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:
 Complexity 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
   max_matrix:
    1
    interpretation:
     [f](x0, x1) = x0 + x1,
     
     [b] = 1,
     
     [a] = 0
    orientation:
     f(a(),f(b(),f(a(),x))) = x + 1 >= x + 2 = 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
     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