NO

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:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [length](x0) = x0,
   
   [and](x0, x1) = x0 + x1,
   
   [take](x0, x1) = x0 + 2x1,
   
   [a__take](x0, x1) = x0 + 2x1,
   
   [s](x0) = 2x0,
   
   [a__length](x0) = x0,
   
   [nil] = 0,
   
   [mark](x0) = x0,
   
   [a__and](x0, x1) = x0 + x1,
   
   [tt] = 2,
   
   [cons](x0, x1) = x0 + 2x1,
   
   [zeros] = 0,
   
   [0] = 0,
   
   [a__zeros] = 0
  orientation:
   a__zeros() = 0 >= 0 = cons(0(),zeros())
   
   a__and(tt(),X) = X + 2 >= X = mark(X)
   
   a__length(nil()) = 0 >= 0 = 0()
   
   a__length(cons(N,L)) = 2L + N >= 2L = s(a__length(mark(L)))
   
   a__take(0(),IL) = 2IL >= 0 = nil()
   
   a__take(s(M),cons(N,IL)) = 4IL + 2M + 2N >= 4IL + 2M + N = cons(mark(N),take(M,IL))
   
   mark(zeros()) = 0 >= 0 = a__zeros()
   
   mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = a__and(mark(X1),X2)
   
   mark(length(X)) = X >= X = a__length(mark(X))
   
   mark(take(X1,X2)) = X1 + 2X2 >= X1 + 2X2 = a__take(mark(X1),mark(X2))
   
   mark(cons(X1,X2)) = X1 + 2X2 >= X1 + 2X2 = cons(mark(X1),X2)
   
   mark(0()) = 0 >= 0 = 0()
   
   mark(tt()) = 2 >= 2 = tt()
   
   mark(nil()) = 0 >= 0 = nil()
   
   mark(s(X)) = 2X >= 2X = s(mark(X))
   
   a__zeros() = 0 >= 0 = zeros()
   
   a__and(X1,X2) = X1 + X2 >= X1 + X2 = and(X1,X2)
   
   a__length(X) = X >= X = length(X)
   
   a__take(X1,X2) = X1 + 2X2 >= X1 + 2X2 = take(X1,X2)
  problem:
   a__zeros() -> cons(0(),zeros())
   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)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [length](x0) = x0,
    
    [and](x0, x1) = x0 + 3x1 + 1,
    
    [take](x0, x1) = x0 + x1 + 1,
    
    [a__take](x0, x1) = x0 + x1 + 1,
    
    [s](x0) = x0,
    
    [a__length](x0) = x0,
    
    [nil] = 0,
    
    [mark](x0) = x0,
    
    [a__and](x0, x1) = x0 + 3x1 + 1,
    
    [tt] = 0,
    
    [cons](x0, x1) = 2x0 + x1,
    
    [zeros] = 0,
    
    [0] = 0,
    
    [a__zeros] = 0
   orientation:
    a__zeros() = 0 >= 0 = cons(0(),zeros())
    
    a__length(nil()) = 0 >= 0 = 0()
    
    a__length(cons(N,L)) = L + 2N >= L = s(a__length(mark(L)))
    
    a__take(0(),IL) = IL + 1 >= 0 = nil()
    
    a__take(s(M),cons(N,IL)) = IL + M + 2N + 1 >= IL + M + 2N + 1 = cons(mark(N),take(M,IL))
    
    mark(zeros()) = 0 >= 0 = a__zeros()
    
    mark(and(X1,X2)) = X1 + 3X2 + 1 >= X1 + 3X2 + 1 = a__and(mark(X1),X2)
    
    mark(length(X)) = X >= X = a__length(mark(X))
    
    mark(take(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__take(mark(X1),mark(X2))
    
    mark(cons(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = cons(mark(X1),X2)
    
    mark(0()) = 0 >= 0 = 0()
    
    mark(tt()) = 0 >= 0 = tt()
    
    mark(nil()) = 0 >= 0 = nil()
    
    mark(s(X)) = X >= X = s(mark(X))
    
    a__zeros() = 0 >= 0 = zeros()
    
    a__and(X1,X2) = X1 + 3X2 + 1 >= X1 + 3X2 + 1 = and(X1,X2)
    
    a__length(X) = X >= X = length(X)
    
    a__take(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = take(X1,X2)
   problem:
    a__zeros() -> cons(0(),zeros())
    a__length(nil()) -> 0()
    a__length(cons(N,L)) -> s(a__length(mark(L)))
    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)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [length](x0) = x0 + 2,
     
     [and](x0, x1) = x0 + x1,
     
     [take](x0, x1) = x0 + x1 + 2,
     
     [a__take](x0, x1) = x0 + x1 + 2,
     
     [s](x0) = x0,
     
     [a__length](x0) = x0 + 2,
     
     [nil] = 0,
     
     [mark](x0) = x0,
     
     [a__and](x0, x1) = x0 + x1,
     
     [tt] = 1,
     
     [cons](x0, x1) = 4x0 + x1,
     
     [zeros] = 4,
     
     [0] = 0,
     
     [a__zeros] = 4
    orientation:
     a__zeros() = 4 >= 4 = cons(0(),zeros())
     
     a__length(nil()) = 2 >= 0 = 0()
     
     a__length(cons(N,L)) = L + 4N + 2 >= L + 2 = s(a__length(mark(L)))
     
     a__take(s(M),cons(N,IL)) = IL + M + 4N + 2 >= IL + M + 4N + 2 = cons(mark(N),take(M,IL))
     
     mark(zeros()) = 4 >= 4 = a__zeros()
     
     mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = a__and(mark(X1),X2)
     
     mark(length(X)) = X + 2 >= X + 2 = a__length(mark(X))
     
     mark(take(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = a__take(mark(X1),mark(X2))
     
     mark(cons(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = cons(mark(X1),X2)
     
     mark(0()) = 0 >= 0 = 0()
     
     mark(tt()) = 1 >= 1 = tt()
     
     mark(nil()) = 0 >= 0 = nil()
     
     mark(s(X)) = X >= X = s(mark(X))
     
     a__zeros() = 4 >= 4 = zeros()
     
     a__and(X1,X2) = X1 + X2 >= X1 + X2 = and(X1,X2)
     
     a__length(X) = X + 2 >= X + 2 = length(X)
     
     a__take(X1,X2) = X1 + X2 + 2 >= X1 + X2 + 2 = take(X1,X2)
    problem:
     a__zeros() -> cons(0(),zeros())
     a__length(cons(N,L)) -> s(a__length(mark(L)))
     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)
    Unfolding Processor:
     loop length: 3
     terms:
      a__length(cons(N,zeros()))
      s(a__length(mark(zeros())))
      s(a__length(a__zeros()))
     context: s([])
     substitution:
      N -> 0()
     Qed