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)))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [L#](x0) = x0,
    
    [c#](x0) = 4x0 + 2,
    
    [b#](x0) = 1/2x0,
    
    [R](x0) = 4,
    
    [L](x0) = 1/2x0 + 6,
    
    [c](x0) = 4x0,
    
    [b](x0) = 1/2x0 + 1,
    
    [a](x0) = 4x0 + 5/2
   orientation:
    b#(a(a(x1))) = 8x1 + 25/4 >= 4x1 + 2 = c#(x1)
    
    b#(a(a(x1))) = 8x1 + 25/4 >= 2x1 = b#(c(x1))
    
    c#(a(x1)) = 16x1 + 12 >= 4x1 + 2 = c#(x1)
    
    c#(b(x1)) = 2x1 + 6 >= 2x1 + 5/4 = b#(a(x1))
    
    L#(a(a(x1))) = 16x1 + 25/2 >= 4x1 + 2 = c#(x1)
    
    L#(a(a(x1))) = 16x1 + 25/2 >= 2x1 = b#(c(x1))
    
    L#(a(a(x1))) = 16x1 + 25/2 >= 8x1 + 13/2 = L#(a(b(c(x1))))
    
    c#(R(x1)) = 18 >= 37/4 = b#(a(R(x1)))
    
    b(a(a(x1))) = 8x1 + 29/4 >= 8x1 + 13/2 = a(b(c(x1)))
    
    c(a(x1)) = 16x1 + 10 >= 16x1 + 5/2 = a(c(x1))
    
    c(b(x1)) = 2x1 + 4 >= 2x1 + 9/4 = b(a(x1))
    
    L(a(a(x1))) = 8x1 + 49/4 >= 4x1 + 37/4 = L(a(b(c(x1))))
    
    c(R(x1)) = 16 >= 41/4 = 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