YES

TRS:

  f(0()) -> s(0())
  f(s(0())) -> s(s(0()))
  f(s(0())) -> *(s(s(0())),f(0()))
  f(+(x,s(0()))) -> +(s(s(0())),f(x))
  f(+(x,y)) -> *(f(x),f(y))

linear polynomial interpretations on N:

  f_A(x1) = x1 + 1
  f#_A(x1) = x1 + 1
  0_A = 0
  0#_A = 2
  s_A(x1) = 0
  s#_A(x1) = 0
  *_A(x1,x2) = 0
  *#_A(x1,x2) = 0
  +_A(x1,x2) = x1 + x2 + 4
  +#_A(x1,x2) = x2 + 3

precedence:

  + > 0 = * > f > s