YES

(VAR x y z)
(RULES
  apply(apply(t(),x),y) -> apply(y,x)
  apply(apply(apply(b(),x),y),z) -> apply(x,apply(y,z))
)

(COMMENT
Termination is shown by EKBO with interpretations on natural numbers

  apply_A(x1,x2) = 1
  b_A = 1
  t_A = 1
  apply#_A(x1,x2) = 0
  b#_A = 0
  t#_A = 0

weights

  w0 = 1
  w(apply) = 0
  w(b) = 1
  w(t) = 1

and precedence:

t > apply > b
)