YES(?,O(n^1))

Problem:
 a(a(x)) -> a(b(a(x)))

Proof:
 RT Transformation Processor:
  strict:
   a(a(x)) -> a(b(a(x)))
  weak:
   
  Bounds Processor:
   bound: 2
   enrichment: match-rt
   automaton:
    final states: {3}
    transitions:
     a1(10) -> 11*
     a1(8) -> 9*
     b1(12) -> 13*
     b1(9) -> 10*
     a2(20) -> 21*
     a2(22) -> 23*
     a0(3) -> 3*
     b2(21) -> 22*
     b0(3) -> 3*
     3 -> 8*
     10 -> 20*
     11 -> 9,12,3
     13 -> 10*
     23 -> 9*
   problem:
    strict:
     
    weak:
     a(a(x)) -> a(b(a(x)))
   Qed