YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(b(a(x1)))) -> b#(x1)
   a#(a(b(a(x1)))) -> b#(b(x1))
   a#(a(b(a(x1)))) -> a#(b(b(x1)))
   b#(b(x1)) -> a#(x1)
   b#(b(x1)) -> a#(a(x1))
   b#(b(x1)) -> a#(a(a(x1)))
   b#(b(x1)) -> b#(a(a(a(x1))))
  TRS:
   a(a(b(a(x1)))) -> a(b(b(x1)))
   b(b(x1)) -> b(a(a(a(x1))))
  TDG Processor:
   DPs:
    a#(a(b(a(x1)))) -> b#(x1)
    a#(a(b(a(x1)))) -> b#(b(x1))
    a#(a(b(a(x1)))) -> a#(b(b(x1)))
    b#(b(x1)) -> a#(x1)
    b#(b(x1)) -> a#(a(x1))
    b#(b(x1)) -> a#(a(a(x1)))
    b#(b(x1)) -> b#(a(a(a(x1))))
   TRS:
    a(a(b(a(x1)))) -> a(b(b(x1)))
    b(b(x1)) -> b(a(a(a(x1))))
   graph:
    b#(b(x1)) -> b#(a(a(a(x1)))) -> b#(b(x1)) -> b#(a(a(a(x1))))
    b#(b(x1)) -> b#(a(a(a(x1)))) -> b#(b(x1)) -> a#(a(a(x1)))
    b#(b(x1)) -> b#(a(a(a(x1)))) -> b#(b(x1)) -> a#(a(x1))
    b#(b(x1)) -> b#(a(a(a(x1)))) -> b#(b(x1)) -> a#(x1)
    b#(b(x1)) -> a#(a(a(x1))) -> a#(a(b(a(x1)))) -> a#(b(b(x1)))
    b#(b(x1)) -> a#(a(a(x1))) -> a#(a(b(a(x1)))) -> b#(b(x1))
    b#(b(x1)) -> a#(a(a(x1))) -> a#(a(b(a(x1)))) -> b#(x1)
    b#(b(x1)) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> a#(b(b(x1)))
    b#(b(x1)) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> b#(b(x1))
    b#(b(x1)) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> b#(x1)
    b#(b(x1)) -> a#(x1) -> a#(a(b(a(x1)))) -> a#(b(b(x1)))
    b#(b(x1)) -> a#(x1) -> a#(a(b(a(x1)))) -> b#(b(x1))
    b#(b(x1)) -> a#(x1) -> a#(a(b(a(x1)))) -> b#(x1)
    a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(x1)) -> b#(a(a(a(x1))))
    a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(x1)) -> a#(a(a(x1)))
    a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(x1)) -> a#(a(x1))
    a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(x1)) -> a#(x1)
    a#(a(b(a(x1)))) -> b#(x1) -> b#(b(x1)) -> b#(a(a(a(x1))))
    a#(a(b(a(x1)))) -> b#(x1) -> b#(b(x1)) -> a#(a(a(x1)))
    a#(a(b(a(x1)))) -> b#(x1) -> b#(b(x1)) -> a#(a(x1))
    a#(a(b(a(x1)))) -> b#(x1) -> b#(b(x1)) -> a#(x1)
    a#(a(b(a(x1)))) -> a#(b(b(x1))) ->
    a#(a(b(a(x1)))) -> a#(b(b(x1)))
    a#(a(b(a(x1)))) -> a#(b(b(x1))) -> a#(a(b(a(x1)))) -> b#(b(x1))
    a#(a(b(a(x1)))) -> a#(b(b(x1))) -> a#(a(b(a(x1)))) -> b#(x1)
   EDG Processor:
    DPs:
     a#(a(b(a(x1)))) -> b#(x1)
     a#(a(b(a(x1)))) -> b#(b(x1))
     a#(a(b(a(x1)))) -> a#(b(b(x1)))
     b#(b(x1)) -> a#(x1)
     b#(b(x1)) -> a#(a(x1))
     b#(b(x1)) -> a#(a(a(x1)))
     b#(b(x1)) -> b#(a(a(a(x1))))
    TRS:
     a(a(b(a(x1)))) -> a(b(b(x1)))
     b(b(x1)) -> b(a(a(a(x1))))
    graph:
     b#(b(x1)) -> a#(a(a(x1))) -> a#(a(b(a(x1)))) -> b#(x1)
     b#(b(x1)) -> a#(a(a(x1))) -> a#(a(b(a(x1)))) -> b#(b(x1))
     b#(b(x1)) -> a#(a(a(x1))) -> a#(a(b(a(x1)))) -> a#(b(b(x1)))
     b#(b(x1)) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> b#(x1)
     b#(b(x1)) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> b#(b(x1))
     b#(b(x1)) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> a#(b(b(x1)))
     b#(b(x1)) -> a#(x1) -> a#(a(b(a(x1)))) -> b#(x1)
     b#(b(x1)) -> a#(x1) -> a#(a(b(a(x1)))) -> b#(b(x1))
     b#(b(x1)) -> a#(x1) -> a#(a(b(a(x1)))) -> a#(b(b(x1)))
     a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(x1)) -> a#(x1)
     a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(x1)) -> a#(a(x1))
     a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(x1)) -> a#(a(a(x1)))
     a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(x1)) -> b#(a(a(a(x1))))
     a#(a(b(a(x1)))) -> b#(x1) -> b#(b(x1)) -> a#(x1)
     a#(a(b(a(x1)))) -> b#(x1) -> b#(b(x1)) -> a#(a(x1))
     a#(a(b(a(x1)))) -> b#(x1) -> b#(b(x1)) -> a#(a(a(x1)))
     a#(a(b(a(x1)))) -> b#(x1) -> b#(b(x1)) -> b#(a(a(a(x1))))
    SCC Processor:
     #sccs: 1
     #rules: 5
     #arcs: 17/49
     DPs:
      b#(b(x1)) -> a#(a(a(x1)))
      a#(a(b(a(x1)))) -> b#(b(x1))
      b#(b(x1)) -> a#(a(x1))
      a#(a(b(a(x1)))) -> b#(x1)
      b#(b(x1)) -> a#(x1)
     TRS:
      a(a(b(a(x1)))) -> a(b(b(x1)))
      b(b(x1)) -> b(a(a(a(x1))))
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       a(a(b(a(x1)))) -> a(b(b(x1)))
       b(b(x1)) -> b(a(a(a(x1))))
      interpretation:
                 [0 0]     [1]
       [b](x0) = [1 0]x0 + [2],
       
       [b#](x0) = [1 0]x0 + [2],
       
                 [0  0 ]     [-&]
       [a](x0) = [-& 0 ]x0 + [0 ],
       
       [a#](x0) = [0 0]x0 + [0]
      orientation:
       b#(b(x1)) = [1 1]x1 + [2] >= [0 0]x1 + [0] = a#(a(a(x1)))
       
       a#(a(b(a(x1)))) = [1 1]x1 + [2] >= [1 1]x1 + [2] = b#(b(x1))
       
       b#(b(x1)) = [1 1]x1 + [2] >= [0 0]x1 + [0] = a#(a(x1))
       
       a#(a(b(a(x1)))) = [1 1]x1 + [2] >= [1 0]x1 + [2] = b#(x1)
       
       b#(b(x1)) = [1 1]x1 + [2] >= [0 0]x1 + [0] = a#(x1)
       
                        [1 1]     [2]    [1 1]     [2]              
       a(a(b(a(x1)))) = [1 1]x1 + [2] >= [1 1]x1 + [2] = a(b(b(x1)))
       
                  [1 0]     [2]    [0 0]     [1]                 
       b(b(x1)) = [1 1]x1 + [2] >= [1 1]x1 + [2] = b(a(a(a(x1))))
      problem:
       DPs:
        a#(a(b(a(x1)))) -> b#(b(x1))
        a#(a(b(a(x1)))) -> b#(x1)
       TRS:
        a(a(b(a(x1)))) -> a(b(b(x1)))
        b(b(x1)) -> b(a(a(a(x1))))
      Restore Modifier:
       DPs:
        a#(a(b(a(x1)))) -> b#(b(x1))
        a#(a(b(a(x1)))) -> b#(x1)
       TRS:
        a(a(b(a(x1)))) -> a(b(b(x1)))
        b(b(x1)) -> b(a(a(a(x1))))
       EDG Processor:
        DPs:
         a#(a(b(a(x1)))) -> b#(b(x1))
         a#(a(b(a(x1)))) -> b#(x1)
        TRS:
         a(a(b(a(x1)))) -> a(b(b(x1)))
         b(b(x1)) -> b(a(a(a(x1))))
        graph:
         
        SCC Processor:
         #sccs: 0
         #rules: 0
         #arcs: 0/4