YES

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

Proof:
 DP Processor:
  DPs:
   a#(b(a(b(x1)))) -> a#(x1)
   a#(b(a(b(x1)))) -> a#(a(x1))
   a#(b(a(b(x1)))) -> a#(b(b(a(a(x1)))))
  TRS:
   a(a(x1)) -> x1
   a(b(a(b(x1)))) -> b(a(b(b(a(a(x1))))))
  EDG Processor:
   DPs:
    a#(b(a(b(x1)))) -> a#(x1)
    a#(b(a(b(x1)))) -> a#(a(x1))
    a#(b(a(b(x1)))) -> a#(b(b(a(a(x1)))))
   TRS:
    a(a(x1)) -> x1
    a(b(a(b(x1)))) -> b(a(b(b(a(a(x1))))))
   graph:
    a#(b(a(b(x1)))) -> a#(a(x1)) -> a#(b(a(b(x1)))) -> a#(x1)
    a#(b(a(b(x1)))) -> a#(a(x1)) -> a#(b(a(b(x1)))) -> a#(a(x1))
    a#(b(a(b(x1)))) -> a#(a(x1)) -> a#(b(a(b(x1)))) -> a#(b(b(a(a(x1)))))
    a#(b(a(b(x1)))) -> a#(x1) -> a#(b(a(b(x1)))) -> a#(x1)
    a#(b(a(b(x1)))) -> a#(x1) -> a#(b(a(b(x1)))) -> a#(a(x1))
    a#(b(a(b(x1)))) -> a#(x1) -> a#(b(a(b(x1)))) -> a#(b(b(a(a(x1)))))
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 6/9
    DPs:
     a#(b(a(b(x1)))) -> a#(a(x1))
     a#(b(a(b(x1)))) -> a#(x1)
    TRS:
     a(a(x1)) -> x1
     a(b(a(b(x1)))) -> b(a(b(b(a(a(x1))))))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
      [a#](x0) = [2 0 0]x0 + [3],
      
                [0 2 0]     [0]
      [b](x0) = [0 0 0]x0 + [0]
                [1 1 0]     [1],
      
                [2 0 0]  
      [a](x0) = [0 0 1]x0
                [1 1 0]  
     orientation:
      a#(b(a(b(x1)))) = [4 4 0]x1 + [7] >= [4 0 0]x1 + [3] = a#(a(x1))
      
      a#(b(a(b(x1)))) = [4 4 0]x1 + [7] >= [2 0 0]x1 + [3] = a#(x1)
      
                 [4 0 0]             
      a(a(x1)) = [1 1 0]x1 >= x1 = x1
                 [2 0 1]             
      
                       [4 4 0]     [4]    [4 4 0]     [2]                       
      a(b(a(b(x1)))) = [1 5 0]x1 + [2] >= [0 0 0]x1 + [0] = b(a(b(b(a(a(x1))))))
                       [2 2 0]     [2]    [2 2 0]     [2]                       
     problem:
      DPs:
       
      TRS:
       a(a(x1)) -> x1
       a(b(a(b(x1)))) -> b(a(b(b(a(a(x1))))))
     Qed