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 KBO with weight

  w0 = 2
  w(eq) = 4
  w(true) = 6
  w(nil) = 2
  w(end) = 3
  w(false) = 2
  w(and) = 0
  w(f) = 3
  w(.) = 0
  w(null) = 2

and precedence:

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