YES

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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [b](x0) = x0 + 4,
   
   [a](x0) = x0 + 6
  orientation:
   a(a(x1)) = x1 + 12 >= x1 + 12 = b(b(b(x1)))
   
   b(b(b(b(b(x1))))) = x1 + 20 >= x1 + 18 = a(a(a(x1)))
  problem:
   a(a(x1)) -> b(b(b(x1)))
  KBO Processor:
   weight function:
    w0 = 1
    w(a) = 1
    w(b) = 0
   precedence:
    b > a
   problem:
    
   Qed