YES

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

Proof:
 DP Processor:
  DPs:
   b#(a(a(x1))) -> c#(x1)
   b#(a(a(x1))) -> b#(c(x1))
   b#(a(a(x1))) -> a#(b(c(x1)))
   c#(a(x1)) -> c#(x1)
   c#(a(x1)) -> a#(c(x1))
   c#(b(x1)) -> a#(x1)
   c#(b(x1)) -> b#(a(x1))
   a#(a(x1)) -> b#(a(x1))
   a#(a(x1)) -> a#(b(a(x1)))
  TRS:
   b(a(a(x1))) -> a(b(c(x1)))
   c(a(x1)) -> a(c(x1))
   c(b(x1)) -> b(a(x1))
   a(a(x1)) -> a(b(a(x1)))
  Matrix Interpretation Processor: dim=1
   
   usable rules:
    b(a(a(x1))) -> a(b(c(x1)))
    c(a(x1)) -> a(c(x1))
    c(b(x1)) -> b(a(x1))
    a(a(x1)) -> a(b(a(x1)))
   interpretation:
    [a#](x0) = 1/2x0 + 2,
    
    [c#](x0) = 2x0 + 5/2,
    
    [b#](x0) = 1/2x0 + 3/2,
    
    [c](x0) = 2x0 + 1/2,
    
    [b](x0) = 1/2x0,
    
    [a](x0) = 2x0 + 1
   orientation:
    b#(a(a(x1))) = 2x1 + 3 >= 2x1 + 5/2 = c#(x1)
    
    b#(a(a(x1))) = 2x1 + 3 >= x1 + 7/4 = b#(c(x1))
    
    b#(a(a(x1))) = 2x1 + 3 >= 1/2x1 + 17/8 = a#(b(c(x1)))
    
    c#(a(x1)) = 4x1 + 9/2 >= 2x1 + 5/2 = c#(x1)
    
    c#(a(x1)) = 4x1 + 9/2 >= x1 + 9/4 = a#(c(x1))
    
    c#(b(x1)) = x1 + 5/2 >= 1/2x1 + 2 = a#(x1)
    
    c#(b(x1)) = x1 + 5/2 >= x1 + 2 = b#(a(x1))
    
    a#(a(x1)) = x1 + 5/2 >= x1 + 2 = b#(a(x1))
    
    a#(a(x1)) = x1 + 5/2 >= 1/2x1 + 9/4 = a#(b(a(x1)))
    
    b(a(a(x1))) = 2x1 + 3/2 >= 2x1 + 3/2 = a(b(c(x1)))
    
    c(a(x1)) = 4x1 + 5/2 >= 4x1 + 2 = a(c(x1))
    
    c(b(x1)) = x1 + 1/2 >= x1 + 1/2 = b(a(x1))
    
    a(a(x1)) = 4x1 + 3 >= 2x1 + 2 = a(b(a(x1)))
   problem:
    DPs:
     
    TRS:
     b(a(a(x1))) -> a(b(c(x1)))
     c(a(x1)) -> a(c(x1))
     c(b(x1)) -> b(a(x1))
     a(a(x1)) -> a(b(a(x1)))
   Qed