MAYBE

Problem:
 a__zeros() -> cons(0(),zeros())
 a__and(tt(),X) -> mark(X)
 a__length(nil()) -> 0()
 a__length(cons(N,L)) -> s(a__length(mark(L)))
 a__take(0(),IL) -> nil()
 a__take(s(M),cons(N,IL)) -> cons(mark(N),take(M,IL))
 mark(zeros()) -> a__zeros()
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(length(X)) -> a__length(mark(X))
 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(nil()) -> nil()
 mark(s(X)) -> s(mark(X))
 a__zeros() -> zeros()
 a__and(X1,X2) -> and(X1,X2)
 a__length(X) -> length(X)
 a__take(X1,X2) -> take(X1,X2)

Proof:
 DP Processor:
  DPs:
   a__and#(tt(),X) -> mark#(X)
   a__length#(cons(N,L)) -> mark#(L)
   a__length#(cons(N,L)) -> a__length#(mark(L))
   a__take#(s(M),cons(N,IL)) -> mark#(N)
   mark#(zeros()) -> a__zeros#()
   mark#(and(X1,X2)) -> mark#(X1)
   mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
   mark#(length(X)) -> mark#(X)
   mark#(length(X)) -> a__length#(mark(X))
   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__and(tt(),X) -> mark(X)
   a__length(nil()) -> 0()
   a__length(cons(N,L)) -> s(a__length(mark(L)))
   a__take(0(),IL) -> nil()
   a__take(s(M),cons(N,IL)) -> cons(mark(N),take(M,IL))
   mark(zeros()) -> a__zeros()
   mark(and(X1,X2)) -> a__and(mark(X1),X2)
   mark(length(X)) -> a__length(mark(X))
   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(nil()) -> nil()
   mark(s(X)) -> s(mark(X))
   a__zeros() -> zeros()
   a__and(X1,X2) -> and(X1,X2)
   a__length(X) -> length(X)
   a__take(X1,X2) -> take(X1,X2)
  ADG Processor:
   DPs:
    a__and#(tt(),X) -> mark#(X)
    a__length#(cons(N,L)) -> mark#(L)
    a__length#(cons(N,L)) -> a__length#(mark(L))
    a__take#(s(M),cons(N,IL)) -> mark#(N)
    mark#(zeros()) -> a__zeros#()
    mark#(and(X1,X2)) -> mark#(X1)
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    mark#(length(X)) -> mark#(X)
    mark#(length(X)) -> a__length#(mark(X))
    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__and(tt(),X) -> mark(X)
    a__length(nil()) -> 0()
    a__length(cons(N,L)) -> s(a__length(mark(L)))
    a__take(0(),IL) -> nil()
    a__take(s(M),cons(N,IL)) -> cons(mark(N),take(M,IL))
    mark(zeros()) -> a__zeros()
    mark(and(X1,X2)) -> a__and(mark(X1),X2)
    mark(length(X)) -> a__length(mark(X))
    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(nil()) -> nil()
    mark(s(X)) -> s(mark(X))
    a__zeros() -> zeros()
    a__and(X1,X2) -> and(X1,X2)
    a__length(X) -> length(X)
    a__take(X1,X2) -> take(X1,X2)
   graph:
    a__take#(s(M),cons(N,IL)) -> mark#(N) ->
    mark#(zeros()) -> a__zeros#()
    a__take#(s(M),cons(N,IL)) -> mark#(N) ->
    mark#(and(X1,X2)) -> mark#(X1)
    a__take#(s(M),cons(N,IL)) -> mark#(N) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    a__take#(s(M),cons(N,IL)) -> mark#(N) ->
    mark#(length(X)) -> mark#(X)
    a__take#(s(M),cons(N,IL)) -> mark#(N) ->
    mark#(length(X)) -> a__length#(mark(X))
    a__take#(s(M),cons(N,IL)) -> mark#(N) ->
    mark#(take(X1,X2)) -> mark#(X2)
    a__take#(s(M),cons(N,IL)) -> mark#(N) ->
    mark#(take(X1,X2)) -> mark#(X1)
    a__take#(s(M),cons(N,IL)) -> mark#(N) ->
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    a__take#(s(M),cons(N,IL)) -> mark#(N) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    a__take#(s(M),cons(N,IL)) -> mark#(N) ->
    mark#(s(X)) -> mark#(X)
    a__length#(cons(N,L)) -> a__length#(mark(L)) ->
    a__length#(cons(N,L)) -> mark#(L)
    a__length#(cons(N,L)) -> a__length#(mark(L)) ->
    a__length#(cons(N,L)) -> a__length#(mark(L))
    a__length#(cons(N,L)) -> mark#(L) ->
    mark#(zeros()) -> a__zeros#()
    a__length#(cons(N,L)) -> mark#(L) ->
    mark#(and(X1,X2)) -> mark#(X1)
    a__length#(cons(N,L)) -> mark#(L) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    a__length#(cons(N,L)) -> mark#(L) ->
    mark#(length(X)) -> mark#(X)
    a__length#(cons(N,L)) -> mark#(L) ->
    mark#(length(X)) -> a__length#(mark(X))
    a__length#(cons(N,L)) -> mark#(L) ->
    mark#(take(X1,X2)) -> mark#(X2)
    a__length#(cons(N,L)) -> mark#(L) ->
    mark#(take(X1,X2)) -> mark#(X1)
    a__length#(cons(N,L)) -> mark#(L) ->
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    a__length#(cons(N,L)) -> mark#(L) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    a__length#(cons(N,L)) -> mark#(L) ->
    mark#(s(X)) -> mark#(X)
    mark#(length(X)) -> a__length#(mark(X)) ->
    a__length#(cons(N,L)) -> mark#(L)
    mark#(length(X)) -> a__length#(mark(X)) ->
    a__length#(cons(N,L)) -> a__length#(mark(L))
    mark#(length(X)) -> mark#(X) -> mark#(zeros()) -> a__zeros#()
    mark#(length(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1)
    mark#(length(X)) -> mark#(X) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    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#(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#(cons(X1,X2)) -> mark#(X1)
    mark#(length(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    mark#(and(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#()
    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),X2)
    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#(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#(cons(X1,X2)) -> mark#(X1)
    mark#(and(X1,X2)) -> mark#(X1) ->
    mark#(s(X)) -> mark#(X)
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2) ->
    a__and#(tt(),X) -> mark#(X)
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) ->
    a__take#(s(M),cons(N,IL)) -> mark#(N)
    mark#(take(X1,X2)) -> mark#(X2) -> mark#(zeros()) -> a__zeros#()
    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),X2)
    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#(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#(cons(X1,X2)) -> mark#(X1)
    mark#(take(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X)
    mark#(take(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#()
    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),X2)
    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#(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#(cons(X1,X2)) -> mark#(X1)
    mark#(take(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
    mark#(s(X)) -> mark#(X) -> mark#(zeros()) -> a__zeros#()
    mark#(s(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    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#(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#(cons(X1,X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#()
    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),X2)
    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#(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#(cons(X1,X2)) -> mark#(X1)
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
    a__and#(tt(),X) -> mark#(X) -> mark#(zeros()) -> a__zeros#()
    a__and#(tt(),X) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1)
    a__and#(tt(),X) -> mark#(X) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    a__and#(tt(),X) -> mark#(X) -> mark#(length(X)) -> mark#(X)
    a__and#(tt(),X) -> mark#(X) ->
    mark#(length(X)) -> a__length#(mark(X))
    a__and#(tt(),X) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X2)
    a__and#(tt(),X) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X1)
    a__and#(tt(),X) -> mark#(X) ->
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    a__and#(tt(),X) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    a__and#(tt(),X) -> mark#(X) -> mark#(s(X)) -> mark#(X)
   SCC Processor:
    #sccs: 1
    #rules: 13
    #arcs: 96/196
    DPs:
     a__take#(s(M),cons(N,IL)) -> mark#(N)
     mark#(s(X)) -> mark#(X)
     mark#(cons(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#(X2)
     mark#(length(X)) -> a__length#(mark(X))
     a__length#(cons(N,L)) -> a__length#(mark(L))
     a__length#(cons(N,L)) -> mark#(L)
     mark#(length(X)) -> mark#(X)
     mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
     a__and#(tt(),X) -> mark#(X)
     mark#(and(X1,X2)) -> mark#(X1)
    TRS:
     a__zeros() -> cons(0(),zeros())
     a__and(tt(),X) -> mark(X)
     a__length(nil()) -> 0()
     a__length(cons(N,L)) -> s(a__length(mark(L)))
     a__take(0(),IL) -> nil()
     a__take(s(M),cons(N,IL)) -> cons(mark(N),take(M,IL))
     mark(zeros()) -> a__zeros()
     mark(and(X1,X2)) -> a__and(mark(X1),X2)
     mark(length(X)) -> a__length(mark(X))
     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(nil()) -> nil()
     mark(s(X)) -> s(mark(X))
     a__zeros() -> zeros()
     a__and(X1,X2) -> and(X1,X2)
     a__length(X) -> length(X)
     a__take(X1,X2) -> take(X1,X2)
    Open