YES(?,O(n^1))

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

Proof:
 Complexity Transformation Processor:
  strict:
   a(b(a(x1))) -> b(a(x1))
   b(b(b(x1))) -> b(a(b(x1)))
   a(a(x1)) -> b(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 + 1 = b(a(x1))
     
     b(b(b(x1))) = x1 + 3 >= x1 + 2 = b(a(b(x1)))
     
     a(a(x1)) = x1 >= x1 + 3 = b(b(b(x1)))
    problem:
     strict:
      a(b(a(x1))) -> b(a(x1))
      a(a(x1)) -> b(b(b(x1)))
     weak:
      b(b(b(x1))) -> b(a(b(x1)))
    Matrix Interpretation Processor:
     dimension: 1
     max_matrix:
      1
      interpretation:
       [b](x0) = x0 + 1,
       
       [a](x0) = x0 + 1
      orientation:
       a(b(a(x1))) = x1 + 3 >= x1 + 2 = b(a(x1))
       
       a(a(x1)) = x1 + 2 >= x1 + 3 = b(b(b(x1)))
       
       b(b(b(x1))) = x1 + 3 >= x1 + 3 = b(a(b(x1)))
      problem:
       strict:
        a(a(x1)) -> b(b(b(x1)))
       weak:
        a(b(a(x1))) -> b(a(x1))
        b(b(b(x1))) -> b(a(b(x1)))
      Bounds Processor:
       bound: 2
       enrichment: match
       automaton:
        final states: {2,1}
        transitions:
         b1(5) -> 6*
         b1(14) -> 15*
         b1(4) -> 5*
         b1(6) -> 7*
         a1(42) -> 43*
         a1(22) -> 23*
         a1(34) -> 35*
         a1(24) -> 25*
         a1(46) -> 47*
         a1(48) -> 49*
         b2(60) -> 61*
         b2(40) -> 41*
         b2(30) -> 31*
         b2(62) -> 63*
         b2(32) -> 33*
         b2(66) -> 67*
         b2(31) -> 32*
         b2(85) -> 86*
         a0(2) -> 1*
         a0(1) -> 1*
         a2(97) -> 98*
         a2(87) -> 88*
         a2(72) -> 73*
         a2(99) -> 100*
         a2(89) -> 90*
         a2(84) -> 85*
         a2(54) -> 55*
         a2(91) -> 92*
         a2(113) -> 114*
         a2(78) -> 79*
         b0(2) -> 2*
         b0(1) -> 2*
         1 -> 48,14
         2 -> 46,1,4
         4 -> 66*
         5 -> 92,49,34
         6 -> 62,22
         7 -> 43,35,23,6,5,42,1
         14 -> 60*
         15 -> 23,47,35,25,2,24,5
         22 -> 87*
         23 -> 14*
         24 -> 99,30
         25 -> 6*
         31 -> 114,86,98,90,100,61,33,7,67,63,73,79,23,47,88,41,78,15,32
         33 -> 63,41,55,54,23
         34 -> 97,40
         35 -> 6*
         41 -> 72,31
         42 -> 84*
         43 -> 14*
         46 -> 89*
         47 -> 14*
         48 -> 91*
         49 -> 14*
         55 -> 30*
         61 -> 54*
         63 -> 54*
         67 -> 54*
         73 -> 32*
         79 -> 32*
         86 -> 114,113,98,90,92,100,88,55
         88 -> 85*
         90 -> 85*
         92 -> 85*
         98 -> 85*
         100 -> 85*
         114 -> 30*
       problem:
        strict:
         
        weak:
         a(a(x1)) -> b(b(b(x1)))
         a(b(a(x1))) -> b(a(x1))
         b(b(b(x1))) -> b(a(b(x1)))
       Qed