YES(?,O(n^1))

Problem:
 0(*(x1)) -> *(1(x1))
 1(*(x1)) -> 0(#(x1))
 #(0(x1)) -> 0(#(x1))
 #(1(x1)) -> 1(#(x1))
 #($(x1)) -> *($(x1))
 #(#(x1)) -> #(x1)
 #(*(x1)) -> *(x1)

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {5,4,3}
   transitions:
    *1(42) -> 43*
    *1(27) -> 28*
    *1(7) -> 8*
    *1(36) -> 37*
    $1(34) -> 35*
    $1(26) -> 27*
    01(17) -> 18*
    #1(24) -> 25*
    #1(16) -> 17*
    11(14) -> 15*
    11(6) -> 7*
    *2(48) -> 49*
    00(2) -> 3*
    00(1) -> 3*
    12(50) -> 51*
    12(47) -> 48*
    12(56) -> 57*
    *0(2) -> 1*
    *0(1) -> 1*
    10(2) -> 4*
    10(1) -> 4*
    #0(2) -> 5*
    #0(1) -> 5*
    $0(2) -> 2*
    $0(1) -> 2*
    1 -> 42,34,24,14
    2 -> 36,26,16,6
    8 -> 3*
    15 -> 7*
    18 -> 48,15,7,4
    25 -> 17*
    27 -> 50*
    28 -> 17,5
    35 -> 27*
    36 -> 56*
    37 -> 25,17,5
    42 -> 47*
    43 -> 25,17,5
    49 -> 18,4,15
    51 -> 48*
    57 -> 48*
  problem:
   
  Qed