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:
 String Reversal Processor:
  a(a(b(x1))) -> c(b(a(x1)))
  a(c(x1)) -> c(a(x1))
  b(c(x1)) -> a(b(x1))
  b(a(a(x1))) -> a(b(d(x1)))
  d(a(x1)) -> a(d(x1))
  d(b(x1)) -> b(a(x1))
  a(a(x1)) -> a(b(a(x1)))
  DP Processor:
   DPs:
    a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> b#(a(x1))
    a#(c(x1)) -> a#(x1)
    b#(c(x1)) -> b#(x1)
    b#(c(x1)) -> a#(b(x1))
    b#(a(a(x1))) -> d#(x1)
    b#(a(a(x1))) -> b#(d(x1))
    b#(a(a(x1))) -> a#(b(d(x1)))
    d#(a(x1)) -> d#(x1)
    d#(a(x1)) -> a#(d(x1))
    d#(b(x1)) -> a#(x1)
    d#(b(x1)) -> b#(a(x1))
    a#(a(x1)) -> b#(a(x1))
    a#(a(x1)) -> a#(b(a(x1)))
   TRS:
    a(a(b(x1))) -> c(b(a(x1)))
    a(c(x1)) -> c(a(x1))
    b(c(x1)) -> a(b(x1))
    b(a(a(x1))) -> a(b(d(x1)))
    d(a(x1)) -> a(d(x1))
    d(b(x1)) -> b(a(x1))
    a(a(x1)) -> a(b(a(x1)))
   TDG Processor:
    DPs:
     a#(a(b(x1))) -> a#(x1)
     a#(a(b(x1))) -> b#(a(x1))
     a#(c(x1)) -> a#(x1)
     b#(c(x1)) -> b#(x1)
     b#(c(x1)) -> a#(b(x1))
     b#(a(a(x1))) -> d#(x1)
     b#(a(a(x1))) -> b#(d(x1))
     b#(a(a(x1))) -> a#(b(d(x1)))
     d#(a(x1)) -> d#(x1)
     d#(a(x1)) -> a#(d(x1))
     d#(b(x1)) -> a#(x1)
     d#(b(x1)) -> b#(a(x1))
     a#(a(x1)) -> b#(a(x1))
     a#(a(x1)) -> a#(b(a(x1)))
    TRS:
     a(a(b(x1))) -> c(b(a(x1)))
     a(c(x1)) -> c(a(x1))
     b(c(x1)) -> a(b(x1))
     b(a(a(x1))) -> a(b(d(x1)))
     d(a(x1)) -> a(d(x1))
     d(b(x1)) -> b(a(x1))
     a(a(x1)) -> a(b(a(x1)))
    graph:
     d#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(d(x1)))
     d#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(d(x1))
     d#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> d#(x1)
     d#(b(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(b(x1))
     d#(b(x1)) -> b#(a(x1)) -> b#(c(x1)) -> b#(x1)
     d#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1)))
     d#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(x1))
     d#(b(x1)) -> a#(x1) -> a#(c(x1)) -> a#(x1)
     d#(b(x1)) -> a#(x1) -> a#(a(b(x1))) -> b#(a(x1))
     d#(b(x1)) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
     d#(a(x1)) -> d#(x1) -> d#(b(x1)) -> b#(a(x1))
     d#(a(x1)) -> d#(x1) -> d#(b(x1)) -> a#(x1)
     d#(a(x1)) -> d#(x1) -> d#(a(x1)) -> a#(d(x1))
     d#(a(x1)) -> d#(x1) -> d#(a(x1)) -> d#(x1)
     d#(a(x1)) -> a#(d(x1)) -> a#(a(x1)) -> a#(b(a(x1)))
     d#(a(x1)) -> a#(d(x1)) -> a#(a(x1)) -> b#(a(x1))
     d#(a(x1)) -> a#(d(x1)) -> a#(c(x1)) -> a#(x1)
     d#(a(x1)) -> a#(d(x1)) -> a#(a(b(x1))) -> b#(a(x1))
     d#(a(x1)) -> a#(d(x1)) -> a#(a(b(x1))) -> a#(x1)
     b#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> a#(b(d(x1)))
     b#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> b#(d(x1))
     b#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> d#(x1)
     b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> a#(b(x1))
     b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
     b#(c(x1)) -> a#(b(x1)) -> a#(a(x1)) -> a#(b(a(x1)))
     b#(c(x1)) -> a#(b(x1)) -> a#(a(x1)) -> b#(a(x1))
     b#(c(x1)) -> a#(b(x1)) -> a#(c(x1)) -> a#(x1)
     b#(c(x1)) -> a#(b(x1)) -> a#(a(b(x1))) -> b#(a(x1))
     b#(c(x1)) -> a#(b(x1)) -> a#(a(b(x1))) -> a#(x1)
     b#(a(a(x1))) -> d#(x1) -> d#(b(x1)) -> b#(a(x1))
     b#(a(a(x1))) -> d#(x1) -> d#(b(x1)) -> a#(x1)
     b#(a(a(x1))) -> d#(x1) -> d#(a(x1)) -> a#(d(x1))
     b#(a(a(x1))) -> d#(x1) -> d#(a(x1)) -> d#(x1)
     b#(a(a(x1))) -> b#(d(x1)) -> b#(a(a(x1))) -> a#(b(d(x1)))
     b#(a(a(x1))) -> b#(d(x1)) -> b#(a(a(x1))) -> b#(d(x1))
     b#(a(a(x1))) -> b#(d(x1)) -> b#(a(a(x1))) -> d#(x1)
     b#(a(a(x1))) -> b#(d(x1)) -> b#(c(x1)) -> a#(b(x1))
     b#(a(a(x1))) -> b#(d(x1)) -> b#(c(x1)) -> b#(x1)
     b#(a(a(x1))) -> a#(b(d(x1))) -> a#(a(x1)) -> a#(b(a(x1)))
     b#(a(a(x1))) -> a#(b(d(x1))) -> a#(a(x1)) -> b#(a(x1))
     b#(a(a(x1))) -> a#(b(d(x1))) -> a#(c(x1)) -> a#(x1)
     b#(a(a(x1))) -> a#(b(d(x1))) -> a#(a(b(x1))) -> b#(a(x1))
     b#(a(a(x1))) -> a#(b(d(x1))) -> a#(a(b(x1))) -> a#(x1)
     a#(c(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1)))
     a#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(x1))
     a#(c(x1)) -> a#(x1) -> a#(c(x1)) -> a#(x1)
     a#(c(x1)) -> a#(x1) -> a#(a(b(x1))) -> b#(a(x1))
     a#(c(x1)) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
     a#(a(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(d(x1)))
     a#(a(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(d(x1))
     a#(a(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> d#(x1)
     a#(a(b(x1))) -> b#(a(x1)) -> b#(c(x1)) -> a#(b(x1))
     a#(a(b(x1))) -> b#(a(x1)) -> b#(c(x1)) -> b#(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#(c(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(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(d(x1)))
     a#(a(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(d(x1))
     a#(a(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> d#(x1)
     a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(b(x1))
     a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> b#(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#(c(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)
    Arctic Interpretation Processor:
     dimension: 1
     usable rules:
      a(a(b(x1))) -> c(b(a(x1)))
      a(c(x1)) -> c(a(x1))
      b(c(x1)) -> a(b(x1))
      b(a(a(x1))) -> a(b(d(x1)))
      d(a(x1)) -> a(d(x1))
      d(b(x1)) -> b(a(x1))
      a(a(x1)) -> a(b(a(x1)))
     interpretation:
      [d#](x0) = 2x0,
      
      [b#](x0) = x0,
      
      [a#](x0) = x0,
      
      [d](x0) = 2x0,
      
      [c](x0) = 2x0,
      
      [b](x0) = x0,
      
      [a](x0) = 2x0
     orientation:
      a#(a(b(x1))) = 2x1 >= x1 = a#(x1)
      
      a#(a(b(x1))) = 2x1 >= 2x1 = b#(a(x1))
      
      a#(c(x1)) = 2x1 >= x1 = a#(x1)
      
      b#(c(x1)) = 2x1 >= x1 = b#(x1)
      
      b#(c(x1)) = 2x1 >= x1 = a#(b(x1))
      
      b#(a(a(x1))) = 4x1 >= 2x1 = d#(x1)
      
      b#(a(a(x1))) = 4x1 >= 2x1 = b#(d(x1))
      
      b#(a(a(x1))) = 4x1 >= 2x1 = a#(b(d(x1)))
      
      d#(a(x1)) = 4x1 >= 2x1 = d#(x1)
      
      d#(a(x1)) = 4x1 >= 2x1 = a#(d(x1))
      
      d#(b(x1)) = 2x1 >= x1 = a#(x1)
      
      d#(b(x1)) = 2x1 >= 2x1 = b#(a(x1))
      
      a#(a(x1)) = 2x1 >= 2x1 = b#(a(x1))
      
      a#(a(x1)) = 2x1 >= 2x1 = a#(b(a(x1)))
      
      a(a(b(x1))) = 4x1 >= 4x1 = c(b(a(x1)))
      
      a(c(x1)) = 4x1 >= 4x1 = c(a(x1))
      
      b(c(x1)) = 2x1 >= 2x1 = a(b(x1))
      
      b(a(a(x1))) = 4x1 >= 4x1 = a(b(d(x1)))
      
      d(a(x1)) = 4x1 >= 4x1 = a(d(x1))
      
      d(b(x1)) = 2x1 >= 2x1 = b(a(x1))
      
      a(a(x1)) = 4x1 >= 4x1 = a(b(a(x1)))
     problem:
      DPs:
       a#(a(b(x1))) -> b#(a(x1))
       d#(b(x1)) -> b#(a(x1))
       a#(a(x1)) -> b#(a(x1))
       a#(a(x1)) -> a#(b(a(x1)))
      TRS:
       a(a(b(x1))) -> c(b(a(x1)))
       a(c(x1)) -> c(a(x1))
       b(c(x1)) -> a(b(x1))
       b(a(a(x1))) -> a(b(d(x1)))
       d(a(x1)) -> a(d(x1))
       d(b(x1)) -> b(a(x1))
       a(a(x1)) -> a(b(a(x1)))
     Restore Modifier:
      DPs:
       a#(a(b(x1))) -> b#(a(x1))
       d#(b(x1)) -> b#(a(x1))
       a#(a(x1)) -> b#(a(x1))
       a#(a(x1)) -> a#(b(a(x1)))
      TRS:
       a(a(b(x1))) -> c(b(a(x1)))
       a(c(x1)) -> c(a(x1))
       b(c(x1)) -> a(b(x1))
       b(a(a(x1))) -> a(b(d(x1)))
       d(a(x1)) -> a(d(x1))
       d(b(x1)) -> b(a(x1))
       a(a(x1)) -> a(b(a(x1)))
      EDG Processor:
       DPs:
        a#(a(b(x1))) -> b#(a(x1))
        d#(b(x1)) -> b#(a(x1))
        a#(a(x1)) -> b#(a(x1))
        a#(a(x1)) -> a#(b(a(x1)))
       TRS:
        a(a(b(x1))) -> c(b(a(x1)))
        a(c(x1)) -> c(a(x1))
        b(c(x1)) -> a(b(x1))
        b(a(a(x1))) -> a(b(d(x1)))
        d(a(x1)) -> a(d(x1))
        d(b(x1)) -> b(a(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:
         a(a(b(x1))) -> c(b(a(x1)))
         a(c(x1)) -> c(a(x1))
         b(c(x1)) -> a(b(x1))
         b(a(a(x1))) -> a(b(d(x1)))
         d(a(x1)) -> a(d(x1))
         d(b(x1)) -> b(a(x1))
         a(a(x1)) -> a(b(a(x1)))
        Arctic Interpretation Processor:
         dimension: 1
         usable rules:
          a(a(b(x1))) -> c(b(a(x1)))
          a(c(x1)) -> c(a(x1))
          b(c(x1)) -> a(b(x1))
          b(a(a(x1))) -> a(b(d(x1)))
          d(a(x1)) -> a(d(x1))
          d(b(x1)) -> b(a(x1))
          a(a(x1)) -> a(b(a(x1)))
         interpretation:
          [a#](x0) = x0 + 0,
          
          [d](x0) = 8x0,
          
          [c](x0) = 8x0 + 9,
          
          [b](x0) = -1x0 + 0,
          
          [a](x0) = 8x0 + 1
         orientation:
          a#(a(x1)) = 8x1 + 1 >= 7x1 + 0 = a#(b(a(x1)))
          
          a(a(b(x1))) = 15x1 + 16 >= 15x1 + 9 = c(b(a(x1)))
          
          a(c(x1)) = 16x1 + 17 >= 16x1 + 9 = c(a(x1))
          
          b(c(x1)) = 7x1 + 8 >= 7x1 + 8 = a(b(x1))
          
          b(a(a(x1))) = 15x1 + 8 >= 15x1 + 8 = a(b(d(x1)))
          
          d(a(x1)) = 16x1 + 9 >= 16x1 + 1 = a(d(x1))
          
          d(b(x1)) = 7x1 + 8 >= 7x1 + 0 = b(a(x1))
          
          a(a(x1)) = 16x1 + 9 >= 15x1 + 8 = a(b(a(x1)))
         problem:
          DPs:
           
          TRS:
           a(a(b(x1))) -> c(b(a(x1)))
           a(c(x1)) -> c(a(x1))
           b(c(x1)) -> a(b(x1))
           b(a(a(x1))) -> a(b(d(x1)))
           d(a(x1)) -> a(d(x1))
           d(b(x1)) -> b(a(x1))
           a(a(x1)) -> a(b(a(x1)))
         Qed