YES

Problem:
 b(c(x1)) -> c(b(x1))
 c(b(x1)) -> a(a(a(x1)))
 a(a(a(a(x1)))) -> b(c(x1))

Proof:
 DP Processor:
  DPs:
   b#(c(x1)) -> b#(x1)
   b#(c(x1)) -> c#(b(x1))
   c#(b(x1)) -> a#(x1)
   c#(b(x1)) -> a#(a(x1))
   c#(b(x1)) -> a#(a(a(x1)))
   a#(a(a(a(x1)))) -> c#(x1)
   a#(a(a(a(x1)))) -> b#(c(x1))
  TRS:
   b(c(x1)) -> c(b(x1))
   c(b(x1)) -> a(a(a(x1)))
   a(a(a(a(x1)))) -> b(c(x1))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [a#](x0) = 8x0 + 8,
    
    [c#](x0) = 8x0 + 16,
    
    [b#](x0) = 8x0 + 21,
    
    [a](x0) = x0 + 2,
    
    [b](x0) = x0 + 4,
    
    [c](x0) = x0 + 4
   orientation:
    b#(c(x1)) = 8x1 + 53 >= 8x1 + 21 = b#(x1)
    
    b#(c(x1)) = 8x1 + 53 >= 8x1 + 48 = c#(b(x1))
    
    c#(b(x1)) = 8x1 + 48 >= 8x1 + 8 = a#(x1)
    
    c#(b(x1)) = 8x1 + 48 >= 8x1 + 24 = a#(a(x1))
    
    c#(b(x1)) = 8x1 + 48 >= 8x1 + 40 = a#(a(a(x1)))
    
    a#(a(a(a(x1)))) = 8x1 + 56 >= 8x1 + 16 = c#(x1)
    
    a#(a(a(a(x1)))) = 8x1 + 56 >= 8x1 + 53 = b#(c(x1))
    
    b(c(x1)) = x1 + 8 >= x1 + 8 = c(b(x1))
    
    c(b(x1)) = x1 + 8 >= x1 + 6 = a(a(a(x1)))
    
    a(a(a(a(x1)))) = x1 + 8 >= x1 + 8 = b(c(x1))
   problem:
    DPs:
     
    TRS:
     b(c(x1)) -> c(b(x1))
     c(b(x1)) -> a(a(a(x1)))
     a(a(a(a(x1)))) -> b(c(x1))
   Qed