YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(b(x1))) -> b#(a(b(x1)))
   b#(a(x1)) -> b#(x1)
   b#(a(x1)) -> b#(b(x1))
   b#(a(x1)) -> a#(b(b(x1)))
   b#(c(a(x1))) -> b#(x1)
   b#(c(a(x1))) -> a#(b(x1))
   b#(c(a(x1))) -> a#(a(b(x1)))
  TRS:
   a(a(b(x1))) -> b(a(b(x1)))
   b(a(x1)) -> a(b(b(x1)))
   b(c(a(x1))) -> c(c(a(a(b(x1)))))
  TDG Processor:
   DPs:
    a#(a(b(x1))) -> b#(a(b(x1)))
    b#(a(x1)) -> b#(x1)
    b#(a(x1)) -> b#(b(x1))
    b#(a(x1)) -> a#(b(b(x1)))
    b#(c(a(x1))) -> b#(x1)
    b#(c(a(x1))) -> a#(b(x1))
    b#(c(a(x1))) -> a#(a(b(x1)))
   TRS:
    a(a(b(x1))) -> b(a(b(x1)))
    b(a(x1)) -> a(b(b(x1)))
    b(c(a(x1))) -> c(c(a(a(b(x1)))))
   graph:
    b#(c(a(x1))) -> b#(x1) -> b#(c(a(x1))) -> a#(a(b(x1)))
    b#(c(a(x1))) -> b#(x1) -> b#(c(a(x1))) -> a#(b(x1))
    b#(c(a(x1))) -> b#(x1) -> b#(c(a(x1))) -> b#(x1)
    b#(c(a(x1))) -> b#(x1) -> b#(a(x1)) -> a#(b(b(x1)))
    b#(c(a(x1))) -> b#(x1) -> b#(a(x1)) -> b#(b(x1))
    b#(c(a(x1))) -> b#(x1) -> b#(a(x1)) -> b#(x1)
    b#(c(a(x1))) -> a#(a(b(x1))) -> a#(a(b(x1))) -> b#(a(b(x1)))
    b#(c(a(x1))) -> a#(b(x1)) -> a#(a(b(x1))) -> b#(a(b(x1)))
    b#(a(x1)) -> b#(b(x1)) -> b#(c(a(x1))) -> a#(a(b(x1)))
    b#(a(x1)) -> b#(b(x1)) -> b#(c(a(x1))) -> a#(b(x1))
    b#(a(x1)) -> b#(b(x1)) -> b#(c(a(x1))) -> b#(x1)
    b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> a#(b(b(x1)))
    b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(b(x1))
    b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(x1)
    b#(a(x1)) -> b#(x1) -> b#(c(a(x1))) -> a#(a(b(x1)))
    b#(a(x1)) -> b#(x1) -> b#(c(a(x1))) -> a#(b(x1))
    b#(a(x1)) -> b#(x1) -> b#(c(a(x1))) -> b#(x1)
    b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(b(x1)))
    b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(b(x1))
    b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
    b#(a(x1)) -> a#(b(b(x1))) -> a#(a(b(x1))) -> b#(a(b(x1)))
    a#(a(b(x1))) -> b#(a(b(x1))) -> b#(c(a(x1))) -> a#(a(b(x1)))
    a#(a(b(x1))) -> b#(a(b(x1))) -> b#(c(a(x1))) -> a#(b(x1))
    a#(a(b(x1))) -> b#(a(b(x1))) -> b#(c(a(x1))) -> b#(x1)
    a#(a(b(x1))) -> b#(a(b(x1))) -> b#(a(x1)) -> a#(b(b(x1)))
    a#(a(b(x1))) -> b#(a(b(x1))) -> b#(a(x1)) -> b#(b(x1))
    a#(a(b(x1))) -> b#(a(b(x1))) -> b#(a(x1)) -> b#(x1)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
     [b#](x0) = [0 1 1]x0,
     
     [a#](x0) = [1 0 1]x0,
     
               [0 0 0]     [0]
     [c](x0) = [1 0 0]x0 + [0]
               [1 0 0]     [1],
     
               [0 1 1]     [1]
     [a](x0) = [0 1 1]x0 + [0]
               [0 0 1]     [1],
     
               [0 1 1]  
     [b](x0) = [0 1 0]x0
               [0 0 1]  
    orientation:
     a#(a(b(x1))) = [0 1 2]x1 + [2] >= [0 1 2]x1 + [1] = b#(a(b(x1)))
     
     b#(a(x1)) = [0 1 2]x1 + [1] >= [0 1 1]x1 = b#(x1)
     
     b#(a(x1)) = [0 1 2]x1 + [1] >= [0 1 1]x1 = b#(b(x1))
     
     b#(a(x1)) = [0 1 2]x1 + [1] >= [0 1 2]x1 = a#(b(b(x1)))
     
     b#(c(a(x1))) = [0 2 2]x1 + [3] >= [0 1 1]x1 = b#(x1)
     
     b#(c(a(x1))) = [0 2 2]x1 + [3] >= [0 1 2]x1 = a#(b(x1))
     
     b#(c(a(x1))) = [0 2 2]x1 + [3] >= [0 1 2]x1 + [2] = a#(a(b(x1)))
     
                   [0 1 2]     [2]    [0 1 2]     [1]              
     a(a(b(x1))) = [0 1 2]x1 + [1] >= [0 1 1]x1 + [0] = b(a(b(x1)))
                   [0 0 1]     [2]    [0 0 1]     [1]              
     
                [0 1 2]     [1]    [0 1 1]     [1]              
     b(a(x1)) = [0 1 1]x1 + [0] >= [0 1 1]x1 + [0] = a(b(b(x1)))
                [0 0 1]     [1]    [0 0 1]     [1]              
     
                   [0 2 2]     [3]    [0]                    
     b(c(a(x1))) = [0 1 1]x1 + [1] >= [0] = c(c(a(a(b(x1)))))
                   [0 1 1]     [2]    [1]                    
    problem:
     DPs:
      
     TRS:
      a(a(b(x1))) -> b(a(b(x1)))
      b(a(x1)) -> a(b(b(x1)))
      b(c(a(x1))) -> c(c(a(a(b(x1)))))
    Qed