YES

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

Proof:
 DP Processor:
  DPs:
   a#(x1) -> b#(x1)
   b#(a(a(b(x1)))) -> a#(x1)
   b#(a(a(b(x1)))) -> b#(a(x1))
   b#(a(a(b(x1)))) -> b#(b(a(x1)))
   b#(a(a(b(x1)))) -> a#(b(b(a(x1))))
   b#(a(a(b(x1)))) -> a#(a(b(b(a(x1)))))
  TRS:
   a(x1) -> b(x1)
   b(a(a(b(x1)))) -> a(a(b(b(a(x1)))))
  TDG Processor:
   DPs:
    a#(x1) -> b#(x1)
    b#(a(a(b(x1)))) -> a#(x1)
    b#(a(a(b(x1)))) -> b#(a(x1))
    b#(a(a(b(x1)))) -> b#(b(a(x1)))
    b#(a(a(b(x1)))) -> a#(b(b(a(x1))))
    b#(a(a(b(x1)))) -> a#(a(b(b(a(x1)))))
   TRS:
    a(x1) -> b(x1)
    b(a(a(b(x1)))) -> a(a(b(b(a(x1)))))
   graph:
    b#(a(a(b(x1)))) -> b#(b(a(x1))) ->
    b#(a(a(b(x1)))) -> a#(a(b(b(a(x1)))))
    b#(a(a(b(x1)))) -> b#(b(a(x1))) ->
    b#(a(a(b(x1)))) -> a#(b(b(a(x1))))
    b#(a(a(b(x1)))) -> b#(b(a(x1))) ->
    b#(a(a(b(x1)))) -> b#(b(a(x1)))
    b#(a(a(b(x1)))) -> b#(b(a(x1))) -> b#(a(a(b(x1)))) -> b#(a(x1))
    b#(a(a(b(x1)))) -> b#(b(a(x1))) -> b#(a(a(b(x1)))) -> a#(x1)
    b#(a(a(b(x1)))) -> b#(a(x1)) ->
    b#(a(a(b(x1)))) -> a#(a(b(b(a(x1)))))
    b#(a(a(b(x1)))) -> b#(a(x1)) -> b#(a(a(b(x1)))) -> a#(b(b(a(x1))))
    b#(a(a(b(x1)))) -> b#(a(x1)) -> b#(a(a(b(x1)))) -> b#(b(a(x1)))
    b#(a(a(b(x1)))) -> b#(a(x1)) -> b#(a(a(b(x1)))) -> b#(a(x1))
    b#(a(a(b(x1)))) -> b#(a(x1)) -> b#(a(a(b(x1)))) -> a#(x1)
    b#(a(a(b(x1)))) -> a#(b(b(a(x1)))) -> a#(x1) -> b#(x1)
    b#(a(a(b(x1)))) -> a#(a(b(b(a(x1))))) -> a#(x1) -> b#(x1)
    b#(a(a(b(x1)))) -> a#(x1) -> a#(x1) -> b#(x1)
    a#(x1) -> b#(x1) -> b#(a(a(b(x1)))) -> a#(a(b(b(a(x1)))))
    a#(x1) -> b#(x1) -> b#(a(a(b(x1)))) -> a#(b(b(a(x1))))
    a#(x1) -> b#(x1) -> b#(a(a(b(x1)))) -> b#(b(a(x1)))
    a#(x1) -> b#(x1) -> b#(a(a(b(x1)))) -> b#(a(x1))
    a#(x1) -> b#(x1) -> b#(a(a(b(x1)))) -> a#(x1)
   Arctic Interpretation Processor:
    dimension: 3
    interpretation:
     [b#](x0) = [-& 0  -&]x0 + [0],
     
     [a#](x0) = [-& 0  0 ]x0 + [0],
     
               [-& 0  0 ]     [0]
     [b](x0) = [-& 0  -&]x0 + [0]
               [-& 0  -&]     [0],
     
               [-& 0  0 ]     [0]
     [a](x0) = [-& 0  0 ]x0 + [0]
               [1  0  -&]     [0]
    orientation:
     a#(x1) = [-& 0  0 ]x1 + [0] >= [-& 0  -&]x1 + [0] = b#(x1)
     
     b#(a(a(b(x1)))) = [-& 1  1 ]x1 + [1] >= [-& 0  0 ]x1 + [0] = a#(x1)
     
     b#(a(a(b(x1)))) = [-& 1  1 ]x1 + [1] >= [-& 0  0 ]x1 + [0] = b#(a(x1))
     
     b#(a(a(b(x1)))) = [-& 1  1 ]x1 + [1] >= [-& 0  0 ]x1 + [0] = b#(b(a(x1)))
     
     b#(a(a(b(x1)))) = [-& 1  1 ]x1 + [1] >= [-& 0  0 ]x1 + [0] = a#(b(b(a(x1))))
     
     b#(a(a(b(x1)))) = [-& 1  1 ]x1 + [1] >= [-& 1  1 ]x1 + [1] = a#(a(b(b(a(x1)))))
     
             [-& 0  0 ]     [0]    [-& 0  0 ]     [0]        
     a(x1) = [-& 0  0 ]x1 + [0] >= [-& 0  -&]x1 + [0] = b(x1)
             [1  0  -&]     [0]    [-& 0  -&]     [0]        
     
                      [-& 1  1 ]     [1]    [-& 1  1 ]     [1]                    
     b(a(a(b(x1)))) = [-& 1  1 ]x1 + [1] >= [-& 1  1 ]x1 + [1] = a(a(b(b(a(x1)))))
                      [-& 1  1 ]     [1]    [-& 1  1 ]     [1]                    
    problem:
     DPs:
      a#(x1) -> b#(x1)
      b#(a(a(b(x1)))) -> a#(a(b(b(a(x1)))))
     TRS:
      a(x1) -> b(x1)
      b(a(a(b(x1)))) -> a(a(b(b(a(x1)))))
    EDG Processor:
     DPs:
      a#(x1) -> b#(x1)
      b#(a(a(b(x1)))) -> a#(a(b(b(a(x1)))))
     TRS:
      a(x1) -> b(x1)
      b(a(a(b(x1)))) -> a(a(b(b(a(x1)))))
     graph:
      b#(a(a(b(x1)))) -> a#(a(b(b(a(x1))))) -> a#(x1) -> b#(x1)
      a#(x1) -> b#(x1) -> b#(a(a(b(x1)))) -> a#(a(b(b(a(x1)))))
     Arctic Interpretation Processor:
      dimension: 3
      interpretation:
       [b#](x0) = [-& 0  1 ]x0 + [0],
       
       [a#](x0) = [0 0 1]x0 + [0],
       
                 [-& 1  1 ]     [1]
       [b](x0) = [-& -& 0 ]x0 + [0]
                 [-& -& 0 ]     [0],
       
                 [0  1  1 ]     [1]
       [a](x0) = [0  0  0 ]x0 + [0]
                 [-& 0  0 ]     [0]
      orientation:
       a#(x1) = [0 0 1]x1 + [0] >= [-& 0  1 ]x1 + [0] = b#(x1)
       
       b#(a(a(b(x1)))) = [-& 2  2 ]x1 + [2] >= [-& 1  1 ]x1 + [1] = a#(a(b(b(a(x1)))))
       
               [0  1  1 ]     [1]    [-& 1  1 ]     [1]        
       a(x1) = [0  0  0 ]x1 + [0] >= [-& -& 0 ]x1 + [0] = b(x1)
               [-& 0  0 ]     [0]    [-& -& 0 ]     [0]        
       
                        [-& 2  2 ]     [2]    [-& 2  2 ]     [2]                    
       b(a(a(b(x1)))) = [-& 1  1 ]x1 + [1] >= [-& 1  1 ]x1 + [1] = a(a(b(b(a(x1)))))
                        [-& 1  1 ]     [1]    [-& 1  1 ]     [1]                    
      problem:
       DPs:
        a#(x1) -> b#(x1)
       TRS:
        a(x1) -> b(x1)
        b(a(a(b(x1)))) -> a(a(b(b(a(x1)))))
      EDG Processor:
       DPs:
        a#(x1) -> b#(x1)
       TRS:
        a(x1) -> b(x1)
        b(a(a(b(x1)))) -> a(a(b(b(a(x1)))))
       graph:
        
       Qed