YES

(VAR x1 x0 x2 y x z)
(RULES
  i(h(x1)) -> h(i(x1))
  h(one()) -> one()
  i(*(x1,x0)) -> *(i(x0),i(x1))
  i(k(x0)) -> k(i(x0))
  *(x0,*(i(x0),x1)) -> x1
  i(f(x0)) -> f(i(x0))
  i(g(x0)) -> g(i(x0))
  k(one()) -> one()
  *(x0,i(x0)) -> one()
  i(i(x0)) -> x0
  i(one()) -> one()
  g(one()) -> one()
  f(one()) -> one()
  *(x0,one()) -> x0
  *(g(x0),*(f(x1),x2)) -> *(f(x1),*(g(x0),x2))
  *(f(x0),*(h(x1),x2)) -> *(h(x1),*(f(x0),x2))
  *(g(x0),*(h(x1),x2)) -> *(h(x1),*(g(x0),x2))
  *(f(x1),*(k(x0),x2)) -> *(k(x0),*(f(x1),x2))
  *(h(x1),*(k(x0),x2)) -> *(k(x0),*(h(x1),x2))
  *(g(x1),*(k(x0),x2)) -> *(k(x0),*(g(x1),x2))
  *(f(x0),*(f(x1),x2)) -> *(f(*(x0,x1)),x2)
  *(g(x0),*(g(x1),x2)) -> *(g(*(x0,x1)),x2)
  *(h(x0),*(h(x1),x2)) -> *(h(*(x0,x1)),x2)
  *(k(x0),*(k(x1),x2)) -> *(k(*(x0,x1)),x2)
  *(i(x1),*(x1,x0)) -> x0
  *(g(y),k(x)) -> *(k(x),g(y))
  *(h(y),k(x)) -> *(k(x),h(y))
  *(f(x),k(y)) -> *(k(y),f(x))
  *(g(y),h(x)) -> *(h(x),g(y))
  *(f(x),h(y)) -> *(h(y),f(x))
  *(g(y),f(x)) -> *(f(x),g(y))
  *(k(x),k(y)) -> k(*(x,y))
  *(h(x),h(y)) -> h(*(x,y))
  *(g(x),g(y)) -> g(*(x,y))
  *(f(x),f(y)) -> f(*(x,y))
  *(*(x,y),z) -> *(x,*(y,z))
  *(i(x),x) -> one()
  *(one(),x) -> x
)

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

  *_A(x1,x2) = x1 + x2
  one_A = 0
  i_A(x1) = x1
  f_A(x1) = 2
  g_A(x1) = x1 + 3
  h_A(x1) = 1
  k_A(x1) = 0
  *#_A(x1,x2) = x1
  one#_A = 0

weights

  w0 = 1
  w(*) = 0
  w(one) = 1
  w(i) = 0
  w(f) = 1
  w(g) = 1
  w(h) = 1
  w(k) = 1

and precedence:

i > k > h > * > f > g > one
)