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:
 DP Processor:
  DPs:
   b#(a(a(x1))) -> c#(x1)
   b#(a(a(x1))) -> b#(c(x1))
   c#(a(x1)) -> c#(x1)
   c#(b(x1)) -> b#(a(x1))
   L#(a(a(x1))) -> c#(x1)
   L#(a(a(x1))) -> b#(c(x1))
   L#(a(a(x1))) -> L#(a(b(c(x1))))
   c#(R(x1)) -> b#(a(R(x1)))
  TRS:
   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)))
  TDG Processor:
   DPs:
    b#(a(a(x1))) -> c#(x1)
    b#(a(a(x1))) -> b#(c(x1))
    c#(a(x1)) -> c#(x1)
    c#(b(x1)) -> b#(a(x1))
    L#(a(a(x1))) -> c#(x1)
    L#(a(a(x1))) -> b#(c(x1))
    L#(a(a(x1))) -> L#(a(b(c(x1))))
    c#(R(x1)) -> b#(a(R(x1)))
   TRS:
    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)))
   graph:
    L#(a(a(x1))) -> L#(a(b(c(x1)))) ->
    L#(a(a(x1))) -> L#(a(b(c(x1))))
    L#(a(a(x1))) -> L#(a(b(c(x1)))) -> L#(a(a(x1))) -> b#(c(x1))
    L#(a(a(x1))) -> L#(a(b(c(x1)))) -> L#(a(a(x1))) -> c#(x1)
    L#(a(a(x1))) -> c#(x1) -> c#(R(x1)) -> b#(a(R(x1)))
    L#(a(a(x1))) -> c#(x1) -> c#(b(x1)) -> b#(a(x1))
    L#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(x1)
    L#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> b#(c(x1))
    L#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> c#(x1)
    c#(R(x1)) -> b#(a(R(x1))) -> b#(a(a(x1))) -> b#(c(x1))
    c#(R(x1)) -> b#(a(R(x1))) -> b#(a(a(x1))) -> 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)) -> c#(x1) -> c#(R(x1)) -> b#(a(R(x1)))
    c#(a(x1)) -> c#(x1) -> c#(b(x1)) -> b#(a(x1))
    c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1)
    b#(a(a(x1))) -> c#(x1) -> c#(R(x1)) -> b#(a(R(x1)))
    b#(a(a(x1))) -> c#(x1) -> c#(b(x1)) -> b#(a(x1))
    b#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> 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)
   EDG Processor:
    DPs:
     b#(a(a(x1))) -> c#(x1)
     b#(a(a(x1))) -> b#(c(x1))
     c#(a(x1)) -> c#(x1)
     c#(b(x1)) -> b#(a(x1))
     L#(a(a(x1))) -> c#(x1)
     L#(a(a(x1))) -> b#(c(x1))
     L#(a(a(x1))) -> L#(a(b(c(x1))))
     c#(R(x1)) -> b#(a(R(x1)))
    TRS:
     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)))
    graph:
     L#(a(a(x1))) -> L#(a(b(c(x1)))) -> L#(a(a(x1))) -> c#(x1)
     L#(a(a(x1))) -> L#(a(b(c(x1)))) -> L#(a(a(x1))) -> b#(c(x1))
     L#(a(a(x1))) -> L#(a(b(c(x1)))) -> L#(a(a(x1))) -> L#(a(b(c(x1))))
     L#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(x1)
     L#(a(a(x1))) -> c#(x1) -> c#(b(x1)) -> b#(a(x1))
     L#(a(a(x1))) -> c#(x1) -> c#(R(x1)) -> b#(a(R(x1)))
     L#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> c#(x1)
     L#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> b#(c(x1))
     c#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> c#(x1)
     c#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(c(x1))
     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1)
     c#(a(x1)) -> c#(x1) -> c#(b(x1)) -> b#(a(x1))
     c#(a(x1)) -> c#(x1) -> c#(R(x1)) -> b#(a(R(x1)))
     b#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(x1)
     b#(a(a(x1))) -> c#(x1) -> c#(b(x1)) -> b#(a(x1))
     b#(a(a(x1))) -> c#(x1) -> c#(R(x1)) -> b#(a(R(x1)))
     b#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> c#(x1)
     b#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> b#(c(x1))
    SCC Processor:
     #sccs: 2
     #rules: 5
     #arcs: 18/64
     DPs:
      L#(a(a(x1))) -> L#(a(b(c(x1))))
     TRS:
      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)))
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [L#](x0) = 4x0,
       
       [R](x0) = 6,
       
       [L](x0) = x0 + 2,
       
       [c](x0) = 9/2x0,
       
       [b](x0) = 1/2x0 + 1,
       
       [a](x0) = 9/2x0 + 11/2
      orientation:
       L#(a(a(x1))) = 81x1 + 121 >= 81/2x1 + 40 = L#(a(b(c(x1))))
       
       b(a(a(x1))) = 81/8x1 + 129/8 >= 81/8x1 + 10 = a(b(c(x1)))
       
       c(a(x1)) = 81/4x1 + 99/4 >= 81/4x1 + 11/2 = a(c(x1))
       
       c(b(x1)) = 9/4x1 + 9/2 >= 9/4x1 + 15/4 = b(a(x1))
       
       L(a(a(x1))) = 81/4x1 + 129/4 >= 81/8x1 + 12 = L(a(b(c(x1))))
       
       c(R(x1)) = 27 >= 69/4 = b(a(R(x1)))
      problem:
       DPs:
        
       TRS:
        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)))
      Qed
     
     DPs:
      b#(a(a(x1))) -> b#(c(x1))
      b#(a(a(x1))) -> c#(x1)
      c#(b(x1)) -> b#(a(x1))
      c#(a(x1)) -> c#(x1)
     TRS:
      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)))
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [c#](x0) = 4x0 + 4,
       
       [b#](x0) = 1/2x0 + 3/2,
       
       [R](x0) = 0,
       
       [L](x0) = 4,
       
       [c](x0) = 4x0 + 1,
       
       [b](x0) = 1/2x0,
       
       [a](x0) = 4x0 + 3/2
      orientation:
       b#(a(a(x1))) = 8x1 + 21/4 >= 2x1 + 2 = b#(c(x1))
       
       b#(a(a(x1))) = 8x1 + 21/4 >= 4x1 + 4 = c#(x1)
       
       c#(b(x1)) = 2x1 + 4 >= 2x1 + 9/4 = b#(a(x1))
       
       c#(a(x1)) = 16x1 + 10 >= 4x1 + 4 = c#(x1)
       
       b(a(a(x1))) = 8x1 + 15/4 >= 8x1 + 7/2 = a(b(c(x1)))
       
       c(a(x1)) = 16x1 + 7 >= 16x1 + 11/2 = a(c(x1))
       
       c(b(x1)) = 2x1 + 1 >= 2x1 + 3/4 = b(a(x1))
       
       L(a(a(x1))) = 4 >= 4 = L(a(b(c(x1))))
       
       c(R(x1)) = 1 >= 3/4 = b(a(R(x1)))
      problem:
       DPs:
        
       TRS:
        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)))
      Qed