YES

Problem:
 b(a(a(x1))) -> a(b(c(x1)))
 c(a(x1)) -> a(c(x1))
 c(b(x1)) -> b(a(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))
  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))
    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))
    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))
     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))
     a(a(x1)) -> a(b(a(x1)))
    graph:
     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)
     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#(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#(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
     interpretation:
      [b#](x0) = x0,
      
      [a#](x0) = x0,
      
      [c](x0) = 2x0 + -16,
      
      [b](x0) = x0,
      
      [a](x0) = 2x0 + -16
     orientation:
      a#(a(b(x1))) = 2x1 + -16 >= x1 = a#(x1)
      
      a#(a(b(x1))) = 2x1 + -16 >= 2x1 + -16 = b#(a(x1))
      
      a#(c(x1)) = 2x1 + -16 >= x1 = a#(x1)
      
      b#(c(x1)) = 2x1 + -16 >= x1 = b#(x1)
      
      b#(c(x1)) = 2x1 + -16 >= x1 = a#(b(x1))
      
      a#(a(x1)) = 2x1 + -16 >= 2x1 + -16 = b#(a(x1))
      
      a#(a(x1)) = 2x1 + -16 >= 2x1 + -16 = a#(b(a(x1)))
      
      a(a(b(x1))) = 4x1 + -14 >= 4x1 + -14 = c(b(a(x1)))
      
      a(c(x1)) = 4x1 + -14 >= 4x1 + -14 = c(a(x1))
      
      b(c(x1)) = 2x1 + -16 >= 2x1 + -16 = a(b(x1))
      
      a(a(x1)) = 4x1 + -14 >= 4x1 + -14 = a(b(a(x1)))
     problem:
      DPs:
       a#(a(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))
       a(a(x1)) -> a(b(a(x1)))
     EDG Processor:
      DPs:
       a#(a(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))
       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: 3/9
       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))
        a(a(x1)) -> a(b(a(x1)))
       Arctic Interpretation Processor:
        dimension: 1
        interpretation:
         [a#](x0) = x0 + 7,
         
         [c](x0) = 3x0 + 12,
         
         [b](x0) = -3x0 + 6,
         
         [a](x0) = 3x0 + 8
        orientation:
         a#(a(x1)) = 3x1 + 8 >= x1 + 7 = a#(b(a(x1)))
         
         a(a(b(x1))) = 3x1 + 12 >= 3x1 + 12 = c(b(a(x1)))
         
         a(c(x1)) = 6x1 + 15 >= 6x1 + 12 = c(a(x1))
         
         b(c(x1)) = x1 + 9 >= x1 + 9 = a(b(x1))
         
         a(a(x1)) = 6x1 + 11 >= 3x1 + 9 = 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))
          a(a(x1)) -> a(b(a(x1)))
        Qed