YES(?,O(n^1))

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

Proof:
 Complexity Transformation Processor:
  strict:
   a(b(a(x1))) -> a(b(b(a(x1))))
   b(b(b(x1))) -> b(b(x1))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [b](x0) = x0 + 1,
     
     [a](x0) = x0
    orientation:
     a(b(a(x1))) = x1 + 1 >= x1 + 2 = a(b(b(a(x1))))
     
     b(b(b(x1))) = x1 + 3 >= x1 + 2 = b(b(x1))
    problem:
     strict:
      a(b(a(x1))) -> a(b(b(a(x1))))
     weak:
      b(b(b(x1))) -> b(b(x1))
    Bounds Processor:
     bound: 1
     enrichment: match
     automaton:
      final states: {3}
      transitions:
       a1(12) -> 13*
       a1(9) -> 10*
       b1(10) -> 11*
       b1(14) -> 15*
       b1(11) -> 12*
       a0(3) -> 3*
       b0(3) -> 3*
       3 -> 9*
       13 -> 10,14,3
       15 -> 11*
     problem:
      strict:
       
      weak:
       a(b(a(x1))) -> a(b(b(a(x1))))
       b(b(b(x1))) -> b(b(x1))
     Qed