YES

Problem:
 a(a(b(x1))) -> b(b(a(a(x1))))
 b(a(x1)) -> a(c(b(x1)))

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {6,1}
   transitions:
    a0(3) -> 4*
    a0(2) -> 3*
    a0(8) -> 6*
    c2(42) -> 43*
    f30() -> 2*
    a1(31) -> 32*
    a1(15) -> 16*
    a1(19) -> 20*
    a2(43) -> 44*
    b1(17) -> 18*
    b1(13) -> 14*
    b1(29) -> 30*
    b1(35) -> 36*
    c1(18) -> 19*
    c1(30) -> 31*
    c1(14) -> 15*
    b0(4) -> 5*
    b0(2) -> 7*
    b0(5) -> 1*
    b2(41) -> 42*
    c0(7) -> 8*
    19 -> 41,35
    16 -> 5*
    2 -> 29*
    6 -> 30,7
    36 -> 14*
    44 -> 14*
    1 -> 3,13,4
    20 -> 1*
    3 -> 13*
    15 -> 17*
    32 -> 14*
  problem:
   
  Qed