YES

Problem:
 *(i(x),x) -> 1()
 *(1(),y) -> y
 *(x,0()) -> 0()
 *(*(x,y),z) -> *(x,*(y,z))

Proof:
 Bounds Processor:
  bound: 1
  enrichment: top
  automaton:
   final states: {9,8,7,6,4,3,2,1}
   transitions:
    f40() -> 7*,5,4,2
    10() -> 8*,5,4,1
    00() -> 9*,5,4,3
    *0(7,5) -> 6*
    *0(2,5) -> 6*,5,4
    *0(7,7) -> 6*
    *0(2,7) -> 6*
    *0(7,9) -> 6*
    *0(2,9) -> 6*
    *0(7,2) -> 6*
    *0(2,2) -> 6*,4,5
    *0(7,6) -> 6*
    *0(2,6) -> 6*
    *0(7,8) -> 6*
    *0(2,8) -> 6*
    01() -> 6,3,4,5,9*
    1 -> 4,5
    2 -> 5*
    3 -> 5*
    4 -> 5*
    5 -> 4*
  problem:
   
  Qed