YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(b(x1))) -> a#(x1)
   a#(a(b(x1))) -> a#(a(x1))
   a#(a(b(x1))) -> b#(a(a(x1)))
   a#(a(b(x1))) -> b#(b(a(a(x1))))
   b#(a(b(a(x1)))) -> b#(x1)
   b#(a(b(a(x1)))) -> a#(b(x1))
   b#(a(b(a(x1)))) -> a#(a(b(x1)))
   b#(a(b(a(x1)))) -> a#(a(a(b(x1))))
  TRS:
   a(a(b(x1))) -> b(b(a(a(x1))))
   b(a(b(a(x1)))) -> a(a(a(b(x1))))
  TDG Processor:
   DPs:
    a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> b#(a(a(x1)))
    a#(a(b(x1))) -> b#(b(a(a(x1))))
    b#(a(b(a(x1)))) -> b#(x1)
    b#(a(b(a(x1)))) -> a#(b(x1))
    b#(a(b(a(x1)))) -> a#(a(b(x1)))
    b#(a(b(a(x1)))) -> a#(a(a(b(x1))))
   TRS:
    a(a(b(x1))) -> b(b(a(a(x1))))
    b(a(b(a(x1)))) -> a(a(a(b(x1))))
   graph:
    b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> a#(a(a(b(x1))))
    b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> a#(a(b(x1)))
    b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> a#(b(x1))
    b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> b#(x1)
    b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) ->
    a#(a(b(x1))) -> b#(b(a(a(x1))))
    b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) ->
    a#(a(b(x1))) -> b#(a(a(x1)))
    b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) ->
    a#(a(b(x1))) -> a#(a(x1))
    b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) -> a#(a(b(x1))) -> a#(x1)
    b#(a(b(a(x1)))) -> a#(a(b(x1))) ->
    a#(a(b(x1))) -> b#(b(a(a(x1))))
    b#(a(b(a(x1)))) -> a#(a(b(x1))) -> a#(a(b(x1))) -> b#(a(a(x1)))
    b#(a(b(a(x1)))) -> a#(a(b(x1))) -> a#(a(b(x1))) -> a#(a(x1))
    b#(a(b(a(x1)))) -> a#(a(b(x1))) -> a#(a(b(x1))) -> a#(x1)
    b#(a(b(a(x1)))) -> a#(b(x1)) -> a#(a(b(x1))) -> b#(b(a(a(x1))))
    b#(a(b(a(x1)))) -> a#(b(x1)) -> a#(a(b(x1))) -> b#(a(a(x1)))
    b#(a(b(a(x1)))) -> a#(b(x1)) -> a#(a(b(x1))) -> a#(a(x1))
    b#(a(b(a(x1)))) -> a#(b(x1)) -> a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> b#(a(a(x1))) -> b#(a(b(a(x1)))) -> a#(a(a(b(x1))))
    a#(a(b(x1))) -> b#(a(a(x1))) -> b#(a(b(a(x1)))) -> a#(a(b(x1)))
    a#(a(b(x1))) -> b#(a(a(x1))) -> b#(a(b(a(x1)))) -> a#(b(x1))
    a#(a(b(x1))) -> b#(a(a(x1))) -> b#(a(b(a(x1)))) -> b#(x1)
    a#(a(b(x1))) -> b#(b(a(a(x1)))) ->
    b#(a(b(a(x1)))) -> a#(a(a(b(x1))))
    a#(a(b(x1))) -> b#(b(a(a(x1)))) ->
    b#(a(b(a(x1)))) -> a#(a(b(x1)))
    a#(a(b(x1))) -> b#(b(a(a(x1)))) -> b#(a(b(a(x1)))) -> a#(b(x1))
    a#(a(b(x1))) -> b#(b(a(a(x1)))) -> b#(a(b(a(x1)))) -> b#(x1)
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(b(a(a(x1))))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(a(x1)))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(b(a(a(x1))))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(a(x1)))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
   CDG Processor:
    DPs:
     a#(a(b(x1))) -> a#(x1)
     a#(a(b(x1))) -> a#(a(x1))
     a#(a(b(x1))) -> b#(a(a(x1)))
     a#(a(b(x1))) -> b#(b(a(a(x1))))
     b#(a(b(a(x1)))) -> b#(x1)
     b#(a(b(a(x1)))) -> a#(b(x1))
     b#(a(b(a(x1)))) -> a#(a(b(x1)))
     b#(a(b(a(x1)))) -> a#(a(a(b(x1))))
    TRS:
     a(a(b(x1))) -> b(b(a(a(x1))))
     b(a(b(a(x1)))) -> a(a(a(b(x1))))
    graph:
     b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> b#(x1)
     b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> a#(b(x1))
     b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> a#(a(b(x1)))
     b#(a(b(a(x1)))) -> b#(x1) ->
     b#(a(b(a(x1)))) -> a#(a(a(b(x1))))
     b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) -> a#(a(b(x1))) -> a#(x1)
     b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) ->
     a#(a(b(x1))) -> a#(a(x1))
     b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) ->
     a#(a(b(x1))) -> b#(a(a(x1)))
     b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) ->
     a#(a(b(x1))) -> b#(b(a(a(x1))))
     b#(a(b(a(x1)))) -> a#(a(b(x1))) -> a#(a(b(x1))) -> a#(x1)
     b#(a(b(a(x1)))) -> a#(a(b(x1))) -> a#(a(b(x1))) -> a#(a(x1))
     b#(a(b(a(x1)))) -> a#(a(b(x1))) -> a#(a(b(x1))) -> b#(a(a(x1)))
     b#(a(b(a(x1)))) -> a#(a(b(x1))) -> a#(a(b(x1))) -> b#(b(a(a(x1))))
     b#(a(b(a(x1)))) -> a#(b(x1)) -> a#(a(b(x1))) -> a#(x1)
     b#(a(b(a(x1)))) -> a#(b(x1)) -> a#(a(b(x1))) -> a#(a(x1))
     b#(a(b(a(x1)))) -> a#(b(x1)) -> a#(a(b(x1))) -> b#(a(a(x1)))
     b#(a(b(a(x1)))) -> a#(b(x1)) -> a#(a(b(x1))) -> b#(b(a(a(x1))))
    SCC Processor:
     #sccs: 1
     #rules: 1
     #arcs: 16/64
     DPs:
      b#(a(b(a(x1)))) -> b#(x1)
     TRS:
      a(a(b(x1))) -> b(b(a(a(x1))))
      b(a(b(a(x1)))) -> a(a(a(b(x1))))
     Matrix Interpretation Processor: dim=4
      
      interpretation:
       [b#](x0) = [0 1 0 0]x0,
       
                 [1 0 0 0]     [0]
                 [0 0 1 0]     [0]
       [a](x0) = [0 0 0 0]x0 + [0]
                 [0 1 0 0]     [1],
       
                 [0 0 0 0]  
                 [0 0 0 0]  
       [b](x0) = [1 0 0 1]x0
                 [0 1 0 0]  
      orientation:
       b#(a(b(a(x1)))) = [1 1 0 0]x1 + [1] >= [0 1 0 0]x1 = b#(x1)
       
                     [0 0 0 0]     [0]    [0]                 
                     [0 0 0 0]     [0]    [0]                 
       a(a(b(x1))) = [0 0 0 0]x1 + [0] >= [0] = b(b(a(a(x1))))
                     [1 0 0 1]     [1]    [0]                 
       
                        [0 0 0 0]     [0]    [0]                 
                        [0 0 0 0]     [0]    [0]                 
       b(a(b(a(x1)))) = [0 0 0 0]x1 + [1] >= [0] = a(a(a(b(x1))))
                        [1 1 0 0]     [1]    [1]                 
      problem:
       DPs:
        
       TRS:
        a(a(b(x1))) -> b(b(a(a(x1))))
        b(a(b(a(x1)))) -> a(a(a(b(x1))))
      Qed