YES

(VAR x y z u v)
(RULES
  and(null(nil()),null(nil())) -> null(nil())
  null(end(x,y)) -> false()
  true() -> null(nil())
  .(end(x,y),z) -> .(x,f(y,z))
  .(nil(),y) -> y
  f(x,end(y,z)) -> end(f(x,y),z)
  f(x,nil()) -> end(nil(),x)
  eq(end(x,y),end(u,v)) -> and(eq(y,v),eq(x,u))
  eq(end(x,y),nil()) -> false()
  eq(nil(),end(y,z)) -> false()
  eq(x,x) -> null(nil())
)

(COMMENT
Termination is shown by EKBO with interpretations on natural numbers

  eq_A(x1,x2) = 0
  true_A = 0
  nil_A = 1
  end_A(x1,x2) = x1 + x2 + 1
  false_A = 0
  and_A(x1,x2) = x1 + x2
  f_A(x1,x2) = x1 + x2 + 1
  ._A(x1,x2) = x1 + x2 + 1
  null_A(x1) = 0
  eq#_A(x1,x2) = x1 + x2
  true#_A = 0
  nil#_A = 0
  end#_A(x1,x2) = x1 + x2
  false#_A = 0
  and#_A(x1,x2) = x1 + x2
  f#_A(x1,x2) = x1 + x2

weights

  w0 = 2
  w(eq) = 0
  w(true) = 3
  w(nil) = 2
  w(end) = 1
  w(false) = 5
  w(and) = 0
  w(f) = 1
  w(.) = 0
  w(null) = 1

and precedence:

eq > and > true > null > nil > false > f > . > end
)