YES

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

Proof:
 DP Processor:
  DPs:
   b#(c(a(x1))) -> b#(x1)
   b#(c(a(x1))) -> a#(b(x1))
   b#(c(a(x1))) -> b#(a(b(x1)))
   b#(c(a(x1))) -> a#(b(a(b(x1))))
   a#(a(x1)) -> b#(a(x1))
   a#(a(x1)) -> a#(c(b(a(x1))))
  TRS:
   b(c(a(x1))) -> a(b(a(b(x1))))
   b(x1) -> c(c(x1))
   a(a(x1)) -> a(c(b(a(x1))))
  TDG Processor:
   DPs:
    b#(c(a(x1))) -> b#(x1)
    b#(c(a(x1))) -> a#(b(x1))
    b#(c(a(x1))) -> b#(a(b(x1)))
    b#(c(a(x1))) -> a#(b(a(b(x1))))
    a#(a(x1)) -> b#(a(x1))
    a#(a(x1)) -> a#(c(b(a(x1))))
   TRS:
    b(c(a(x1))) -> a(b(a(b(x1))))
    b(x1) -> c(c(x1))
    a(a(x1)) -> a(c(b(a(x1))))
   graph:
    a#(a(x1)) -> a#(c(b(a(x1)))) -> a#(a(x1)) -> a#(c(b(a(x1))))
    a#(a(x1)) -> a#(c(b(a(x1)))) -> a#(a(x1)) -> b#(a(x1))
    a#(a(x1)) -> b#(a(x1)) -> b#(c(a(x1))) -> a#(b(a(b(x1))))
    a#(a(x1)) -> b#(a(x1)) -> b#(c(a(x1))) -> b#(a(b(x1)))
    a#(a(x1)) -> b#(a(x1)) -> b#(c(a(x1))) -> a#(b(x1))
    a#(a(x1)) -> b#(a(x1)) -> b#(c(a(x1))) -> b#(x1)
    b#(c(a(x1))) -> a#(b(a(b(x1)))) -> a#(a(x1)) -> a#(c(b(a(x1))))
    b#(c(a(x1))) -> a#(b(a(b(x1)))) -> a#(a(x1)) -> b#(a(x1))
    b#(c(a(x1))) -> a#(b(x1)) -> a#(a(x1)) -> a#(c(b(a(x1))))
    b#(c(a(x1))) -> a#(b(x1)) -> a#(a(x1)) -> b#(a(x1))
    b#(c(a(x1))) -> b#(a(b(x1))) -> b#(c(a(x1))) -> a#(b(a(b(x1))))
    b#(c(a(x1))) -> b#(a(b(x1))) -> b#(c(a(x1))) -> b#(a(b(x1)))
    b#(c(a(x1))) -> b#(a(b(x1))) -> b#(c(a(x1))) -> a#(b(x1))
    b#(c(a(x1))) -> b#(a(b(x1))) -> b#(c(a(x1))) -> b#(x1)
    b#(c(a(x1))) -> b#(x1) -> b#(c(a(x1))) -> a#(b(a(b(x1))))
    b#(c(a(x1))) -> b#(x1) -> b#(c(a(x1))) -> b#(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)
   EDG Processor:
    DPs:
     b#(c(a(x1))) -> b#(x1)
     b#(c(a(x1))) -> a#(b(x1))
     b#(c(a(x1))) -> b#(a(b(x1)))
     b#(c(a(x1))) -> a#(b(a(b(x1))))
     a#(a(x1)) -> b#(a(x1))
     a#(a(x1)) -> a#(c(b(a(x1))))
    TRS:
     b(c(a(x1))) -> a(b(a(b(x1))))
     b(x1) -> c(c(x1))
     a(a(x1)) -> a(c(b(a(x1))))
    graph:
     a#(a(x1)) -> b#(a(x1)) -> b#(c(a(x1))) -> b#(x1)
     a#(a(x1)) -> b#(a(x1)) -> b#(c(a(x1))) -> a#(b(x1))
     a#(a(x1)) -> b#(a(x1)) -> b#(c(a(x1))) -> b#(a(b(x1)))
     a#(a(x1)) -> b#(a(x1)) -> b#(c(a(x1))) -> a#(b(a(b(x1))))
     b#(c(a(x1))) -> a#(b(a(b(x1)))) -> a#(a(x1)) -> b#(a(x1))
     b#(c(a(x1))) -> a#(b(a(b(x1)))) -> a#(a(x1)) -> a#(c(b(a(x1))))
     b#(c(a(x1))) -> a#(b(x1)) -> a#(a(x1)) -> b#(a(x1))
     b#(c(a(x1))) -> a#(b(x1)) -> a#(a(x1)) -> a#(c(b(a(x1))))
     b#(c(a(x1))) -> b#(a(b(x1))) -> b#(c(a(x1))) -> b#(x1)
     b#(c(a(x1))) -> b#(a(b(x1))) -> b#(c(a(x1))) -> a#(b(x1))
     b#(c(a(x1))) -> b#(a(b(x1))) -> b#(c(a(x1))) -> b#(a(b(x1)))
     b#(c(a(x1))) -> b#(a(b(x1))) -> b#(c(a(x1))) -> a#(b(a(b(x1))))
     b#(c(a(x1))) -> b#(x1) -> b#(c(a(x1))) -> 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#(a(b(x1)))
     b#(c(a(x1))) -> b#(x1) -> b#(c(a(x1))) -> a#(b(a(b(x1))))
    CDG Processor:
     DPs:
      b#(c(a(x1))) -> b#(x1)
      b#(c(a(x1))) -> a#(b(x1))
      b#(c(a(x1))) -> b#(a(b(x1)))
      b#(c(a(x1))) -> a#(b(a(b(x1))))
      a#(a(x1)) -> b#(a(x1))
      a#(a(x1)) -> a#(c(b(a(x1))))
     TRS:
      b(c(a(x1))) -> a(b(a(b(x1))))
      b(x1) -> c(c(x1))
      a(a(x1)) -> a(c(b(a(x1))))
     graph:
      b#(c(a(x1))) -> a#(b(x1)) -> a#(a(x1)) -> a#(c(b(a(x1))))
      b#(c(a(x1))) -> a#(b(x1)) -> a#(a(x1)) -> b#(a(x1))
      b#(c(a(x1))) -> b#(x1) -> b#(c(a(x1))) -> a#(b(a(b(x1))))
      b#(c(a(x1))) -> b#(x1) -> b#(c(a(x1))) -> b#(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)
     SCC Processor:
      #sccs: 1
      #rules: 1
      #arcs: 6/36
      DPs:
       b#(c(a(x1))) -> b#(x1)
      TRS:
       b(c(a(x1))) -> a(b(a(b(x1))))
       b(x1) -> c(c(x1))
       a(a(x1)) -> a(c(b(a(x1))))
      Matrix Interpretation Processor: dim=4
       
       interpretation:
        [b#](x0) = [0 0 1 0]x0,
        
                  [0 0 1 0]  
                  [0 0 1 0]  
        [b](x0) = [1 0 1 0]x0
                  [0 0 1 0]  ,
        
                  [0 0 0 0]  
                  [0 0 0 0]  
        [c](x0) = [1 0 0 1]x0
                  [1 0 0 0]  ,
        
                  [0 0 0 0]     [1]
                  [0 0 0 0]     [0]
        [a](x0) = [0 0 0 0]x0 + [0]
                  [0 0 1 0]     [0]
       orientation:
        b#(c(a(x1))) = [0 0 1 0]x1 + [1] >= [0 0 1 0]x1 = b#(x1)
        
                      [0 0 1 0]     [1]    [1]                 
                      [0 0 1 0]     [1]    [0]                 
        b(c(a(x1))) = [0 0 1 0]x1 + [1] >= [0] = a(b(a(b(x1))))
                      [0 0 1 0]     [1]    [1]                 
        
                [0 0 1 0]      [0 0 0 0]             
                [0 0 1 0]      [0 0 0 0]             
        b(x1) = [1 0 1 0]x1 >= [1 0 0 0]x1 = c(c(x1))
                [0 0 1 0]      [0 0 0 0]             
        
                   [1]    [1]                 
                   [0]    [0]                 
        a(a(x1)) = [0] >= [0] = a(c(b(a(x1))))
                   [0]    [0]                 
       problem:
        DPs:
         
        TRS:
         b(c(a(x1))) -> a(b(a(b(x1))))
         b(x1) -> c(c(x1))
         a(a(x1)) -> a(c(b(a(x1))))
       Qed