YES

TRS:

  del(.(x,.(y,z))) -> f(=(x,y),x,y,z)
  f(true(),x,y,z) -> del(.(y,z))
  f(false(),x,y,z) -> .(x,del(.(y,z)))
  =(nil(),nil()) -> true()
  =(.(x,y),nil()) -> false()
  =(nil(),.(y,z)) -> false()
  =(.(x,y),.(u(),v())) -> and(=(x,u()),=(y,v()))

linear polynomial interpretations on N:

  del_A(x1) = x1
  del#_A(x1) = x1 + 1
  ._A(x1,x2) = x1 + x2 + 2
  .#_A(x1,x2) = 3
  f_A(x1,x2,x3,x4) = x2 + x3 + x4 + 4
  f#_A(x1,x2,x3,x4) = x2 + x3 + x4 + 4
  =_A(x1,x2) = x1 + x2 + 1
  =#_A(x1,x2) = 3
  true_A = 3
  true#_A = 2
  false_A = 1
  false#_A = 0
  nil_A = 1
  nil#_A = 1
  u_A = 1
  u#_A = 1
  v_A = 1
  v#_A = 0
  and_A(x1,x2) = x1 + x2
  and#_A(x1,x2) = 0

precedence:

  del = . > f = and > = > true = u > nil = v > false