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()))

max/plus interpretations on N:

  del_A(x1) = max{3, -10 + x1}
  del#_A(x1) = max{2, 20}
  ._A(x1,x2) = max{15, -10, 11 + x2}
  .#_A(x1,x2) = max{21, 18, 13 + x2}
  f_A(x1,x2,x3,x4) = max{16, 13, 13, -11, 12 + x4}
  f#_A(x1,x2,x3,x4) = max{19, 22, 2, 19, 17 + x4}
  =_A(x1,x2) = max{45, 29 + x1, 1 + x2}
  =#_A(x1,x2) = max{23, 21, 1}
  true_A = 31
  true#_A = 0
  false_A = 45
  false#_A = 24
  nil_A = 1
  nil#_A = 25
  u_A = 28
  u#_A = 20
  v_A = 16
  v#_A = 21
  and_A(x1,x2) = max{45, -9, x2}
  and#_A(x1,x2) = max{22, 0, 21}

precedence:

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