YES(?,O(n^1))

Problem:
 a(b(x)) -> b(a(a(x)))
 b(c(x)) -> c(b(b(x)))
 c(a(x)) -> a(c(c(x)))
 u(a(x)) -> x
 v(b(x)) -> x
 w(c(x)) -> x
 a(u(x)) -> x
 b(v(x)) -> x
 c(w(x)) -> x

Proof:
 Bounds Processor:
  bound: 0
  enrichment: match
  automaton:
   final states: {7,6,5,4,3,2}
   transitions:
    a0(1) -> 2*
    b0(1) -> 3*
    c0(1) -> 4*
    u0(1) -> 5*
    v0(1) -> 6*
    w0(1) -> 7*
    f120() -> 1*
  problem:
   
  Qed