YES

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

Proof:
 String Reversal Processor:
  a(b(a(x1))) -> a(b(b(b(x1))))
  a(b(b(b(x1)))) -> b(a(a(a(x1))))
  DP Processor:
   DPs:
    a#(b(a(x1))) -> a#(b(b(b(x1))))
    a#(b(b(b(x1)))) -> a#(x1)
    a#(b(b(b(x1)))) -> a#(a(x1))
    a#(b(b(b(x1)))) -> a#(a(a(x1)))
   TRS:
    a(b(a(x1))) -> a(b(b(b(x1))))
    a(b(b(b(x1)))) -> b(a(a(a(x1))))
   EDG Processor:
    DPs:
     a#(b(a(x1))) -> a#(b(b(b(x1))))
     a#(b(b(b(x1)))) -> a#(x1)
     a#(b(b(b(x1)))) -> a#(a(x1))
     a#(b(b(b(x1)))) -> a#(a(a(x1)))
    TRS:
     a(b(a(x1))) -> a(b(b(b(x1))))
     a(b(b(b(x1)))) -> b(a(a(a(x1))))
    graph:
     a#(b(b(b(x1)))) -> a#(a(a(x1))) ->
     a#(b(a(x1))) -> a#(b(b(b(x1))))
     a#(b(b(b(x1)))) -> a#(a(a(x1))) -> a#(b(b(b(x1)))) -> a#(x1)
     a#(b(b(b(x1)))) -> a#(a(a(x1))) -> a#(b(b(b(x1)))) -> a#(a(x1))
     a#(b(b(b(x1)))) -> a#(a(a(x1))) -> a#(b(b(b(x1)))) -> a#(a(a(x1)))
     a#(b(b(b(x1)))) -> a#(a(x1)) -> a#(b(a(x1))) -> a#(b(b(b(x1))))
     a#(b(b(b(x1)))) -> a#(a(x1)) -> a#(b(b(b(x1)))) -> a#(x1)
     a#(b(b(b(x1)))) -> a#(a(x1)) -> a#(b(b(b(x1)))) -> a#(a(x1))
     a#(b(b(b(x1)))) -> a#(a(x1)) -> a#(b(b(b(x1)))) -> a#(a(a(x1)))
     a#(b(b(b(x1)))) -> a#(x1) -> a#(b(a(x1))) -> a#(b(b(b(x1))))
     a#(b(b(b(x1)))) -> a#(x1) -> a#(b(b(b(x1)))) -> a#(x1)
     a#(b(b(b(x1)))) -> a#(x1) -> a#(b(b(b(x1)))) -> a#(a(x1))
     a#(b(b(b(x1)))) -> a#(x1) -> a#(b(b(b(x1)))) -> a#(a(a(x1)))
     a#(b(a(x1))) -> a#(b(b(b(x1)))) -> a#(b(b(b(x1)))) -> a#(x1)
     a#(b(a(x1))) -> a#(b(b(b(x1)))) -> a#(b(b(b(x1)))) -> a#(a(x1))
     a#(b(a(x1))) -> a#(b(b(b(x1)))) -> a#(b(b(b(x1)))) -> a#(a(a(x1)))
    Matrix Interpretation Processor: dim=4
     
     interpretation:
                [0 1 0 0]     [0]
                [0 0 1 0]     [0]
      [b](x0) = [1 0 0 0]x0 + [1]
                [0 0 0 1]     [0],
      
                [0 0 1 1]  
                [0 0 1 1]  
      [a](x0) = [0 0 1 1]x0
                [0 0 0 0]  ,
      
      [a#](x0) = [0 0 1 1]x0
     orientation:
      a#(b(a(x1))) = [0 0 1 1]x1 + [1] >= [0 0 1 1]x1 + [1] = a#(b(b(b(x1))))
      
      a#(b(b(b(x1)))) = [0 0 1 1]x1 + [1] >= [0 0 1 1]x1 = a#(x1)
      
      a#(b(b(b(x1)))) = [0 0 1 1]x1 + [1] >= [0 0 1 1]x1 = a#(a(x1))
      
      a#(b(b(b(x1)))) = [0 0 1 1]x1 + [1] >= [0 0 1 1]x1 = a#(a(a(x1)))
      
                    [0 0 1 1]     [1]    [0 0 1 1]     [1]                 
                    [0 0 1 1]     [1]    [0 0 1 1]     [1]                 
      a(b(a(x1))) = [0 0 1 1]x1 + [1] >= [0 0 1 1]x1 + [1] = a(b(b(b(x1))))
                    [0 0 0 0]     [0]    [0 0 0 0]     [0]                 
      
                       [0 0 1 1]     [1]    [0 0 1 1]     [0]                 
                       [0 0 1 1]     [1]    [0 0 1 1]     [0]                 
      a(b(b(b(x1)))) = [0 0 1 1]x1 + [1] >= [0 0 1 1]x1 + [1] = b(a(a(a(x1))))
                       [0 0 0 0]     [0]    [0 0 0 0]     [0]                 
     problem:
      DPs:
       a#(b(a(x1))) -> a#(b(b(b(x1))))
      TRS:
       a(b(a(x1))) -> a(b(b(b(x1))))
       a(b(b(b(x1)))) -> b(a(a(a(x1))))
     Restore Modifier:
      DPs:
       a#(b(a(x1))) -> a#(b(b(b(x1))))
      TRS:
       a(b(a(x1))) -> a(b(b(b(x1))))
       a(b(b(b(x1)))) -> b(a(a(a(x1))))
      EDG Processor:
       DPs:
        a#(b(a(x1))) -> a#(b(b(b(x1))))
       TRS:
        a(b(a(x1))) -> a(b(b(b(x1))))
        a(b(b(b(x1)))) -> b(a(a(a(x1))))
       graph:
        
       SCC Processor:
        #sccs: 0
        #rules: 0
        #arcs: 0/1