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{34, 6 + x1}
  del#_A(x1) = max{34, 6 + x1}
  ._A(x1,x2) = max{30, 36 + x1, 25 + x2}
  .#_A(x1,x2) = max{30, 36 + x1, 25 + x2}
  f_A(x1,x2,x3,x4) = max{62, 19 + x1, 42 + x2, 67 + x3, 56 + x4}
  f#_A(x1,x2,x3,x4) = max{62, 19 + x1, 42 + x2, 67 + x3, 56 + x4}
  =_A(x1,x2) = max{43, 23 + x1, 15 + x2}
  =#_A(x1,x2) = max{43, 23 + x1, 15 + x2}
  true_A = 18
  true#_A = 18
  false_A = 16
  false#_A = 16
  nil_A = 19
  nil#_A = 19
  u_A = 26
  u#_A = 26
  v_A = 31
  v#_A = 31
  and_A(x1,x2) = max{42, 1 + x1, 1 + x2}
  and#_A(x1,x2) = max{42, 1 + x1, 1 + x2}

precedence:

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