YES

Problem:
 b(a(a(x1))) -> a(b(c(x1)))
 c(a(x1)) -> a(c(x1))
 c(b(x1)) -> b(a(x1))
 L(a(a(x1))) -> L(a(b(c(x1))))
 c(R(x1)) -> b(a(R(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(L(x1))) -> c(b(a(L(x1))))
  R(c(x1)) -> R(a(b(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(L(x1))) -> b#(a(L(x1)))
    R#(c(x1)) -> b#(x1)
    R#(c(x1)) -> a#(b(x1))
    R#(c(x1)) -> R#(a(b(x1)))
   TRS:
    a(a(b(x1))) -> c(b(a(x1)))
    a(c(x1)) -> c(a(x1))
    b(c(x1)) -> a(b(x1))
    a(a(L(x1))) -> c(b(a(L(x1))))
    R(c(x1)) -> R(a(b(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(L(x1))) -> b#(a(L(x1)))
     R#(c(x1)) -> b#(x1)
     R#(c(x1)) -> a#(b(x1))
     R#(c(x1)) -> R#(a(b(x1)))
    TRS:
     a(a(b(x1))) -> c(b(a(x1)))
     a(c(x1)) -> c(a(x1))
     b(c(x1)) -> a(b(x1))
     a(a(L(x1))) -> c(b(a(L(x1))))
     R(c(x1)) -> R(a(b(x1)))
    graph:
     R#(c(x1)) -> R#(a(b(x1))) -> R#(c(x1)) -> R#(a(b(x1)))
     R#(c(x1)) -> R#(a(b(x1))) -> R#(c(x1)) -> a#(b(x1))
     R#(c(x1)) -> R#(a(b(x1))) -> R#(c(x1)) -> b#(x1)
     R#(c(x1)) -> b#(x1) -> b#(c(x1)) -> a#(b(x1))
     R#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
     R#(c(x1)) -> a#(b(x1)) -> a#(a(L(x1))) -> b#(a(L(x1)))
     R#(c(x1)) -> a#(b(x1)) -> a#(c(x1)) -> a#(x1)
     R#(c(x1)) -> a#(b(x1)) -> a#(a(b(x1))) -> b#(a(x1))
     R#(c(x1)) -> a#(b(x1)) -> a#(a(b(x1))) -> a#(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(L(x1))) -> b#(a(L(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(L(x1))) -> b#(a(L(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(L(x1))) -> b#(a(L(x1))) -> b#(c(x1)) -> a#(b(x1))
     a#(a(L(x1))) -> b#(a(L(x1))) -> b#(c(x1)) -> b#(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(L(x1))) -> b#(a(L(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)
    EDG 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(L(x1))) -> b#(a(L(x1)))
      R#(c(x1)) -> b#(x1)
      R#(c(x1)) -> a#(b(x1))
      R#(c(x1)) -> R#(a(b(x1)))
     TRS:
      a(a(b(x1))) -> c(b(a(x1)))
      a(c(x1)) -> c(a(x1))
      b(c(x1)) -> a(b(x1))
      a(a(L(x1))) -> c(b(a(L(x1))))
      R(c(x1)) -> R(a(b(x1)))
     graph:
      R#(c(x1)) -> R#(a(b(x1))) -> R#(c(x1)) -> b#(x1)
      R#(c(x1)) -> R#(a(b(x1))) -> R#(c(x1)) -> a#(b(x1))
      R#(c(x1)) -> R#(a(b(x1))) -> R#(c(x1)) -> R#(a(b(x1)))
      R#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
      R#(c(x1)) -> b#(x1) -> b#(c(x1)) -> a#(b(x1))
      R#(c(x1)) -> a#(b(x1)) -> a#(a(b(x1))) -> a#(x1)
      R#(c(x1)) -> a#(b(x1)) -> a#(a(b(x1))) -> b#(a(x1))
      R#(c(x1)) -> a#(b(x1)) -> a#(c(x1)) -> a#(x1)
      b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
      b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> a#(b(x1))
      b#(c(x1)) -> a#(b(x1)) -> a#(a(b(x1))) -> a#(x1)
      b#(c(x1)) -> a#(b(x1)) -> a#(a(b(x1))) -> b#(a(x1))
      b#(c(x1)) -> a#(b(x1)) -> a#(c(x1)) -> a#(x1)
      a#(c(x1)) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
      a#(c(x1)) -> a#(x1) -> a#(a(b(x1))) -> b#(a(x1))
      a#(c(x1)) -> a#(x1) -> a#(c(x1)) -> a#(x1)
      a#(c(x1)) -> a#(x1) -> a#(a(L(x1))) -> b#(a(L(x1)))
      a#(a(b(x1))) -> b#(a(x1)) -> b#(c(x1)) -> b#(x1)
      a#(a(b(x1))) -> b#(a(x1)) -> b#(c(x1)) -> a#(b(x1))
      a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
      a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(x1))
      a#(a(b(x1))) -> a#(x1) -> a#(c(x1)) -> a#(x1)
      a#(a(b(x1))) -> a#(x1) -> a#(a(L(x1))) -> b#(a(L(x1)))
     SCC Processor:
      #sccs: 2
      #rules: 6
      #arcs: 23/81
      DPs:
       R#(c(x1)) -> R#(a(b(x1)))
      TRS:
       a(a(b(x1))) -> c(b(a(x1)))
       a(c(x1)) -> c(a(x1))
       b(c(x1)) -> a(b(x1))
       a(a(L(x1))) -> c(b(a(L(x1))))
       R(c(x1)) -> R(a(b(x1)))
      Usable Rule Processor:
       DPs:
        R#(c(x1)) -> R#(a(b(x1)))
       TRS:
        b(c(x1)) -> a(b(x1))
        a(a(b(x1))) -> c(b(a(x1)))
        a(c(x1)) -> c(a(x1))
        a(a(L(x1))) -> c(b(a(L(x1))))
       Arctic Interpretation Processor:
        dimension: 1
        usable rules:
         b(c(x1)) -> a(b(x1))
         a(a(b(x1))) -> c(b(a(x1)))
         a(c(x1)) -> c(a(x1))
         a(a(L(x1))) -> c(b(a(L(x1))))
        interpretation:
         [b](x0) = -4x0 + 4,
         
         [L](x0) = 8,
         
         [a](x0) = 4x0 + 8,
         
         [R#](x0) = -4x0 + 0,
         
         [c](x0) = 4x0 + 12
        orientation:
         R#(c(x1)) = x1 + 8 >= -4x1 + 4 = R#(a(b(x1)))
         
         b(c(x1)) = x1 + 8 >= x1 + 8 = a(b(x1))
         
         a(a(b(x1))) = 4x1 + 12 >= 4x1 + 12 = c(b(a(x1)))
         
         a(c(x1)) = 8x1 + 16 >= 8x1 + 12 = c(a(x1))
         
         a(a(L(x1))) = 16 >= 12 = c(b(a(L(x1))))
        problem:
         DPs:
          
         TRS:
          b(c(x1)) -> a(b(x1))
          a(a(b(x1))) -> c(b(a(x1)))
          a(c(x1)) -> c(a(x1))
          a(a(L(x1))) -> c(b(a(L(x1))))
        Qed
      
      DPs:
       a#(c(x1)) -> a#(x1)
       a#(a(b(x1))) -> b#(a(x1))
       b#(c(x1)) -> a#(b(x1))
       a#(a(b(x1))) -> a#(x1)
       b#(c(x1)) -> b#(x1)
      TRS:
       a(a(b(x1))) -> c(b(a(x1)))
       a(c(x1)) -> c(a(x1))
       b(c(x1)) -> a(b(x1))
       a(a(L(x1))) -> c(b(a(L(x1))))
       R(c(x1)) -> R(a(b(x1)))
      Usable Rule Processor:
       DPs:
        a#(c(x1)) -> a#(x1)
        a#(a(b(x1))) -> b#(a(x1))
        b#(c(x1)) -> a#(b(x1))
        a#(a(b(x1))) -> a#(x1)
        b#(c(x1)) -> b#(x1)
       TRS:
        a(a(b(x1))) -> c(b(a(x1)))
        a(c(x1)) -> c(a(x1))
        a(a(L(x1))) -> c(b(a(L(x1))))
        b(c(x1)) -> a(b(x1))
       KBO Processor:
        weight function:
         w0 = 1
         w(b#) = w(a#) = w(L) = w(c) = w(a) = 1
         w(b) = 0
        precedence:
         b > L > a# > a > c > b#
        problem:
         DPs:
          
         TRS:
          
        Qed