a__isNatIList#(IL) ->
    a__isNatIList#(cons(N,IL)) -> a__isNatIList#(IL)
    a__take#(s(M),cons(N,IL)) -> a__isNatIList#(IL) ->
    a__isNatIList#(cons(N,IL)) -> a__isNat#(N)
    a__take#(s(M),cons(N,IL)) -> a__isNatIList#(IL) ->
    a__isNatIList#(cons(N,IL)) -> a__and#(a__isNat(N),a__isNatIList(IL))
    a__take#(s(M),cons(N,IL)) -> a__and#(a__isNat(M),a__and(a__isNat(N),a__isNatIList(IL))) ->
    a__and#(tt(),T) -> mark#(T)
    a__take#(s(M),cons(N,IL)) -> a__and#(a__isNat(N),a__isNatIList(IL)) ->
    a__and#(tt(),T) -> mark#(T)
    a__take#(0(),IL) -> a__isNatIList#(IL) ->
    a__isNatIList#(IL) -> a__isNatList#(IL)
    a__take#(0(),IL) -> a__isNatIList#(IL) ->
    a__isNatIList#(cons(N,IL)) -> a__isNatIList#(IL)
    a__take#(0(),IL) -> a__isNatIList#(IL) ->
    a__isNatIList#(cons(N,IL)) -> a__isNat#(N)
    a__take#(0(),IL) -> a__isNatIList#(IL) ->
    a__isNatIList#(cons(N,IL)) -> a__and#(a__isNat(N),a__isNatIList(IL))
    a__isNat#(length(L)) -> a__isNatList#(L) ->
    a__isNatList#(cons(N,L)) -> a__isNatList#(L)
    a__isNat#(length(L)) -> a__isNatList#(L) ->
    a__isNatList#(cons(N,L)) -> a__isNat#(N)
    a__isNat#(length(L)) -> a__isNatList#(L) ->
    a__isNatList#(cons(N,L)) -> a__and#(a__isNat(N),a__isNatList(L))
    a__isNat#(length(L)) -> a__isNatList#(L) ->
    a__isNatList#(take(N,IL)) -> a__isNatIList#(IL)
    a__isNat#(length(L)) -> a__isNatList#(L) ->
    a__isNatList#(take(N,IL)) -> a__isNat#(N)
    a__isNat#(length(L)) -> a__isNatList#(L) ->
    a__isNatList#(take(N,IL)) -> a__and#(a__isNat(N),a__isNatIList(IL))
    a__isNat#(s(N)) -> a__isNat#(N) ->
    a__isNat#(s(N)) -> a__isNat#(N)
    a__isNat#(s(N)) -> a__isNat#(N) ->
    a__isNat#(length(L)) -> a__isNatList#(L)
    a__isNatList#(take(N,IL)) -> a__isNat#(N) ->
    a__isNat#(s(N)) -> a__isNat#(N)
    a__isNatList#(take(N,IL)) -> a__isNat#(N) ->
    a__isNat#(length(L)) -> a__isNatList#(L)
    a__isNatList#(take(N,IL)) -> a__isNatIList#(IL) ->
    a__isNatIList#(IL) -> a__isNatList#(IL)
    a__isNatList#(take(N,IL)) -> a__isNatIList#(IL) ->
    a__isNatIList#(cons(N,IL)) -> a__isNatIList#(IL)
    a__isNatList#(take(N,IL)) -> a__isNatIList#(IL) ->
    a__isNatIList#(cons(N,IL)) -> a__isNat#(N)
    a__isNatList#(take(N,IL)) -> a__isNatIList#(IL) ->
    a__isNatIList#(cons(N,IL)) -> a__and#(a__isNat(N),a__isNatIList(IL))
    a__isNatList#(take(N,IL)) -> a__and#(a__isNat(N),a__isNatIList(IL)) ->
    a__and#(tt(),T) -> mark#(T)
    a__isNatList#(cons(N,L)) -> a__isNat#(N) ->
    a__isNat#(s(N)) -> a__isNat#(N)
    a__isNatList#(cons(N,L)) -> a__isNat#(N) ->
    a__isNat#(length(L)) -> a__isNatList#(L)
    a__isNatList#(cons(N,L)) -> a__isNatList#(L) ->
    a__isNatList#(cons(N,L)) -> a__isNatList#(L)
    a__isNatList#(cons(N,L)) -> a__isNatList#(L) ->
    a__isNatList#(cons(N,L)) -> a__isNat#(N)
    a__isNatList#(cons(N,L)) -> a__isNatList#(L) ->
    a__isNatList#(cons(N,L)) -> a__and#(a__isNat(N),a__isNatList(L))
    a__isNatList#(cons(N,L)) -> a__isNatList#(L) ->
    a__isNatList#(take(N,IL)) -> a__isNatIList#(IL)
    a__isNatList#(cons(N,L)) -> a__isNatList#(L) ->
    a__isNatList#(take(N,IL)) -> a__isNat#(N)
    a__isNatList#(cons(N,L)) -> a__isNatList#(L) ->
    a__isNatList#(take(N,IL)) -> a__and#(a__isNat(N),a__isNatIList(IL))
    a__isNatList#(cons(N,L)) -> a__and#(a__isNat(N),a__isNatList(L)) ->
    a__and#(tt(),T) -> mark#(T)
    a__isNatIList#(cons(N,IL)) -> a__isNat#(N) ->
    a__isNat#(s(N)) -> a__isNat#(N)
    a__isNatIList#(cons(N,IL)) -> a__isNat#(N) ->
    a__isNat#(length(L)) -> a__isNatList#(L)
    a__isNatIList#(cons(N,IL)) -> a__isNatIList#(IL) ->
    a__isNatIList#(IL) -> a__isNatList#(IL)
    a__isNatIList#(cons(N,IL)) -> a__isNatIList#(IL) ->
    a__isNatIList#(cons(N,IL)) -> a__isNatIList#(IL)
    a__isNatIList#(cons(N,IL)) -> a__isNatIList#(IL) ->
    a__isNatIList#(cons(N,IL)) -> a__isNat#(N)
    a__isNatIList#(cons(N,IL)) -> a__isNatIList#(IL) ->
    a__isNatIList#(cons(N,IL)) -> a__and#(a__isNat(N),a__isNatIList(IL))
    a__isNatIList#(cons(N,IL)) -> a__and#(a__isNat(N),a__isNatIList(IL)) ->
    a__and#(tt(),T) -> mark#(T)
    a__isNatIList#(IL) -> a__isNatList#(IL) ->
    a__isNatList#(cons(N,L)) -> a__isNatList#(L)
    a__isNatIList#(IL) -> a__isNatList#(IL) ->
    a__isNatList#(cons(N,L)) -> a__isNat#(N)
    a__isNatIList#(IL) -> a__isNatList#(IL) ->
    a__isNatList#(cons(N,L)) -> a__and#(a__isNat(N),a__isNatList(L))
    a__isNatIList#(IL) -> a__isNatList#(IL) ->
    a__isNatList#(take(N,IL)) -> a__isNatIList#(IL)
    a__isNatIList#(IL) -> a__isNatList#(IL) ->
    a__isNatList#(take(N,IL)) -> a__isNat#(N)
    a__isNatIList#(IL) -> a__isNatList#(IL) ->
    a__isNatList#(take(N,IL)) -> a__and#(a__isNat(N),a__isNatIList(IL))
    mark#(uLength(X1,X2)) -> a__uLength#(mark(X1),X2) ->
    a__uLength#(tt(),L) -> mark#(L)
    mark#(uLength(X1,X2)) -> a__uLength#(mark(X1),X2) ->
    a__uLength#(tt(),L) -> a__length#(mark(L))
    mark#(uLength(X1,X2)) -> mark#(X1) ->
    mark#(and(X1,X2)) -> mark#(X2)
    mark#(uLength(X1,X2)) -> mark#(X1) ->
    mark#(and(X1,X2)) -> mark#(X1)
    mark#(uLength(X1,X2)) -> mark#(X1) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),mark(X2))
    mark#(uLength(X1,X2)) -> mark#(X1) ->
    mark#(isNatIList(X)) -> a__isNatIList#(X)
    mark#(uLength(X1,X2)) -> mark#(X1) ->
    mark#(isNatList(X)) -> a__isNatList#(X)
    mark#(uLength(X1,X2)) -> mark#(X1) ->
    mark#(isNat(X)) -> a__isNat#(X)
    mark#(uLength(X1,X2)) -> mark#(X1) ->
    mark#(length(X)) -> mark#(X)
    mark#(uLength(X1,X2)) -> mark#(X1) ->
    mark#(length(X)) -> a__length#(mark(X))
    mark#(uLength(X1,X2)) -> mark#(X1) ->
    mark#(zeros()) -> a__zeros#()
    mark#(uLength(X1,X2)) -> mark#(X1) ->
    mark#(take(X1,X2)) -> mark#(X2)
    mark#(uLength(X1,X2)) -> mark#(X1) ->
    mark#(take(X1,X2)) -> mark#(X1)
    mark#(uLength(X1,X2)) -> mark#(X1) ->
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    mark#(uLength(X1,X2)) -> mark#(X1) ->
    mark#(uTake1(X)) -> mark#(X)
    mark#(uLength(X1,X2)) -> mark#(X1) ->
    mark#(uTake1(X)) -> a__uTake1#(mark(X))
    mark#(uLength(X1,X2)) -> mark#(X1) ->
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1)
    mark#(uLength(X1,X2)) -> mark#(X1) ->
    mark#(uTake2(X1,X2,X3,X4)) -> a__uTake2#(mark(X1),X2,X3,X4)
    mark#(uLength(X1,X2)) -> mark#(X1) ->
    mark#(uLength(X1,X2)) -> mark#(X1)
    mark#(uLength(X1,X2)) -> mark#(X1) ->
    mark#(uLength(X1,X2)) -> a__uLength#(mark(X1),X2)
    mark#(uLength(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
    mark#(uLength(X1,X2)) -> mark#(X1) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(uTake2(X1,X2,X3,X4)) -> a__uTake2#(mark(X1),X2,X3,X4) ->
    a__uTake2#(tt(),M,N,IL) -> mark#(N)
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(and(X1,X2)) -> mark#(X2)
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(and(X1,X2)) -> mark#(X1)
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),mark(X2))
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(isNatIList(X)) -> a__isNatIList#(X)
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(isNatList(X)) -> a__isNatList#(X)
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(isNat(X)) -> a__isNat#(X)
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(length(X)) -> mark#(X)
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(length(X)) -> a__length#(mark(X))
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(zeros()) -> a__zeros#()
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(take(X1,X2)) -> mark#(X2)
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(take(X1,X2)) -> mark#(X1)
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(uTake1(X)) -> mark#(X)
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(uTake1(X)) -> a__uTake1#(mark(X))
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1)
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(uTake2(X1,X2,X3,X4)) -> a__uTake2#(mark(X1),X2,X3,X4)
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(uLength(X1,X2)) -> mark#(X1)
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(uLength(X1,X2)) -> a__uLength#(mark(X1),X2)
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(s(X)) -> mark#(X)
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(uTake1(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X2)
    mark#(uTake1(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1)
    mark#(uTake1(X)) -> mark#(X) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),mark(X2))
    mark#(uTake1(X)) -> mark#(X) ->
    mark#(isNatIList(X)) -> a__isNatIList#(X)
    mark#(uTake1(X)) -> mark#(X) ->
    mark#(isNatList(X)) -> a__isNatList#(X)
    mark#(uTake1(X)) -> mark#(X) -> mark#(isNat(X)) -> a__isNat#(X)
    mark#(uTake1(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X)
    mark#(uTake1(X)) -> mark#(X) ->
    mark#(length(X)) -> a__length#(mark(X))
    mark#(uTake1(X)) -> mark#(X) -> mark#(zeros()) -> a__zeros#()
    mark#(uTake1(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X2)
    mark#(uTake1(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X1)
    mark#(uTake1(X)) -> mark#(X) ->
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    mark#(uTake1(X)) -> mark#(X) -> mark#(uTake1(X)) -> mark#(X)
    mark#(uTake1(X)) -> mark#(X) ->
    mark#(uTake1(X)) -> a__uTake1#(mark(X))
    mark#(uTake1(X)) -> mark#(X) ->
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1)
    mark#(uTake1(X)) -> mark#(X) ->
    mark#(uTake2(X1,X2,X3,X4)) -> a__uTake2#(mark(X1),X2,X3,X4)
    mark#(uTake1(X)) -> mark#(X) -> mark#(uLength(X1,X2)) -> mark#(X1)
    mark#(uTake1(X)) -> mark#(X) ->
    mark#(uLength(X1,X2)) -> a__uLength#(mark(X1),X2)
    mark#(uTake1(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    mark#(uTake1(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    mark#(isNat(X)) -> a__isNat#(X) ->
    a__isNat#(s(N)) -> a__isNat#(N)
    mark#(isNat(X)) -> a__isNat#(X) ->
    a__isNat#(length(L)) -> a__isNatList#(L)
    mark#(isNatList(X)) -> a__isNatList#(X) ->
    a__isNatList#(cons(N,L)) -> a__isNatList#(L)
    mark#(isNatList(X)) -> a__isNatList#(X) ->
    a__isNatList#(cons(N,L)) -> a__isNat#(N)
    mark#(isNatList(X)) -> a__isNatList#(X) ->
    a__isNatList#(cons(N,L)) -> a__and#(a__isNat(N),a__isNatList(L))
    mark#(isNatList(X)) -> a__isNatList#(X) ->
    a__isNatList#(take(N,IL)) -> a__isNatIList#(IL)
    mark#(isNatList(X)) -> a__isNatList#(X) ->
    a__isNatList#(take(N,IL)) -> a__isNat#(N)
    mark#(isNatList(X)) -> a__isNatList#(X) ->
    a__isNatList#(take(N,IL)) -> a__and#(a__isNat(N),a__isNatIList(IL))
    mark#(isNatIList(X)) -> a__isNatIList#(X) ->
    a__isNatIList#(IL) -> a__isNatList#(IL)
    mark#(isNatIList(X)) -> a__isNatIList#(X) ->
    a__isNatIList#(cons(N,IL)) -> a__isNatIList#(IL)
    mark#(isNatIList(X)) -> a__isNatIList#(X) ->
    a__isNatIList#(cons(N,IL)) -> a__isNat#(N)
    mark#(isNatIList(X)) -> a__isNatIList#(X) ->
    a__isNatIList#(cons(N,IL)) -> a__and#(a__isNat(N),a__isNatIList(IL))
    mark#(and(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> mark#(X2)
    mark#(and(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> mark#(X1)
    mark#(and(X1,X2)) -> mark#(X2) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),mark(X2))
    mark#(and(X1,X2)) -> mark#(X2) ->
    mark#(isNatIList(X)) -> a__isNatIList#(X)
    mark#(and(X1,X2)) -> mark#(X2) ->
    mark#(isNatList(X)) -> a__isNatList#(X)
    mark#(and(X1,X2)) -> mark#(X2) -> mark#(isNat(X)) -> a__isNat#(X)
    mark#(and(X1,X2)) -> mark#(X2) -> mark#(length(X)) -> mark#(X)
    mark#(and(X1,X2)) -> mark#(X2) ->
    mark#(length(X)) -> a__length#(mark(X))
    mark#(and(X1,X2)) -> mark#(X2) -> mark#(zeros()) -> a__zeros#()
    mark#(and(X1,X2)) -> mark#(X2) -> mark#(take(X1,X2)) -> mark#(X2)
    mark#(and(X1,X2)) -> mark#(X2) -> mark#(take(X1,X2)) -> mark#(X1)
    mark#(and(X1,X2)) -> mark#(X2) ->
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    mark#(and(X1,X2)) -> mark#(X2) -> mark#(uTake1(X)) -> mark#(X)
    mark#(and(X1,X2)) -> mark#(X2) ->
    mark#(uTake1(X)) -> a__uTake1#(mark(X))
    mark#(and(X1,X2)) -> mark#(X2) ->
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1)
    mark#(and(X1,X2)) -> mark#(X2) ->
    mark#(uTake2(X1,X2,X3,X4)) -> a__uTake2#(mark(X1),X2,X3,X4)
    mark#(and(X1,X2)) -> mark#(X2) ->
    mark#(uLength(X1,X2)) -> mark#(X1)
    mark#(and(X1,X2)) -> mark#(X2) ->
    mark#(uLength(X1,X2)) -> a__uLength#(mark(X1),X2)
    mark#(and(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X)
    mark#(and(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> mark#(X1)
    mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X2)
    mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1)
    mark#(and(X1,X2)) -> mark#(X1) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),mark(X2))
    mark#(and(X1,X2)) -> mark#(X1) ->
    mark#(isNatIList(X)) -> a__isNatIList#(X)
    mark#(and(X1,X2)) -> mark#(X1) ->
    mark#(isNatList(X)) -> a__isNatList#(X)
    mark#(and(X1,X2)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X)
    mark#(and(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X)
    mark#(and(X1,X2)) -> mark#(X1) ->
    mark#(length(X)) -> a__length#(mark(X))
    mark#(and(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#()
    mark#(and(X1,X2)) -> mark#(X1) -> mark#(take(X1,X2)) -> mark#(X2)
    mark#(and(X1,X2)) -> mark#(X1) -> mark#(take(X1,X2)) -> mark#(X1)
    mark#(and(X1,X2)) -> mark#(X1) ->
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    mark#(and(X1,X2)) -> mark#(X1) -> mark#(uTake1(X)) -> mark#(X)
    mark#(and(X1,X2)) -> mark#(X1) ->
    mark#(uTake1(X)) -> a__uTake1#(mark(X))
    mark#(and(X1,X2)) -> mark#(X1) ->
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1)
    mark#(and(X1,X2)) -> mark#(X1) ->
    mark#(uTake2(X1,X2,X3,X4)) -> a__uTake2#(mark(X1),X2,X3,X4)
    mark#(and(X1,X2)) -> mark#(X1) ->
    mark#(uLength(X1,X2)) -> mark#(X1)
    mark#(and(X1,X2)) -> mark#(X1) ->
    mark#(uLength(X1,X2)) -> a__uLength#(mark(X1),X2)
    mark#(and(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
    mark#(and(X1,X2)) -> mark#(X1) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(and(X1,X2)) -> a__and#(mark(X1),mark(X2)) ->
    a__and#(tt(),T) -> mark#(T)
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) ->
    a__take#(0(),IL) -> a__isNatIList#(IL)
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) ->
    a__take#(0(),IL) -> a__uTake1#(a__isNatIList(IL))
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) ->
    a__take#(s(M),cons(N,IL)) -> a__isNatIList#(IL)
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) ->
    a__take#(s(M),cons(N,IL)) -> a__isNat#(N)
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) ->
    a__take#(s(M),cons(N,IL)) -> a__and#(a__isNat(N),a__isNatIList(IL))
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) ->
    a__take#(s(M),cons(N,IL)) -> a__isNat#(M)
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) ->
    a__take#(s(M),cons(N,IL)) -> a__and#(a__isNat(M),a__and(a__isNat(N),a__isNatIList(IL)))
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) ->
    a__take#(s(M),cons(N,IL)) ->
    a__uTake2#(a__and(a__isNat(M),a__and(a__isNat(N),a__isNatIList(IL))),M,N,IL)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(and(X1,X2)) -> mark#(X2)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(and(X1,X2)) -> mark#(X1)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),mark(X2))
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(isNatIList(X)) -> a__isNatIList#(X)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(isNatList(X)) -> a__isNatList#(X)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(isNat(X)) -> a__isNat#(X)
    mark#(take(X1,X2)) -> mark#(X2) -> mark#(length(X)) -> mark#(X)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(length(X)) -> a__length#(mark(X))
    mark#(take(X1,X2)) -> mark#(X2) -> mark#(zeros()) -> a__zeros#()
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(take(X1,X2)) -> mark#(X2)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(take(X1,X2)) -> mark#(X1)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    mark#(take(X1,X2)) -> mark#(X2) -> mark#(uTake1(X)) -> mark#(X)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(uTake1(X)) -> a__uTake1#(mark(X))
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(uTake2(X1,X2,X3,X4)) -> a__uTake2#(mark(X1),X2,X3,X4)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(uLength(X1,X2)) -> mark#(X1)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(uLength(X1,X2)) -> a__uLength#(mark(X1),X2)
    mark#(take(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(and(X1,X2)) -> mark#(X2)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(and(X1,X2)) -> mark#(X1)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),mark(X2))
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(isNatIList(X)) -> a__isNatIList#(X)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(isNatList(X)) -> a__isNatList#(X)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(isNat(X)) -> a__isNat#(X)
    mark#(take(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(length(X)) -> a__length#(mark(X))
    mark#(take(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#()
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(take(X1,X2)) -> mark#(X2)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(take(X1,X2)) -> mark#(X1)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    mark#(take(X1,X2)) -> mark#(X1) -> mark#(uTake1(X)) -> mark#(X)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(uTake1(X)) -> a__uTake1#(mark(X))
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(uTake2(X1,X2,X3,X4)) -> a__uTake2#(mark(X1),X2,X3,X4)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(uLength(X1,X2)) -> mark#(X1)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(uLength(X1,X2)) -> a__uLength#(mark(X1),X2)
    mark#(take(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(and(X1,X2)) -> mark#(X2)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(and(X1,X2)) -> mark#(X1)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),mark(X2))
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(isNatIList(X)) -> a__isNatIList#(X)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(isNatList(X)) -> a__isNatList#(X)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(isNat(X)) -> a__isNat#(X)
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(length(X)) -> a__length#(mark(X))
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#()
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(take(X1,X2)) -> mark#(X2)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(take(X1,X2)) -> mark#(X1)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(uTake1(X)) -> mark#(X)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(uTake1(X)) -> a__uTake1#(mark(X))
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(uTake2(X1,X2,X3,X4)) -> a__uTake2#(mark(X1),X2,X3,X4)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(uLength(X1,X2)) -> mark#(X1)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(uLength(X1,X2)) -> a__uLength#(mark(X1),X2)
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(length(X)) -> a__length#(mark(X)) ->
    a__length#(cons(N,L)) -> a__isNatList#(L)
    mark#(length(X)) -> a__length#(mark(X)) ->
    a__length#(cons(N,L)) -> a__isNat#(N)
    mark#(length(X)) -> a__length#(mark(X)) ->
    a__length#(cons(N,L)) -> a__and#(a__isNat(N),a__isNatList(L))
    mark#(length(X)) -> a__length#(mark(X)) ->
    a__length#(cons(N,L)) -> a__uLength#(a__and(a__isNat(N),a__isNatList(L)),L)
    mark#(length(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X2)
    mark#(length(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1)
    mark#(length(X)) -> mark#(X) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),mark(X2))
    mark#(length(X)) -> mark#(X) ->
    mark#(isNatIList(X)) -> a__isNatIList#(X)
    mark#(length(X)) -> mark#(X) ->
    mark#(isNatList(X)) -> a__isNatList#(X)
    mark#(length(X)) -> mark#(X) -> mark#(isNat(X)) -> a__isNat#(X)
    mark#(length(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X)
    mark#(length(X)) -> mark#(X) ->
    mark#(length(X)) -> a__length#(mark(X))
    mark#(length(X)) -> mark#(X) -> mark#(zeros()) -> a__zeros#()
    mark#(length(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X2)
    mark#(length(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X1)
    mark#(length(X)) -> mark#(X) ->
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    mark#(length(X)) -> mark#(X) -> mark#(uTake1(X)) -> mark#(X)
    mark#(length(X)) -> mark#(X) ->
    mark#(uTake1(X)) -> a__uTake1#(mark(X))
    mark#(length(X)) -> mark#(X) ->
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1)
    mark#(length(X)) -> mark#(X) ->
    mark#(uTake2(X1,X2,X3,X4)) -> a__uTake2#(mark(X1),X2,X3,X4)
    mark#(length(X)) -> mark#(X) -> mark#(uLength(X1,X2)) -> mark#(X1)
    mark#(length(X)) -> mark#(X) ->
    mark#(uLength(X1,X2)) -> a__uLength#(mark(X1),X2)
    mark#(length(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    mark#(length(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X2)
    mark#(s(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),mark(X2))
    mark#(s(X)) -> mark#(X) -> mark#(isNatIList(X)) -> a__isNatIList#(X)
    mark#(s(X)) -> mark#(X) -> mark#(isNatList(X)) -> a__isNatList#(X)
    mark#(s(X)) -> mark#(X) -> mark#(isNat(X)) -> a__isNat#(X)
    mark#(s(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X)
    mark#(s(X)) -> mark#(X) -> mark#(length(X)) -> a__length#(mark(X))
    mark#(s(X)) -> mark#(X) -> mark#(zeros()) -> a__zeros#()
    mark#(s(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X2)
    mark#(s(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X) ->
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    mark#(s(X)) -> mark#(X) -> mark#(uTake1(X)) -> mark#(X)
    mark#(s(X)) -> mark#(X) -> mark#(uTake1(X)) -> a__uTake1#(mark(X))
    mark#(s(X)) -> mark#(X) -> mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1)
    mark#(s(X)) -> mark#(X) ->
    mark#(uTake2(X1,X2,X3,X4)) -> a__uTake2#(mark(X1),X2,X3,X4)
    mark#(s(X)) -> mark#(X) -> mark#(uLength(X1,X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X) ->
    mark#(uLength(X1,X2)) -> a__uLength#(mark(X1),X2)
    mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    a__and#(tt(),T) -> mark#(T) -> mark#(and(X1,X2)) -> mark#(X2)
    a__and#(tt(),T) -> mark#(T) -> mark#(and(X1,X2)) -> mark#(X1)
    a__and#(tt(),T) -> mark#(T) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),mark(X2))
    a__and#(tt(),T) -> mark#(T) ->
    mark#(isNatIList(X)) -> a__isNatIList#(X)
    a__and#(tt(),T) -> mark#(T) ->
    mark#(isNatList(X)) -> a__isNatList#(X)
    a__and#(tt(),T) -> mark#(T) -> mark#(isNat(X)) -> a__isNat#(X)
    a__and#(tt(),T) -> mark#(T) -> mark#(length(X)) -> mark#(X)
    a__and#(tt(),T) -> mark#(T) ->
    mark#(length(X)) -> a__length#(mark(X))
    a__and#(tt(),T) -> mark#(T) -> mark#(zeros()) -> a__zeros#()
    a__and#(tt(),T) -> mark#(T) -> mark#(take(X1,X2)) -> mark#(X2)
    a__and#(tt(),T) -> mark#(T) -> mark#(take(X1,X2)) -> mark#(X1)
    a__and#(tt(),T) -> mark#(T) ->
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    a__and#(tt(),T) -> mark#(T) -> mark#(uTake1(X)) -> mark#(X)
    a__and#(tt(),T) -> mark#(T) ->
    mark#(uTake1(X)) -> a__uTake1#(mark(X))
    a__and#(tt(),T) -> mark#(T) ->
    mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1)
    a__and#(tt(),T) -> mark#(T) ->
    mark#(uTake2(X1,X2,X3,X4)) -> a__uTake2#(mark(X1),X2,X3,X4)
    a__and#(tt(),T) -> mark#(T) -> mark#(uLength(X1,X2)) -> mark#(X1)
    a__and#(tt(),T) -> mark#(T) ->
    mark#(uLength(X1,X2)) -> a__uLength#(mark(X1),X2)
    a__and#(tt(),T) -> mark#(T) -> mark#(s(X)) -> mark#(X)
    a__and#(tt(),T) -> mark#(T) -> mark#(cons(X1,X2)) -> mark#(X1)
   SCC Processor:
    #sccs: 1
    #rules: 45
    #arcs: 355/2304
    DPs:
     a__uLength#(tt(),L) -> a__length#(mark(L))
     a__length#(cons(N,L)) -> a__uLength#(a__and(a__isNat(N),a__isNatList(L)),L)
     a__uLength#(tt(),L) -> mark#(L)
     mark#(cons(X1,X2)) -> mark#(X1)
     mark#(s(X)) -> mark#(X)
     mark#(uLength(X1,X2)) -> a__uLength#(mark(X1),X2)
     mark#(uLength(X1,X2)) -> mark#(X1)
     mark#(uTake2(X1,X2,X3,X4)) -> a__uTake2#(mark(X1),X2,X3,X4)
     a__uTake2#(tt(),M,N,IL) -> mark#(N)
     mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1)
     mark#(uTake1(X)) -> mark#(X)
     mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
     a__take#(s(M),cons(N,IL)) ->
     a__uTake2#(a__and(a__isNat(M),a__and(a__isNat(N),a__isNatIList(IL))),M,N,IL)
     a__take#(s(M),cons(N,IL)) -> a__and#(a__isNat(M),a__and(a__isNat(N),a__isNatIList(IL)))
     a__and#(tt(),T) -> mark#(T)
     mark#(take(X1,X2)) -> mark#(X1)
     mark#(take(X1,X2)) -> mark#(X2)
     mark#(length(X)) -> a__length#(mark(X))
     a__length#(cons(N,L)) -> a__and#(a__isNat(N),a__isNatList(L))
     a__length#(cons(N,L)) -> a__isNat#(N)
     a__isNat#(length(L)) -> a__isNatList#(L)
     a__isNatList#(take(N,IL)) -> a__and#(a__isNat(N),a__isNatIList(IL))
     a__isNatList#(take(N,IL)) -> a__isNat#(N)
     a__isNat#(s(N)) -> a__isNat#(N)
     a__isNatList#(take(N,IL)) -> a__isNatIList#(IL)
     a__isNatIList#(cons(N,IL)) -> a__and#(a__isNat(N),a__isNatIList(IL))
     a__isNatIList#(cons(N,IL)) -> a__isNat#(N)
     a__isNatIList#(cons(N,IL)) -> a__isNatIList#(IL)
     a__isNatIList#(IL) -> a__isNatList#(IL)
     a__isNatList#(cons(N,L)) -> a__and#(a__isNat(N),a__isNatList(L))
     a__isNatList#(cons(N,L)) -> a__isNat#(N)
     a__isNatList#(cons(N,L)) -> a__isNatList#(L)
     a__length#(cons(N,L)) -> a__isNatList#(L)
     mark#(length(X)) -> mark#(X)
     mark#(isNat(X)) -> a__isNat#(X)
     mark#(isNatList(X)) -> a__isNatList#(X)
     mark#(isNatIList(X)) -> a__isNatIList#(X)
     mark#(and(X1,X2)) -> a__and#(mark(X1),mark(X2))
     mark#(and(X1,X2)) -> mark#(X1)
     mark#(and(X1,X2)) -> mark#(X2)
     a__take#(s(M),cons(N,IL)) -> a__isNat#(M)
     a__take#(s(M),cons(N,IL)) -> a__and#(a__isNat(N),a__isNatIList(IL))
     a__take#(s(M),cons(N,IL)) -> a__isNat#(N)
     a__take#(s(M),cons(N,IL)) -> a__isNatIList#(IL)
     a__take#(0(),IL) -> a__isNatIList#(IL)
    TRS:
     a__and(tt(),T) -> mark(T)
     a__isNatIList(IL) -> a__isNatList(IL)
     a__isNat(0()) -> tt()
     a__isNat(s(N)) -> a__isNat(N)
     a__isNat(length(L)) -> a__isNatList(L)
     a__isNatIList(zeros()) -> tt()
     a__isNatIList(cons(N,IL)) -> a__and(a__isNat(N),a__isNatIList(IL))
     a__isNatList(nil()) -> tt()
     a__isNatList(cons(N,L)) -> a__and(a__isNat(N),a__isNatList(L))
     a__isNatList(take(N,IL)) -> a__and(a__isNat(N),a__isNatIList(IL))
     a__zeros() -> cons(0(),zeros())
     a__take(0(),IL) -> a__uTake1(a__isNatIList(IL))
     a__uTake1(tt()) -> nil()
     a__take(s(M),cons(N,IL)) ->
     a__uTake2(a__and(a__isNat(M),a__and(a__isNat(N),a__isNatIList(IL))),M,N,IL)
     a__uTake2(tt(),M,N,IL) -> cons(mark(N),take(M,IL))
     a__length(cons(N,L)) -> a__uLength(a__and(a__isNat(N),a__isNatList(L)),L)
     a__uLength(tt(),L) -> s(a__length(mark(L)))
     mark(and(X1,X2)) -> a__and(mark(X1),mark(X2))
     mark(isNatIList(X)) -> a__isNatIList(X)
     mark(isNatList(X)) -> a__isNatList(X)
     mark(isNat(X)) -> a__isNat(X)
     mark(length(X)) -> a__length(mark(X))
     mark(zeros()) -> a__zeros()
     mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
     mark(uTake1(X)) -> a__uTake1(mark(X))
     mark(uTake2(X1,X2,X3,X4)) -> a__uTake2(mark(X1),X2,X3,X4)
     mark(uLength(X1,X2)) -> a__uLength(mark(X1),X2)
     mark(tt()) -> tt()
     mark(0()) -> 0()
     mark(s(X)) -> s(mark(X))
     mark(cons(X1,X2)) -> cons(mark(X1),X2)
     mark(nil()) -> nil()
     a__and(X1,X2) -> and(X1,X2)
     a__isNatIList(X) -> isNatIList(X)
     a__isNatList(X) -> isNatList(X)
     a__isNat(X) -> isNat(X)
     a__length(X) -> length(X)
     a__zeros() -> zeros()
     a__take(X1,X2) -> take(X1,X2)
     a__uTake1(X) -> uTake1(X)
     a__uTake2(X1,X2,X3,X4) -> uTake2(X1,X2,X3,X4)
     a__uLength(X1,X2) -> uLength(X1,X2)
    Open