YES

(VAR x0 x1 x y z)
(RULES
  *(x0,*(1(),x1)) -> *(x0,x1)
  exp(+(x,y)) -> *(exp(x),exp(y))
  exp(0()) -> 1()
  *(x,1()) -> x
  *(*(x,y),z) -> *(x,*(y,z))
  +(x,0()) -> x
  +(x,+(y,z)) -> +(+(x,y),z)
)

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

  +_A(x1,x2) = x1 + x2 + 2
  0_A = 1
  *_A(x1,x2) = x1 + x2 + 1
  1_A = 2
  exp_A(x1) = x1 + 1
  +#_A(x1,x2) = x2
  0#_A = 0
  *#_A(x1,x2) = x1 + x2
  1#_A = 0
  exp#_A(x1) = x1

weights

  w0 = 1
  w(+) = 1
  w(0) = 1
  w(*) = 0
  w(1) = 1
  w(exp) = 1

and precedence:

exp > * > 1 > + > 0
)