YES(?,O(n^1))

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

Proof:
 RT Transformation Processor:
  strict:
   a(a(x1)) -> b(b(b(x1)))
   b(b(b(b(b(x1))))) -> a(a(a(x1)))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [b](x0) = x0 + 1,
    
    [a](x0) = x0
   orientation:
    a(a(x1)) = x1 >= x1 + 3 = b(b(b(x1)))
    
    b(b(b(b(b(x1))))) = x1 + 5 >= x1 = a(a(a(x1)))
   problem:
    strict:
     a(a(x1)) -> b(b(b(x1)))
    weak:
     b(b(b(b(b(x1))))) -> a(a(a(x1)))
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [b](x0) = x0 + 12,
     
     [a](x0) = x0 + 20
    orientation:
     a(a(x1)) = x1 + 40 >= x1 + 36 = b(b(b(x1)))
     
     b(b(b(b(b(x1))))) = x1 + 60 >= x1 + 60 = a(a(a(x1)))
    problem:
     strict:
      
     weak:
      a(a(x1)) -> b(b(b(x1)))
      b(b(b(b(b(x1))))) -> a(a(a(x1)))
    Qed