YES

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

Proof:
 DP Processor:
  DPs:
   b#(a(a(x1))) -> c#(x1)
   b#(a(a(x1))) -> b#(c(x1))
   b#(a(a(x1))) -> a#(b(c(x1)))
   c#(a(x1)) -> c#(x1)
   c#(a(x1)) -> a#(c(x1))
   c#(b(x1)) -> a#(x1)
   c#(b(x1)) -> b#(a(x1))
   a#(a(b(x1))) -> a#(x1)
   a#(a(b(x1))) -> b#(a(x1))
   a#(d(x1)) -> a#(x1)
   b#(d(x1)) -> b#(x1)
   b#(d(x1)) -> a#(b(x1))
   a#(a(x1)) -> b#(a(x1))
   a#(a(x1)) -> a#(b(a(x1)))
  TRS:
   b(a(a(x1))) -> a(b(c(x1)))
   c(a(x1)) -> a(c(x1))
   c(b(x1)) -> b(a(x1))
   a(a(b(x1))) -> d(b(a(x1)))
   a(d(x1)) -> d(a(x1))
   b(d(x1)) -> a(b(x1))
   a(a(x1)) -> a(b(a(x1)))
  TDG Processor:
   DPs:
    b#(a(a(x1))) -> c#(x1)
    b#(a(a(x1))) -> b#(c(x1))
    b#(a(a(x1))) -> a#(b(c(x1)))
    c#(a(x1)) -> c#(x1)
    c#(a(x1)) -> a#(c(x1))
    c#(b(x1)) -> a#(x1)
    c#(b(x1)) -> b#(a(x1))
    a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> b#(a(x1))
    a#(d(x1)) -> a#(x1)
    b#(d(x1)) -> b#(x1)
    b#(d(x1)) -> a#(b(x1))
    a#(a(x1)) -> b#(a(x1))
    a#(a(x1)) -> a#(b(a(x1)))
   TRS:
    b(a(a(x1))) -> a(b(c(x1)))
    c(a(x1)) -> a(c(x1))
    c(b(x1)) -> b(a(x1))
    a(a(b(x1))) -> d(b(a(x1)))
    a(d(x1)) -> d(a(x1))
    b(d(x1)) -> a(b(x1))
    a(a(x1)) -> a(b(a(x1)))
   graph:
    a#(d(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1)))
    a#(d(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(x1))
    a#(d(x1)) -> a#(x1) -> a#(d(x1)) -> a#(x1)
    a#(d(x1)) -> a#(x1) -> a#(a(b(x1))) -> b#(a(x1))
    a#(d(x1)) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1)))
    a#(a(b(x1))) -> a#(x1) -> a#(a(x1)) -> b#(a(x1))
    a#(a(b(x1))) -> a#(x1) -> a#(d(x1)) -> a#(x1)
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(x1))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> b#(a(x1)) -> b#(d(x1)) -> a#(b(x1))
    a#(a(b(x1))) -> b#(a(x1)) -> b#(d(x1)) -> b#(x1)
    a#(a(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(c(x1)))
    a#(a(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(c(x1))
    a#(a(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> c#(x1)
    a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1)))
    a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(x1))
    a#(a(x1)) -> a#(b(a(x1))) -> a#(d(x1)) -> a#(x1)
    a#(a(x1)) -> a#(b(a(x1))) -> a#(a(b(x1))) -> b#(a(x1))
    a#(a(x1)) -> a#(b(a(x1))) -> a#(a(b(x1))) -> a#(x1)
    a#(a(x1)) -> b#(a(x1)) -> b#(d(x1)) -> a#(b(x1))
    a#(a(x1)) -> b#(a(x1)) -> b#(d(x1)) -> b#(x1)
    a#(a(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(c(x1)))
    a#(a(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(c(x1))
    a#(a(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> c#(x1)
    c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1)))
    c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(x1))
    c#(b(x1)) -> a#(x1) -> a#(d(x1)) -> a#(x1)
    c#(b(x1)) -> a#(x1) -> a#(a(b(x1))) -> b#(a(x1))
    c#(b(x1)) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
    c#(b(x1)) -> b#(a(x1)) -> b#(d(x1)) -> a#(b(x1))
    c#(b(x1)) -> b#(a(x1)) -> b#(d(x1)) -> b#(x1)
    c#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(c(x1)))
    c#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(c(x1))
    c#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> c#(x1)
    c#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(a(x1)))
    c#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(a(x1))
    c#(a(x1)) -> a#(c(x1)) -> a#(d(x1)) -> a#(x1)
    c#(a(x1)) -> a#(c(x1)) -> a#(a(b(x1))) -> b#(a(x1))
    c#(a(x1)) -> a#(c(x1)) -> a#(a(b(x1))) -> a#(x1)
    c#(a(x1)) -> c#(x1) -> c#(b(x1)) -> b#(a(x1))
    c#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(x1)
    c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(c(x1))
    c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1)
    b#(d(x1)) -> a#(b(x1)) -> a#(a(x1)) -> a#(b(a(x1)))
    b#(d(x1)) -> a#(b(x1)) -> a#(a(x1)) -> b#(a(x1))
    b#(d(x1)) -> a#(b(x1)) -> a#(d(x1)) -> a#(x1)
    b#(d(x1)) -> a#(b(x1)) -> a#(a(b(x1))) -> b#(a(x1))
    b#(d(x1)) -> a#(b(x1)) -> a#(a(b(x1))) -> a#(x1)
    b#(d(x1)) -> b#(x1) -> b#(d(x1)) -> a#(b(x1))
    b#(d(x1)) -> b#(x1) -> b#(d(x1)) -> b#(x1)
    b#(d(x1)) -> b#(x1) -> b#(a(a(x1))) -> a#(b(c(x1)))
    b#(d(x1)) -> b#(x1) -> b#(a(a(x1))) -> b#(c(x1))
    b#(d(x1)) -> b#(x1) -> b#(a(a(x1))) -> c#(x1)
    b#(a(a(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> a#(b(a(x1)))
    b#(a(a(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(a(x1))
    b#(a(a(x1))) -> a#(b(c(x1))) -> a#(d(x1)) -> a#(x1)
    b#(a(a(x1))) -> a#(b(c(x1))) -> a#(a(b(x1))) -> b#(a(x1))
    b#(a(a(x1))) -> a#(b(c(x1))) -> a#(a(b(x1))) -> a#(x1)
    b#(a(a(x1))) -> c#(x1) -> c#(b(x1)) -> b#(a(x1))
    b#(a(a(x1))) -> c#(x1) -> c#(b(x1)) -> a#(x1)
    b#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> a#(c(x1))
    b#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(x1)
    b#(a(a(x1))) -> b#(c(x1)) -> b#(d(x1)) -> a#(b(x1))
    b#(a(a(x1))) -> b#(c(x1)) -> b#(d(x1)) -> b#(x1)
    b#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> a#(b(c(x1)))
    b#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> b#(c(x1))
    b#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> c#(x1)
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     b(a(a(x1))) -> a(b(c(x1)))
     c(a(x1)) -> a(c(x1))
     c(b(x1)) -> b(a(x1))
     a(a(b(x1))) -> d(b(a(x1)))
     a(d(x1)) -> d(a(x1))
     b(d(x1)) -> a(b(x1))
     a(a(x1)) -> a(b(a(x1)))
    interpretation:
     [b#](x0) = x0,
     
     [b](x0) = x0,
     
     [d](x0) = 2x0,
     
     [c#](x0) = 2x0,
     
     [a](x0) = 2x0,
     
     [a#](x0) = x0,
     
     [c](x0) = 2x0
    orientation:
     b#(a(a(x1))) = 4x1 >= 2x1 = c#(x1)
     
     b#(a(a(x1))) = 4x1 >= 2x1 = b#(c(x1))
     
     b#(a(a(x1))) = 4x1 >= 2x1 = a#(b(c(x1)))
     
     c#(a(x1)) = 4x1 >= 2x1 = c#(x1)
     
     c#(a(x1)) = 4x1 >= 2x1 = a#(c(x1))
     
     c#(b(x1)) = 2x1 >= x1 = a#(x1)
     
     c#(b(x1)) = 2x1 >= 2x1 = b#(a(x1))
     
     a#(a(b(x1))) = 2x1 >= x1 = a#(x1)
     
     a#(a(b(x1))) = 2x1 >= 2x1 = b#(a(x1))
     
     a#(d(x1)) = 2x1 >= x1 = a#(x1)
     
     b#(d(x1)) = 2x1 >= x1 = b#(x1)
     
     b#(d(x1)) = 2x1 >= x1 = a#(b(x1))
     
     a#(a(x1)) = 2x1 >= 2x1 = b#(a(x1))
     
     a#(a(x1)) = 2x1 >= 2x1 = a#(b(a(x1)))
     
     b(a(a(x1))) = 4x1 >= 4x1 = a(b(c(x1)))
     
     c(a(x1)) = 4x1 >= 4x1 = a(c(x1))
     
     c(b(x1)) = 2x1 >= 2x1 = b(a(x1))
     
     a(a(b(x1))) = 4x1 >= 4x1 = d(b(a(x1)))
     
     a(d(x1)) = 4x1 >= 4x1 = d(a(x1))
     
     b(d(x1)) = 2x1 >= 2x1 = a(b(x1))
     
     a(a(x1)) = 4x1 >= 4x1 = a(b(a(x1)))
    problem:
     DPs:
      c#(b(x1)) -> b#(a(x1))
      a#(a(b(x1))) -> b#(a(x1))
      a#(a(x1)) -> b#(a(x1))
      a#(a(x1)) -> a#(b(a(x1)))
     TRS:
      b(a(a(x1))) -> a(b(c(x1)))
      c(a(x1)) -> a(c(x1))
      c(b(x1)) -> b(a(x1))
      a(a(b(x1))) -> d(b(a(x1)))
      a(d(x1)) -> d(a(x1))
      b(d(x1)) -> a(b(x1))
      a(a(x1)) -> a(b(a(x1)))
    Restore Modifier:
     DPs:
      c#(b(x1)) -> b#(a(x1))
      a#(a(b(x1))) -> b#(a(x1))
      a#(a(x1)) -> b#(a(x1))
      a#(a(x1)) -> a#(b(a(x1)))
     TRS:
      b(a(a(x1))) -> a(b(c(x1)))
      c(a(x1)) -> a(c(x1))
      c(b(x1)) -> b(a(x1))
      a(a(b(x1))) -> d(b(a(x1)))
      a(d(x1)) -> d(a(x1))
      b(d(x1)) -> a(b(x1))
      a(a(x1)) -> a(b(a(x1)))
     EDG Processor:
      DPs:
       c#(b(x1)) -> b#(a(x1))
       a#(a(b(x1))) -> b#(a(x1))
       a#(a(x1)) -> b#(a(x1))
       a#(a(x1)) -> a#(b(a(x1)))
      TRS:
       b(a(a(x1))) -> a(b(c(x1)))
       c(a(x1)) -> a(c(x1))
       c(b(x1)) -> b(a(x1))
       a(a(b(x1))) -> d(b(a(x1)))
       a(d(x1)) -> d(a(x1))
       b(d(x1)) -> a(b(x1))
       a(a(x1)) -> a(b(a(x1)))
      graph:
       a#(a(x1)) -> a#(b(a(x1))) -> a#(a(b(x1))) -> b#(a(x1))
       a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(x1))
       a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1)))
      SCC Processor:
       #sccs: 1
       #rules: 1
       #arcs: 3/16
       DPs:
        a#(a(x1)) -> a#(b(a(x1)))
       TRS:
        b(a(a(x1))) -> a(b(c(x1)))
        c(a(x1)) -> a(c(x1))
        c(b(x1)) -> b(a(x1))
        a(a(b(x1))) -> d(b(a(x1)))
        a(d(x1)) -> d(a(x1))
        b(d(x1)) -> a(b(x1))
        a(a(x1)) -> a(b(a(x1)))
       Arctic Interpretation Processor:
        dimension: 1
        usable rules:
         b(a(a(x1))) -> a(b(c(x1)))
         c(a(x1)) -> a(c(x1))
         c(b(x1)) -> b(a(x1))
         a(a(b(x1))) -> d(b(a(x1)))
         a(d(x1)) -> d(a(x1))
         b(d(x1)) -> a(b(x1))
         a(a(x1)) -> a(b(a(x1)))
        interpretation:
         [b](x0) = -5x0 + 2,
         
         [d](x0) = 8x0 + 15,
         
         [a](x0) = 8x0 + 8,
         
         [a#](x0) = x0 + 0,
         
         [c](x0) = 8x0 + -5
        orientation:
         a#(a(x1)) = 8x1 + 8 >= 3x1 + 3 = a#(b(a(x1)))
         
         b(a(a(x1))) = 11x1 + 11 >= 11x1 + 10 = a(b(c(x1)))
         
         c(a(x1)) = 16x1 + 16 >= 16x1 + 8 = a(c(x1))
         
         c(b(x1)) = 3x1 + 10 >= 3x1 + 3 = b(a(x1))
         
         a(a(b(x1))) = 11x1 + 18 >= 11x1 + 15 = d(b(a(x1)))
         
         a(d(x1)) = 16x1 + 23 >= 16x1 + 16 = d(a(x1))
         
         b(d(x1)) = 3x1 + 10 >= 3x1 + 10 = a(b(x1))
         
         a(a(x1)) = 16x1 + 16 >= 11x1 + 11 = a(b(a(x1)))
        problem:
         DPs:
          
         TRS:
          b(a(a(x1))) -> a(b(c(x1)))
          c(a(x1)) -> a(c(x1))
          c(b(x1)) -> b(a(x1))
          a(a(b(x1))) -> d(b(a(x1)))
          a(d(x1)) -> d(a(x1))
          b(d(x1)) -> a(b(x1))
          a(a(x1)) -> a(b(a(x1)))
        Qed