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)))
 mark(zeros()) -> a__zeros()
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(length(X)) -> a__length(mark(X))
 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)

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))
   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#(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)))
   mark(zeros()) -> a__zeros()
   mark(and(X1,X2)) -> a__and(mark(X1),X2)
   mark(length(X)) -> a__length(mark(X))
   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)
  TDG Processor:
   DPs:
    a__and#(tt(),X) -> mark#(X)
    a__length#(cons(N,L)) -> mark#(L)
    a__length#(cons(N,L)) -> a__length#(mark(L))
    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#(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)))
    mark(zeros()) -> a__zeros()
    mark(and(X1,X2)) -> a__and(mark(X1),X2)
    mark(length(X)) -> a__length(mark(X))
    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)
   graph:
    a__length#(cons(N,L)) -> a__length#(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)
    a__length#(cons(N,L)) -> mark#(L) -> mark#(s(X)) -> mark#(X)
    a__length#(cons(N,L)) -> mark#(L) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    a__length#(cons(N,L)) -> mark#(L) ->
    mark#(length(X)) -> a__length#(mark(X))
    a__length#(cons(N,L)) -> mark#(L) ->
    mark#(length(X)) -> mark#(X)
    a__length#(cons(N,L)) -> mark#(L) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    a__length#(cons(N,L)) -> mark#(L) ->
    mark#(and(X1,X2)) -> mark#(X1)
    a__length#(cons(N,L)) -> mark#(L) ->
    mark#(zeros()) -> a__zeros#()
    mark#(length(X)) -> a__length#(mark(X)) ->
    a__length#(cons(N,L)) -> a__length#(mark(L))
    mark#(length(X)) -> a__length#(mark(X)) ->
    a__length#(cons(N,L)) -> mark#(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#(length(X)) -> a__length#(mark(X))
    mark#(length(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X)
    mark#(length(X)) -> mark#(X) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    mark#(length(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1)
    mark#(length(X)) -> mark#(X) -> mark#(zeros()) -> a__zeros#()
    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)) -> mark#(X1) ->
    mark#(length(X)) -> a__length#(mark(X))
    mark#(and(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X)
    mark#(and(X1,X2)) -> mark#(X1) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1)
    mark#(and(X1,X2)) -> mark#(X1) ->
    mark#(zeros()) -> a__zeros#()
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2) -> a__and#(tt(),X) -> mark#(X)
    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#(length(X)) -> a__length#(mark(X))
    mark#(s(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X)
    mark#(s(X)) -> mark#(X) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    mark#(s(X)) -> mark#(X) -> mark#(and(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#(length(X)) -> a__length#(mark(X))
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(and(X1,X2)) -> mark#(X1)
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#()
    a__and#(tt(),X) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    a__and#(tt(),X) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    a__and#(tt(),X) -> mark#(X) ->
    mark#(length(X)) -> a__length#(mark(X))
    a__and#(tt(),X) -> mark#(X) -> mark#(length(X)) -> mark#(X)
    a__and#(tt(),X) -> mark#(X) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    a__and#(tt(),X) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1)
    a__and#(tt(),X) -> mark#(X) -> mark#(zeros()) -> a__zeros#()
   SCC Processor:
    #sccs: 1
    #rules: 9
    #arcs: 47/100
    DPs:
     a__length#(cons(N,L)) -> a__length#(mark(L))
     a__length#(cons(N,L)) -> mark#(L)
     mark#(and(X1,X2)) -> mark#(X1)
     mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
     a__and#(tt(),X) -> mark#(X)
     mark#(length(X)) -> mark#(X)
     mark#(length(X)) -> a__length#(mark(X))
     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)))
     mark(zeros()) -> a__zeros()
     mark(and(X1,X2)) -> a__and(mark(X1),X2)
     mark(length(X)) -> a__length(mark(X))
     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)
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [a__length#](x0) = x0,
      
      [mark#](x0) = x0,
      
      [a__and#](x0, x1) = 1x0 + x1,
      
      [length](x0) = 1x0,
      
      [and](x0, x1) = 1x0 + x1 + 4,
      
      [s](x0) = x0 + 0,
      
      [a__length](x0) = 1x0,
      
      [nil] = 0,
      
      [mark](x0) = x0,
      
      [a__and](x0, x1) = 1x0 + x1 + 4,
      
      [tt] = 0,
      
      [cons](x0, x1) = x0 + x1 + 0,
      
      [zeros] = 0,
      
      [0] = 0,
      
      [a__zeros] = 0
     orientation:
      a__length#(cons(N,L)) = L + N + 0 >= L = a__length#(mark(L))
      
      a__length#(cons(N,L)) = L + N + 0 >= L = mark#(L)
      
      mark#(and(X1,X2)) = 1X1 + X2 + 4 >= X1 = mark#(X1)
      
      mark#(and(X1,X2)) = 1X1 + X2 + 4 >= 1X1 + X2 = a__and#(mark(X1),X2)
      
      a__and#(tt(),X) = X + 1 >= X = mark#(X)
      
      mark#(length(X)) = 1X >= X = mark#(X)
      
      mark#(length(X)) = 1X >= X = a__length#(mark(X))
      
      mark#(cons(X1,X2)) = X1 + X2 + 0 >= X1 = mark#(X1)
      
      mark#(s(X)) = X + 0 >= X = mark#(X)
      
      a__zeros() = 0 >= 0 = cons(0(),zeros())
      
      a__and(tt(),X) = X + 4 >= X = mark(X)
      
      a__length(nil()) = 1 >= 0 = 0()
      
      a__length(cons(N,L)) = 1L + 1N + 1 >= 1L + 0 = s(a__length(mark(L)))
      
      mark(zeros()) = 0 >= 0 = a__zeros()
      
      mark(and(X1,X2)) = 1X1 + X2 + 4 >= 1X1 + X2 + 4 = a__and(mark(X1),X2)
      
      mark(length(X)) = 1X >= 1X = a__length(mark(X))
      
      mark(cons(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = cons(mark(X1),X2)
      
      mark(0()) = 0 >= 0 = 0()
      
      mark(tt()) = 0 >= 0 = tt()
      
      mark(nil()) = 0 >= 0 = nil()
      
      mark(s(X)) = X + 0 >= X + 0 = s(mark(X))
      
      a__zeros() = 0 >= 0 = zeros()
      
      a__and(X1,X2) = 1X1 + X2 + 4 >= 1X1 + X2 + 4 = and(X1,X2)
      
      a__length(X) = 1X >= 1X = length(X)
     problem:
      DPs:
       a__length#(cons(N,L)) -> a__length#(mark(L))
       a__length#(cons(N,L)) -> mark#(L)
       mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
       a__and#(tt(),X) -> mark#(X)
       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)))
       mark(zeros()) -> a__zeros()
       mark(and(X1,X2)) -> a__and(mark(X1),X2)
       mark(length(X)) -> a__length(mark(X))
       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)
     SCC Processor:
      #sccs: 2
      #rules: 5
      #arcs: 41/36
      DPs:
       a__length#(cons(N,L)) -> a__length#(mark(L))
      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)))
       mark(zeros()) -> a__zeros()
       mark(and(X1,X2)) -> a__and(mark(X1),X2)
       mark(length(X)) -> a__length(mark(X))
       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)
      Open
      
      DPs:
       mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
       a__and#(tt(),X) -> mark#(X)
       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)))
       mark(zeros()) -> a__zeros()
       mark(and(X1,X2)) -> a__and(mark(X1),X2)
       mark(length(X)) -> a__length(mark(X))
       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)
      Subterm Criterion Processor:
       simple projection:
        pi(a__and#) = 1
        pi(mark#) = 0
       problem:
        DPs:
         a__and#(tt(),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)))
         mark(zeros()) -> a__zeros()
         mark(and(X1,X2)) -> a__and(mark(X1),X2)
         mark(length(X)) -> a__length(mark(X))
         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)
       SCC Processor:
        #sccs: 0
        #rules: 0
        #arcs: 10/1