YES(?,O(n^1))

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {5,4,3,2}
   transitions:
    b1(17) -> 18*
    b1(19) -> 20*
    b1(16) -> 17*
    b1(18) -> 19*
    a1(12) -> 13*
    a1(14) -> 15*
    a1(11) -> 12*
    a1(13) -> 14*
    c0(1) -> 2*
    a0(1) -> 5*
    d0(1) -> 3*
    b0(1) -> 4*
    f80() -> 1*
    1 -> 16,11
    15 -> 2*
    20 -> 3*
  problem:
   
  Qed