MAYBE

Problem:
 a__zeros() -> cons(0(),zeros())
 a__U11(tt(),L) -> a__U12(tt(),L)
 a__U12(tt(),L) -> s(a__length(mark(L)))
 a__U21(tt(),IL,M,N) -> a__U22(tt(),IL,M,N)
 a__U22(tt(),IL,M,N) -> a__U23(tt(),IL,M,N)
 a__U23(tt(),IL,M,N) -> cons(mark(N),take(M,IL))
 a__length(nil()) -> 0()
 a__length(cons(N,L)) -> a__U11(tt(),L)
 a__take(0(),IL) -> nil()
 a__take(s(M),cons(N,IL)) -> a__U21(tt(),IL,M,N)
 mark(zeros()) -> a__zeros()
 mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
 mark(U12(X1,X2)) -> a__U12(mark(X1),X2)
 mark(length(X)) -> a__length(mark(X))
 mark(U21(X1,X2,X3,X4)) -> a__U21(mark(X1),X2,X3,X4)
 mark(U22(X1,X2,X3,X4)) -> a__U22(mark(X1),X2,X3,X4)
 mark(U23(X1,X2,X3,X4)) -> a__U23(mark(X1),X2,X3,X4)
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(0()) -> 0()
 mark(tt()) -> tt()
 mark(s(X)) -> s(mark(X))
 mark(nil()) -> nil()
 a__zeros() -> zeros()
 a__U11(X1,X2) -> U11(X1,X2)
 a__U12(X1,X2) -> U12(X1,X2)
 a__length(X) -> length(X)
 a__U21(X1,X2,X3,X4) -> U21(X1,X2,X3,X4)
 a__U22(X1,X2,X3,X4) -> U22(X1,X2,X3,X4)
 a__U23(X1,X2,X3,X4) -> U23(X1,X2,X3,X4)
 a__take(X1,X2) -> take(X1,X2)

Proof:
 DP Processor:
  DPs:
   a__U11#(tt(),L) -> a__U12#(tt(),L)
   a__U12#(tt(),L) -> mark#(L)
   a__U12#(tt(),L) -> a__length#(mark(L))
   a__U21#(tt(),IL,M,N) -> a__U22#(tt(),IL,M,N)
   a__U22#(tt(),IL,M,N) -> a__U23#(tt(),IL,M,N)
   a__U23#(tt(),IL,M,N) -> mark#(N)
   a__length#(cons(N,L)) -> a__U11#(tt(),L)
   a__take#(s(M),cons(N,IL)) -> a__U21#(tt(),IL,M,N)
   mark#(zeros()) -> a__zeros#()
   mark#(U11(X1,X2)) -> mark#(X1)
   mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2)
   mark#(U12(X1,X2)) -> mark#(X1)
   mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2)
   mark#(length(X)) -> mark#(X)
   mark#(length(X)) -> a__length#(mark(X))
   mark#(U21(X1,X2,X3,X4)) -> mark#(X1)
   mark#(U21(X1,X2,X3,X4)) -> a__U21#(mark(X1),X2,X3,X4)
   mark#(U22(X1,X2,X3,X4)) -> mark#(X1)
   mark#(U22(X1,X2,X3,X4)) -> a__U22#(mark(X1),X2,X3,X4)
   mark#(U23(X1,X2,X3,X4)) -> mark#(X1)
   mark#(U23(X1,X2,X3,X4)) -> a__U23#(mark(X1),X2,X3,X4)
   mark#(take(X1,X2)) -> mark#(X2)
   mark#(take(X1,X2)) -> mark#(X1)
   mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
   mark#(cons(X1,X2)) -> mark#(X1)
   mark#(s(X)) -> mark#(X)
  TRS:
   a__zeros() -> cons(0(),zeros())
   a__U11(tt(),L) -> a__U12(tt(),L)
   a__U12(tt(),L) -> s(a__length(mark(L)))
   a__U21(tt(),IL,M,N) -> a__U22(tt(),IL,M,N)
   a__U22(tt(),IL,M,N) -> a__U23(tt(),IL,M,N)
   a__U23(tt(),IL,M,N) -> cons(mark(N),take(M,IL))
   a__length(nil()) -> 0()
   a__length(cons(N,L)) -> a__U11(tt(),L)
   a__take(0(),IL) -> nil()
   a__take(s(M),cons(N,IL)) -> a__U21(tt(),IL,M,N)
   mark(zeros()) -> a__zeros()
   mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
   mark(U12(X1,X2)) -> a__U12(mark(X1),X2)
   mark(length(X)) -> a__length(mark(X))
   mark(U21(X1,X2,X3,X4)) -> a__U21(mark(X1),X2,X3,X4)
   mark(U22(X1,X2,X3,X4)) -> a__U22(mark(X1),X2,X3,X4)
   mark(U23(X1,X2,X3,X4)) -> a__U23(mark(X1),X2,X3,X4)
   mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
   mark(cons(X1,X2)) -> cons(mark(X1),X2)
   mark(0()) -> 0()
   mark(tt()) -> tt()
   mark(s(X)) -> s(mark(X))
   mark(nil()) -> nil()
   a__zeros() -> zeros()
   a__U11(X1,X2) -> U11(X1,X2)
   a__U12(X1,X2) -> U12(X1,X2)
   a__length(X) -> length(X)
   a__U21(X1,X2,X3,X4) -> U21(X1,X2,X3,X4)
   a__U22(X1,X2,X3,X4) -> U22(X1,X2,X3,X4)
   a__U23(X1,X2,X3,X4) -> U23(X1,X2,X3,X4)
   a__take(X1,X2) -> take(X1,X2)
  TDG Processor:
   DPs:
    a__U11#(tt(),L) -> a__U12#(tt(),L)
    a__U12#(tt(),L) -> mark#(L)
    a__U12#(tt(),L) -> a__length#(mark(L))
    a__U21#(tt(),IL,M,N) -> a__U22#(tt(),IL,M,N)
    a__U22#(tt(),IL,M,N) -> a__U23#(tt(),IL,M,N)
    a__U23#(tt(),IL,M,N) -> mark#(N)
    a__length#(cons(N,L)) -> a__U11#(tt(),L)
    a__take#(s(M),cons(N,IL)) -> a__U21#(tt(),IL,M,N)
    mark#(zeros()) -> a__zeros#()
    mark#(U11(X1,X2)) -> mark#(X1)
    mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2)
    mark#(U12(X1,X2)) -> mark#(X1)
    mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2)
    mark#(length(X)) -> mark#(X)
    mark#(length(X)) -> a__length#(mark(X))
    mark#(U21(X1,X2,X3,X4)) -> mark#(X1)
    mark#(U21(X1,X2,X3,X4)) -> a__U21#(mark(X1),X2,X3,X4)
    mark#(U22(X1,X2,X3,X4)) -> mark#(X1)
    mark#(U22(X1,X2,X3,X4)) -> a__U22#(mark(X1),X2,X3,X4)
    mark#(U23(X1,X2,X3,X4)) -> mark#(X1)
    mark#(U23(X1,X2,X3,X4)) -> a__U23#(mark(X1),X2,X3,X4)
    mark#(take(X1,X2)) -> mark#(X2)
    mark#(take(X1,X2)) -> mark#(X1)
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X)
   TRS:
    a__zeros() -> cons(0(),zeros())
    a__U11(tt(),L) -> a__U12(tt(),L)
    a__U12(tt(),L) -> s(a__length(mark(L)))
    a__U21(tt(),IL,M,N) -> a__U22(tt(),IL,M,N)
    a__U22(tt(),IL,M,N) -> a__U23(tt(),IL,M,N)
    a__U23(tt(),IL,M,N) -> cons(mark(N),take(M,IL))
    a__length(nil()) -> 0()
    a__length(cons(N,L)) -> a__U11(tt(),L)
    a__take(0(),IL) -> nil()
    a__take(s(M),cons(N,IL)) -> a__U21(tt(),IL,M,N)
    mark(zeros()) -> a__zeros()
    mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
    mark(U12(X1,X2)) -> a__U12(mark(X1),X2)
    mark(length(X)) -> a__length(mark(X))
    mark(U21(X1,X2,X3,X4)) -> a__U21(mark(X1),X2,X3,X4)
    mark(U22(X1,X2,X3,X4)) -> a__U22(mark(X1),X2,X3,X4)
    mark(U23(X1,X2,X3,X4)) -> a__U23(mark(X1),X2,X3,X4)
    mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
    mark(cons(X1,X2)) -> cons(mark(X1),X2)
    mark(0()) -> 0()
    mark(tt()) -> tt()
    mark(s(X)) -> s(mark(X))
    mark(nil()) -> nil()
    a__zeros() -> zeros()
    a__U11(X1,X2) -> U11(X1,X2)
    a__U12(X1,X2) -> U12(X1,X2)
    a__length(X) -> length(X)
    a__U21(X1,X2,X3,X4) -> U21(X1,X2,X3,X4)
    a__U22(X1,X2,X3,X4) -> U22(X1,X2,X3,X4)
    a__U23(X1,X2,X3,X4) -> U23(X1,X2,X3,X4)
    a__take(X1,X2) -> take(X1,X2)
   graph:
    a__take#(s(M),cons(N,IL)) -> a__U21#(tt(),IL,M,N) ->
    a__U21#(tt(),IL,M,N) -> a__U22#(tt(),IL,M,N)
    a__U23#(tt(),IL,M,N) -> mark#(N) -> mark#(s(X)) -> mark#(X)
    a__U23#(tt(),IL,M,N) -> mark#(N) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    a__U23#(tt(),IL,M,N) -> mark#(N) ->
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    a__U23#(tt(),IL,M,N) -> mark#(N) ->
    mark#(take(X1,X2)) -> mark#(X1)
    a__U23#(tt(),IL,M,N) -> mark#(N) ->
    mark#(take(X1,X2)) -> mark#(X2)
    a__U23#(tt(),IL,M,N) -> mark#(N) ->
    mark#(U23(X1,X2,X3,X4)) -> a__U23#(mark(X1),X2,X3,X4)
    a__U23#(tt(),IL,M,N) -> mark#(N) ->
    mark#(U23(X1,X2,X3,X4)) -> mark#(X1)
    a__U23#(tt(),IL,M,N) -> mark#(N) ->
    mark#(U22(X1,X2,X3,X4)) -> a__U22#(mark(X1),X2,X3,X4)
    a__U23#(tt(),IL,M,N) -> mark#(N) ->
    mark#(U22(X1,X2,X3,X4)) -> mark#(X1)
    a__U23#(tt(),IL,M,N) -> mark#(N) ->
    mark#(U21(X1,X2,X3,X4)) -> a__U21#(mark(X1),X2,X3,X4)
    a__U23#(tt(),IL,M,N) -> mark#(N) ->
    mark#(U21(X1,X2,X3,X4)) -> mark#(X1)
    a__U23#(tt(),IL,M,N) -> mark#(N) ->
    mark#(length(X)) -> a__length#(mark(X))
    a__U23#(tt(),IL,M,N) -> mark#(N) ->
    mark#(length(X)) -> mark#(X)
    a__U23#(tt(),IL,M,N) -> mark#(N) ->
    mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2)
    a__U23#(tt(),IL,M,N) -> mark#(N) ->
    mark#(U12(X1,X2)) -> mark#(X1)
    a__U23#(tt(),IL,M,N) -> mark#(N) ->
    mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2)
    a__U23#(tt(),IL,M,N) -> mark#(N) ->
    mark#(U11(X1,X2)) -> mark#(X1)
    a__U23#(tt(),IL,M,N) -> mark#(N) ->
    mark#(zeros()) -> a__zeros#()
    a__U22#(tt(),IL,M,N) -> a__U23#(tt(),IL,M,N) ->
    a__U23#(tt(),IL,M,N) -> mark#(N)
    a__U21#(tt(),IL,M,N) -> a__U22#(tt(),IL,M,N) ->
    a__U22#(tt(),IL,M,N) -> a__U23#(tt(),IL,M,N)
    a__length#(cons(N,L)) -> a__U11#(tt(),L) ->
    a__U11#(tt(),L) -> a__U12#(tt(),L)
    mark#(U23(X1,X2,X3,X4)) -> a__U23#(mark(X1),X2,X3,X4) ->
    a__U23#(tt(),IL,M,N) -> mark#(N)
    mark#(U23(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(s(X)) -> mark#(X)
    mark#(U23(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(U23(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    mark#(U23(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(take(X1,X2)) -> mark#(X1)
    mark#(U23(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(take(X1,X2)) -> mark#(X2)
    mark#(U23(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U23(X1,X2,X3,X4)) -> a__U23#(mark(X1),X2,X3,X4)
    mark#(U23(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U23(X1,X2,X3,X4)) -> mark#(X1)
    mark#(U23(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U22(X1,X2,X3,X4)) -> a__U22#(mark(X1),X2,X3,X4)
    mark#(U23(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U22(X1,X2,X3,X4)) -> mark#(X1)
    mark#(U23(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U21(X1,X2,X3,X4)) -> a__U21#(mark(X1),X2,X3,X4)
    mark#(U23(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U21(X1,X2,X3,X4)) -> mark#(X1)
    mark#(U23(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(length(X)) -> a__length#(mark(X))
    mark#(U23(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(length(X)) -> mark#(X)
    mark#(U23(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2)
    mark#(U23(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U12(X1,X2)) -> mark#(X1)
    mark#(U23(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2)
    mark#(U23(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U11(X1,X2)) -> mark#(X1)
    mark#(U23(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(zeros()) -> a__zeros#()
    mark#(U22(X1,X2,X3,X4)) -> a__U22#(mark(X1),X2,X3,X4) ->
    a__U22#(tt(),IL,M,N) -> a__U23#(tt(),IL,M,N)
    mark#(U22(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(s(X)) -> mark#(X)
    mark#(U22(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(U22(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    mark#(U22(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(take(X1,X2)) -> mark#(X1)
    mark#(U22(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(take(X1,X2)) -> mark#(X2)
    mark#(U22(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U23(X1,X2,X3,X4)) -> a__U23#(mark(X1),X2,X3,X4)
    mark#(U22(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U23(X1,X2,X3,X4)) -> mark#(X1)
    mark#(U22(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U22(X1,X2,X3,X4)) -> a__U22#(mark(X1),X2,X3,X4)
    mark#(U22(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U22(X1,X2,X3,X4)) -> mark#(X1)
    mark#(U22(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U21(X1,X2,X3,X4)) -> a__U21#(mark(X1),X2,X3,X4)
    mark#(U22(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U21(X1,X2,X3,X4)) -> mark#(X1)
    mark#(U22(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(length(X)) -> a__length#(mark(X))
    mark#(U22(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(length(X)) -> mark#(X)
    mark#(U22(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2)
    mark#(U22(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U12(X1,X2)) -> mark#(X1)
    mark#(U22(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2)
    mark#(U22(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U11(X1,X2)) -> mark#(X1)
    mark#(U22(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(zeros()) -> a__zeros#()
    mark#(U21(X1,X2,X3,X4)) -> a__U21#(mark(X1),X2,X3,X4) ->
    a__U21#(tt(),IL,M,N) -> a__U22#(tt(),IL,M,N)
    mark#(U21(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(s(X)) -> mark#(X)
    mark#(U21(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(U21(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    mark#(U21(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(take(X1,X2)) -> mark#(X1)
    mark#(U21(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(take(X1,X2)) -> mark#(X2)
    mark#(U21(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U23(X1,X2,X3,X4)) -> a__U23#(mark(X1),X2,X3,X4)
    mark#(U21(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U23(X1,X2,X3,X4)) -> mark#(X1)
    mark#(U21(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U22(X1,X2,X3,X4)) -> a__U22#(mark(X1),X2,X3,X4)
    mark#(U21(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U22(X1,X2,X3,X4)) -> mark#(X1)
    mark#(U21(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U21(X1,X2,X3,X4)) -> a__U21#(mark(X1),X2,X3,X4)
    mark#(U21(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U21(X1,X2,X3,X4)) -> mark#(X1)
    mark#(U21(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(length(X)) -> a__length#(mark(X))
    mark#(U21(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(length(X)) -> mark#(X)
    mark#(U21(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2)
    mark#(U21(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U12(X1,X2)) -> mark#(X1)
    mark#(U21(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2)
    mark#(U21(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(U11(X1,X2)) -> mark#(X1)
    mark#(U21(X1,X2,X3,X4)) -> mark#(X1) ->
    mark#(zeros()) -> a__zeros#()
    mark#(length(X)) -> a__length#(mark(X)) ->
    a__length#(cons(N,L)) -> a__U11#(tt(),L)
    mark#(length(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    mark#(length(X)) -> mark#(X) -> mark#(cons(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#(take(X1,X2)) -> mark#(X1)
    mark#(length(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X2)
    mark#(length(X)) -> mark#(X) ->
    mark#(U23(X1,X2,X3,X4)) -> a__U23#(mark(X1),X2,X3,X4)
    mark#(length(X)) -> mark#(X) ->
    mark#(U23(X1,X2,X3,X4)) -> mark#(X1)
    mark#(length(X)) -> mark#(X) ->
    mark#(U22(X1,X2,X3,X4)) -> a__U22#(mark(X1),X2,X3,X4)
    mark#(length(X)) -> mark#(X) ->
    mark#(U22(X1,X2,X3,X4)) -> mark#(X1)
    mark#(length(X)) -> mark#(X) ->
    mark#(U21(X1,X2,X3,X4)) -> a__U21#(mark(X1),X2,X3,X4)
    mark#(length(X)) -> mark#(X) ->
    mark#(U21(X1,X2,X3,X4)) -> mark#(X1)
    mark#(length(X)) -> mark#(X) ->
    mark#(length(X)) -> a__length#(mark(X))
    mark#(length(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X)
    mark#(length(X)) -> mark#(X) ->
    mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2)
    mark#(length(X)) -> mark#(X) -> mark#(U12(X1,X2)) -> mark#(X1)
    mark#(length(X)) -> mark#(X) ->
    mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2)
    mark#(length(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1)
    mark#(length(X)) -> mark#(X) -> mark#(zeros()) -> a__zeros#()
    mark#(U12(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
    mark#(U12(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1)
    mark#(U12(X1,X2)) -> mark#(X1) ->
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    mark#(U12(X1,X2)) -> mark#(X1) -> mark#(take(X1,X2)) -> mark#(X1)
    mark#(U12(X1,X2)) -> mark#(X1) -> mark#(take(X1,X2)) -> mark#(X2)
    mark#(U12(X1,X2)) -> mark#(X1) ->
    mark#(U23(X1,X2,X3,X4)) -> a__U23#(mark(X1),X2,X3,X4)
    mark#(U12(X1,X2)) -> mark#(X1) ->
    mark#(U23(X1,X2,X3,X4)) -> mark#(X1)
    mark#(U12(X1,X2)) -> mark#(X1) ->
    mark#(U22(X1,X2,X3,X4)) -> a__U22#(mark(X1),X2,X3,X4)
    mark#(U12(X1,X2)) -> mark#(X1) ->
    mark#(U22(X1,X2,X3,X4)) -> mark#(X1)
    mark#(U12(X1,X2)) -> mark#(X1) ->
    mark#(U21(X1,X2,X3,X4)) -> a__U21#(mark(X1),X2,X3,X4)
    mark#(U12(X1,X2)) -> mark#(X1) ->
    mark#(U21(X1,X2,X3,X4)) -> mark#(X1)
    mark#(U12(X1,X2)) -> mark#(X1) ->
    mark#(length(X)) -> a__length#(mark(X))
    mark#(U12(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X)
    mark#(U12(X1,X2)) -> mark#(X1) ->
    mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2)
    mark#(U12(X1,X2)) -> mark#(X1) -> mark#(U12(X1,X2)) -> mark#(X1)
    mark#(U12(X1,X2)) -> mark#(X1) ->
    mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2)
    mark#(U12(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1)
    mark#(U12(X1,X2)) -> mark#(X1) ->
    mark#(zeros()) -> a__zeros#()
    mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2) ->
    a__U12#(tt(),L) -> a__length#(mark(L))
    mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2) ->
    a__U12#(tt(),L) -> mark#(L)
    mark#(U11(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
    mark#(U11(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1)
    mark#(U11(X1,X2)) -> mark#(X1) ->
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    mark#(U11(X1,X2)) -> mark#(X1) -> mark#(take(X1,X2)) -> mark#(X1)
    mark#(U11(X1,X2)) -> mark#(X1) -> mark#(take(X1,X2)) -> mark#(X2)
    mark#(U11(X1,X2)) -> mark#(X1) ->
    mark#(U23(X1,X2,X3,X4)) -> a__U23#(mark(X1),X2,X3,X4)
    mark#(U11(X1,X2)) -> mark#(X1) ->
    mark#(U23(X1,X2,X3,X4)) -> mark#(X1)
    mark#(U11(X1,X2)) -> mark#(X1) ->
    mark#(U22(X1,X2,X3,X4)) -> a__U22#(mark(X1),X2,X3,X4)
    mark#(U11(X1,X2)) -> mark#(X1) ->
    mark#(U22(X1,X2,X3,X4)) -> mark#(X1)
    mark#(U11(X1,X2)) -> mark#(X1) ->
    mark#(U21(X1,X2,X3,X4)) -> a__U21#(mark(X1),X2,X3,X4)
    mark#(U11(X1,X2)) -> mark#(X1) ->
    mark#(U21(X1,X2,X3,X4)) -> mark#(X1)
    mark#(U11(X1,X2)) -> mark#(X1) ->
    mark#(length(X)) -> a__length#(mark(X))
    mark#(U11(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X)
    mark#(U11(X1,X2)) -> mark#(X1) ->
    mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2)
    mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U12(X1,X2)) -> mark#(X1)
    mark#(U11(X1,X2)) -> mark#(X1) ->
    mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2)
    mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1)
    mark#(U11(X1,X2)) -> mark#(X1) ->
    mark#(zeros()) -> a__zeros#()
    mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) ->
    a__U11#(tt(),L) -> a__U12#(tt(),L)
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) ->
    a__take#(s(M),cons(N,IL)) -> a__U21#(tt(),IL,M,N)
    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#(X2) ->
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(take(X1,X2)) -> mark#(X1)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(take(X1,X2)) -> mark#(X2)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(U23(X1,X2,X3,X4)) -> a__U23#(mark(X1),X2,X3,X4)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(U23(X1,X2,X3,X4)) -> mark#(X1)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(U22(X1,X2,X3,X4)) -> a__U22#(mark(X1),X2,X3,X4)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(U22(X1,X2,X3,X4)) -> mark#(X1)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(U21(X1,X2,X3,X4)) -> a__U21#(mark(X1),X2,X3,X4)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(U21(X1,X2,X3,X4)) -> mark#(X1)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(length(X)) -> a__length#(mark(X))
    mark#(take(X1,X2)) -> mark#(X2) -> mark#(length(X)) -> mark#(X)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(U12(X1,X2)) -> mark#(X1)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(U11(X1,X2)) -> mark#(X1)
    mark#(take(X1,X2)) -> mark#(X2) -> mark#(zeros()) -> a__zeros#()
    mark#(take(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(cons(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#(take(X1,X2)) -> mark#(X1)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(take(X1,X2)) -> mark#(X2)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(U23(X1,X2,X3,X4)) -> a__U23#(mark(X1),X2,X3,X4)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(U23(X1,X2,X3,X4)) -> mark#(X1)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(U22(X1,X2,X3,X4)) -> a__U22#(mark(X1),X2,X3,X4)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(U22(X1,X2,X3,X4)) -> mark#(X1)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(U21(X1,X2,X3,X4)) -> a__U21#(mark(X1),X2,X3,X4)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(U21(X1,X2,X3,X4)) -> mark#(X1)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(length(X)) -> a__length#(mark(X))
    mark#(take(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(U12(X1,X2)) -> mark#(X1)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(U11(X1,X2)) -> mark#(X1)
    mark#(take(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#()
    mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    mark#(s(X)) -> mark#(X) -> mark#(cons(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#(take(X1,X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X2)
    mark#(s(X)) -> mark#(X) ->
    mark#(U23(X1,X2,X3,X4)) -> a__U23#(mark(X1),X2,X3,X4)
    mark#(s(X)) -> mark#(X) -> mark#(U23(X1,X2,X3,X4)) -> mark#(X1)
    mark#(s(X)) -> mark#(X) ->
    mark#(U22(X1,X2,X3,X4)) -> a__U22#(mark(X1),X2,X3,X4)
    mark#(s(X)) -> mark#(X) -> mark#(U22(X1,X2,X3,X4)) -> mark#(X1)
    mark#(s(X)) -> mark#(X) ->
    mark#(U21(X1,X2,X3,X4)) -> a__U21#(mark(X1),X2,X3,X4)
    mark#(s(X)) -> mark#(X) -> mark#(U21(X1,X2,X3,X4)) -> mark#(X1)
    mark#(s(X)) -> mark#(X) -> mark#(length(X)) -> a__length#(mark(X))
    mark#(s(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X)
    mark#(s(X)) -> mark#(X) -> mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2)
    mark#(s(X)) -> mark#(X) -> mark#(U12(X1,X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2)
    mark#(s(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X) -> mark#(zeros()) -> a__zeros#()
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(cons(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#(take(X1,X2)) -> mark#(X1)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(take(X1,X2)) -> mark#(X2)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(U23(X1,X2,X3,X4)) -> a__U23#(mark(X1),X2,X3,X4)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(U23(X1,X2,X3,X4)) -> mark#(X1)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(U22(X1,X2,X3,X4)) -> a__U22#(mark(X1),X2,X3,X4)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(U22(X1,X2,X3,X4)) -> mark#(X1)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(U21(X1,X2,X3,X4)) -> a__U21#(mark(X1),X2,X3,X4)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(U21(X1,X2,X3,X4)) -> mark#(X1)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(length(X)) -> a__length#(mark(X))
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(U12(X1,X2)) -> mark#(X1)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(U11(X1,X2)) -> mark#(X1)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(zeros()) -> a__zeros#()
    a__U12#(tt(),L) -> a__length#(mark(L)) ->
    a__length#(cons(N,L)) -> a__U11#(tt(),L)
    a__U12#(tt(),L) -> mark#(L) -> mark#(s(X)) -> mark#(X)
    a__U12#(tt(),L) -> mark#(L) -> mark#(cons(X1,X2)) -> mark#(X1)
    a__U12#(tt(),L) -> mark#(L) ->
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    a__U12#(tt(),L) -> mark#(L) -> mark#(take(X1,X2)) -> mark#(X1)
    a__U12#(tt(),L) -> mark#(L) -> mark#(take(X1,X2)) -> mark#(X2)
    a__U12#(tt(),L) -> mark#(L) ->
    mark#(U23(X1,X2,X3,X4)) -> a__U23#(mark(X1),X2,X3,X4)
    a__U12#(tt(),L) -> mark#(L) -> mark#(U23(X1,X2,X3,X4)) -> mark#(X1)
    a__U12#(tt(),L) -> mark#(L) ->
    mark#(U22(X1,X2,X3,X4)) -> a__U22#(mark(X1),X2,X3,X4)
    a__U12#(tt(),L) -> mark#(L) -> mark#(U22(X1,X2,X3,X4)) -> mark#(X1)
    a__U12#(tt(),L) -> mark#(L) ->
    mark#(U21(X1,X2,X3,X4)) -> a__U21#(mark(X1),X2,X3,X4)
    a__U12#(tt(),L) -> mark#(L) -> mark#(U21(X1,X2,X3,X4)) -> mark#(X1)
    a__U12#(tt(),L) -> mark#(L) ->
    mark#(length(X)) -> a__length#(mark(X))
    a__U12#(tt(),L) -> mark#(L) -> mark#(length(X)) -> mark#(X)
    a__U12#(tt(),L) -> mark#(L) ->
    mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2)
    a__U12#(tt(),L) -> mark#(L) -> mark#(U12(X1,X2)) -> mark#(X1)
    a__U12#(tt(),L) -> mark#(L) ->
    mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2)
    a__U12#(tt(),L) -> mark#(L) -> mark#(U11(X1,X2)) -> mark#(X1)
    a__U12#(tt(),L) -> mark#(L) -> mark#(zeros()) -> a__zeros#()
    a__U11#(tt(),L) -> a__U12#(tt(),L) ->
    a__U12#(tt(),L) -> a__length#(mark(L))
    a__U11#(tt(),L) -> a__U12#(tt(),L) -> a__U12#(tt(),L) -> mark#(L)
   SCC Processor:
    #sccs: 1
    #rules: 25
    #arcs: 231/676
    DPs:
     a__take#(s(M),cons(N,IL)) -> a__U21#(tt(),IL,M,N)
     a__U21#(tt(),IL,M,N) -> a__U22#(tt(),IL,M,N)
     a__U22#(tt(),IL,M,N) -> a__U23#(tt(),IL,M,N)
     a__U23#(tt(),IL,M,N) -> mark#(N)
     mark#(U11(X1,X2)) -> mark#(X1)
     mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2)
     a__U11#(tt(),L) -> a__U12#(tt(),L)
     a__U12#(tt(),L) -> mark#(L)
     mark#(U12(X1,X2)) -> mark#(X1)
     mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2)
     a__U12#(tt(),L) -> a__length#(mark(L))
     a__length#(cons(N,L)) -> a__U11#(tt(),L)
     mark#(length(X)) -> mark#(X)
     mark#(length(X)) -> a__length#(mark(X))
     mark#(U21(X1,X2,X3,X4)) -> mark#(X1)
     mark#(U21(X1,X2,X3,X4)) -> a__U21#(mark(X1),X2,X3,X4)
     mark#(U22(X1,X2,X3,X4)) -> mark#(X1)
     mark#(U22(X1,X2,X3,X4)) -> a__U22#(mark(X1),X2,X3,X4)
     mark#(U23(X1,X2,X3,X4)) -> mark#(X1)
     mark#(U23(X1,X2,X3,X4)) -> a__U23#(mark(X1),X2,X3,X4)
     mark#(take(X1,X2)) -> mark#(X2)
     mark#(take(X1,X2)) -> mark#(X1)
     mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
     mark#(cons(X1,X2)) -> mark#(X1)
     mark#(s(X)) -> mark#(X)
    TRS:
     a__zeros() -> cons(0(),zeros())
     a__U11(tt(),L) -> a__U12(tt(),L)
     a__U12(tt(),L) -> s(a__length(mark(L)))
     a__U21(tt(),IL,M,N) -> a__U22(tt(),IL,M,N)
     a__U22(tt(),IL,M,N) -> a__U23(tt(),IL,M,N)
     a__U23(tt(),IL,M,N) -> cons(mark(N),take(M,IL))
     a__length(nil()) -> 0()
     a__length(cons(N,L)) -> a__U11(tt(),L)
     a__take(0(),IL) -> nil()
     a__take(s(M),cons(N,IL)) -> a__U21(tt(),IL,M,N)
     mark(zeros()) -> a__zeros()
     mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
     mark(U12(X1,X2)) -> a__U12(mark(X1),X2)
     mark(length(X)) -> a__length(mark(X))
     mark(U21(X1,X2,X3,X4)) -> a__U21(mark(X1),X2,X3,X4)
     mark(U22(X1,X2,X3,X4)) -> a__U22(mark(X1),X2,X3,X4)
     mark(U23(X1,X2,X3,X4)) -> a__U23(mark(X1),X2,X3,X4)
     mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
     mark(cons(X1,X2)) -> cons(mark(X1),X2)
     mark(0()) -> 0()
     mark(tt()) -> tt()
     mark(s(X)) -> s(mark(X))
     mark(nil()) -> nil()
     a__zeros() -> zeros()
     a__U11(X1,X2) -> U11(X1,X2)
     a__U12(X1,X2) -> U12(X1,X2)
     a__length(X) -> length(X)
     a__U21(X1,X2,X3,X4) -> U21(X1,X2,X3,X4)
     a__U22(X1,X2,X3,X4) -> U22(X1,X2,X3,X4)
     a__U23(X1,X2,X3,X4) -> U23(X1,X2,X3,X4)
     a__take(X1,X2) -> take(X1,X2)
    Open