YES

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

(COMMENT
Termination is shown by LPO with precedence:

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