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)))
  Usable Rule 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:
    c(a(x1)) -> a(c(x1))
    c(b(x1)) -> b(a(x1))
    c(R(x1)) -> b(a(R(x1)))
    b(a(a(x1))) -> a(b(c(x1)))
   Matrix Interpretation Processor: dim=1
    
    usable rules:
     c(a(x1)) -> a(c(x1))
     c(b(x1)) -> b(a(x1))
     c(R(x1)) -> b(a(R(x1)))
     b(a(a(x1))) -> a(b(c(x1)))
    interpretation:
     [L#](x0) = 5/2x0,
     
     [c#](x0) = 7/2x0 + 2,
     
     [b#](x0) = 1/2x0,
     
     [R](x0) = 4x0,
     
     [c](x0) = 7/2x0 + 1/2,
     
     [b](x0) = 1/2x0,
     
     [a](x0) = 7/2x0 + 1
    orientation:
     b#(a(a(x1))) = 49/8x1 + 9/4 >= 7/2x1 + 2 = c#(x1)
     
     b#(a(a(x1))) = 49/8x1 + 9/4 >= 7/4x1 + 1/4 = b#(c(x1))
     
     c#(a(x1)) = 49/4x1 + 11/2 >= 7/2x1 + 2 = c#(x1)
     
     c#(b(x1)) = 7/4x1 + 2 >= 7/4x1 + 1/2 = b#(a(x1))
     
     L#(a(a(x1))) = 245/8x1 + 45/4 >= 7/2x1 + 2 = c#(x1)
     
     L#(a(a(x1))) = 245/8x1 + 45/4 >= 7/4x1 + 1/4 = b#(c(x1))
     
     L#(a(a(x1))) = 245/8x1 + 45/4 >= 245/16x1 + 75/16 = L#(a(b(c(x1))))
     
     c#(R(x1)) = 14x1 + 2 >= 7x1 + 1/2 = b#(a(R(x1)))
     
     c(a(x1)) = 49/4x1 + 4 >= 49/4x1 + 11/4 = a(c(x1))
     
     c(b(x1)) = 7/4x1 + 1/2 >= 7/4x1 + 1/2 = b(a(x1))
     
     c(R(x1)) = 14x1 + 1/2 >= 7x1 + 1/2 = b(a(R(x1)))
     
     b(a(a(x1))) = 49/8x1 + 9/4 >= 49/8x1 + 15/8 = a(b(c(x1)))
    problem:
     DPs:
      
     TRS:
      c(a(x1)) -> a(c(x1))
      c(b(x1)) -> b(a(x1))
      c(R(x1)) -> b(a(R(x1)))
      b(a(a(x1))) -> a(b(c(x1)))
    Qed