YES(?,O(n^1))

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

Proof:
 RT Transformation Processor:
  strict:
   f(a(),f(b(),f(a(),x))) -> f(a(),f(b(),f(b(),f(a(),x))))
   f(b(),f(b(),f(b(),x))) -> f(b(),f(b(),x))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [f](x0, x1) = x0 + x1 + 1,
    
    [b] = 0,
    
    [a] = 14
   orientation:
    f(a(),f(b(),f(a(),x))) = x + 31 >= x + 32 = f(a(),f(b(),f(b(),f(a(),x))))
    
    f(b(),f(b(),f(b(),x))) = x + 3 >= x + 2 = f(b(),f(b(),x))
   problem:
    strict:
     f(a(),f(b(),f(a(),x))) -> f(a(),f(b(),f(b(),f(a(),x))))
    weak:
     f(b(),f(b(),f(b(),x))) -> f(b(),f(b(),x))
   Bounds Processor:
    bound: 1
    enrichment: match-rt
    automaton:
     final states: {4}
     transitions:
      f1(12,11) -> 13*
      f1(12,13) -> 13,14
      f1(10,4) -> 11*
      f1(10,14) -> 11,4
      f1(12,4) -> 13*
      a1() -> 10*
      b1() -> 12*
      f0(4,4) -> 4*
      a0() -> 4*
      b0() -> 4*
    problem:
     strict:
      
     weak:
      f(a(),f(b(),f(a(),x))) -> f(a(),f(b(),f(b(),f(a(),x))))
      f(b(),f(b(),f(b(),x))) -> f(b(),f(b(),x))
    Qed