YES

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

Proof:
 DP Processor:
  DPs:
   a#(b(b(a(x1)))) -> a#(b(x1))
   a#(b(b(a(x1)))) -> c#(a(b(x1)))
   a#(b(b(a(x1)))) -> a#(c(a(b(x1))))
   a#(c(x1)) -> a#(x1)
   a#(c(x1)) -> c#(a(x1))
   a#(c(x1)) -> c#(c(a(x1)))
   c#(c(c(x1))) -> c#(b(x1))
  TRS:
   a(b(b(a(x1)))) -> a(c(a(b(x1))))
   a(c(x1)) -> c(c(a(x1)))
   c(c(c(x1))) -> b(c(b(x1)))
  TDG Processor:
   DPs:
    a#(b(b(a(x1)))) -> a#(b(x1))
    a#(b(b(a(x1)))) -> c#(a(b(x1)))
    a#(b(b(a(x1)))) -> a#(c(a(b(x1))))
    a#(c(x1)) -> a#(x1)
    a#(c(x1)) -> c#(a(x1))
    a#(c(x1)) -> c#(c(a(x1)))
    c#(c(c(x1))) -> c#(b(x1))
   TRS:
    a(b(b(a(x1)))) -> a(c(a(b(x1))))
    a(c(x1)) -> c(c(a(x1)))
    c(c(c(x1))) -> b(c(b(x1)))
   graph:
    c#(c(c(x1))) -> c#(b(x1)) -> c#(c(c(x1))) -> c#(b(x1))
    a#(c(x1)) -> c#(c(a(x1))) -> c#(c(c(x1))) -> c#(b(x1))
    a#(c(x1)) -> c#(a(x1)) -> c#(c(c(x1))) -> c#(b(x1))
    a#(c(x1)) -> a#(x1) -> a#(c(x1)) -> c#(c(a(x1)))
    a#(c(x1)) -> a#(x1) -> a#(c(x1)) -> c#(a(x1))
    a#(c(x1)) -> a#(x1) -> a#(c(x1)) -> a#(x1)
    a#(c(x1)) -> a#(x1) -> a#(b(b(a(x1)))) -> a#(c(a(b(x1))))
    a#(c(x1)) -> a#(x1) -> a#(b(b(a(x1)))) -> c#(a(b(x1)))
    a#(c(x1)) -> a#(x1) -> a#(b(b(a(x1)))) -> a#(b(x1))
    a#(b(b(a(x1)))) -> c#(a(b(x1))) -> c#(c(c(x1))) -> c#(b(x1))
    a#(b(b(a(x1)))) -> a#(c(a(b(x1)))) ->
    a#(c(x1)) -> c#(c(a(x1)))
    a#(b(b(a(x1)))) -> a#(c(a(b(x1)))) -> a#(c(x1)) -> c#(a(x1))
    a#(b(b(a(x1)))) -> a#(c(a(b(x1)))) -> a#(c(x1)) -> a#(x1)
    a#(b(b(a(x1)))) -> a#(c(a(b(x1)))) ->
    a#(b(b(a(x1)))) -> a#(c(a(b(x1))))
    a#(b(b(a(x1)))) -> a#(c(a(b(x1)))) ->
    a#(b(b(a(x1)))) -> c#(a(b(x1)))
    a#(b(b(a(x1)))) -> a#(c(a(b(x1)))) -> a#(b(b(a(x1)))) -> a#(b(x1))
    a#(b(b(a(x1)))) -> a#(b(x1)) -> a#(c(x1)) -> c#(c(a(x1)))
    a#(b(b(a(x1)))) -> a#(b(x1)) -> a#(c(x1)) -> c#(a(x1))
    a#(b(b(a(x1)))) -> a#(b(x1)) -> a#(c(x1)) -> a#(x1)
    a#(b(b(a(x1)))) -> a#(b(x1)) -> a#(b(b(a(x1)))) -> a#(c(a(b(x1))))
    a#(b(b(a(x1)))) -> a#(b(x1)) -> a#(b(b(a(x1)))) -> c#(a(b(x1)))
    a#(b(b(a(x1)))) -> a#(b(x1)) -> a#(b(b(a(x1)))) -> a#(b(x1))
   EDG Processor:
    DPs:
     a#(b(b(a(x1)))) -> a#(b(x1))
     a#(b(b(a(x1)))) -> c#(a(b(x1)))
     a#(b(b(a(x1)))) -> a#(c(a(b(x1))))
     a#(c(x1)) -> a#(x1)
     a#(c(x1)) -> c#(a(x1))
     a#(c(x1)) -> c#(c(a(x1)))
     c#(c(c(x1))) -> c#(b(x1))
    TRS:
     a(b(b(a(x1)))) -> a(c(a(b(x1))))
     a(c(x1)) -> c(c(a(x1)))
     c(c(c(x1))) -> b(c(b(x1)))
    graph:
     a#(c(x1)) -> c#(c(a(x1))) -> c#(c(c(x1))) -> c#(b(x1))
     a#(c(x1)) -> c#(a(x1)) -> c#(c(c(x1))) -> c#(b(x1))
     a#(c(x1)) -> a#(x1) -> a#(b(b(a(x1)))) -> a#(b(x1))
     a#(c(x1)) -> a#(x1) -> a#(b(b(a(x1)))) -> c#(a(b(x1)))
     a#(c(x1)) -> a#(x1) -> a#(b(b(a(x1)))) -> a#(c(a(b(x1))))
     a#(c(x1)) -> a#(x1) -> a#(c(x1)) -> a#(x1)
     a#(c(x1)) -> a#(x1) -> a#(c(x1)) -> c#(a(x1))
     a#(c(x1)) -> a#(x1) -> a#(c(x1)) -> c#(c(a(x1)))
     a#(b(b(a(x1)))) -> c#(a(b(x1))) -> c#(c(c(x1))) -> c#(b(x1))
     a#(b(b(a(x1)))) -> a#(c(a(b(x1)))) ->
     a#(b(b(a(x1)))) -> a#(b(x1))
     a#(b(b(a(x1)))) -> a#(c(a(b(x1)))) ->
     a#(b(b(a(x1)))) -> c#(a(b(x1)))
     a#(b(b(a(x1)))) -> a#(c(a(b(x1)))) ->
     a#(b(b(a(x1)))) -> a#(c(a(b(x1))))
     a#(b(b(a(x1)))) -> a#(c(a(b(x1)))) -> a#(c(x1)) -> a#(x1)
     a#(b(b(a(x1)))) -> a#(c(a(b(x1)))) -> a#(c(x1)) -> c#(a(x1))
     a#(b(b(a(x1)))) -> a#(c(a(b(x1)))) -> a#(c(x1)) -> c#(c(a(x1)))
     a#(b(b(a(x1)))) -> a#(b(x1)) -> a#(b(b(a(x1)))) -> a#(b(x1))
     a#(b(b(a(x1)))) -> a#(b(x1)) -> a#(b(b(a(x1)))) -> c#(a(b(x1)))
     a#(b(b(a(x1)))) -> a#(b(x1)) -> a#(b(b(a(x1)))) -> a#(c(a(b(x1))))
    CDG Processor:
     DPs:
      a#(b(b(a(x1)))) -> a#(b(x1))
      a#(b(b(a(x1)))) -> c#(a(b(x1)))
      a#(b(b(a(x1)))) -> a#(c(a(b(x1))))
      a#(c(x1)) -> a#(x1)
      a#(c(x1)) -> c#(a(x1))
      a#(c(x1)) -> c#(c(a(x1)))
      c#(c(c(x1))) -> c#(b(x1))
     TRS:
      a(b(b(a(x1)))) -> a(c(a(b(x1))))
      a(c(x1)) -> c(c(a(x1)))
      c(c(c(x1))) -> b(c(b(x1)))
     graph:
      a#(c(x1)) -> c#(c(a(x1))) -> c#(c(c(x1))) -> c#(b(x1))
      a#(c(x1)) -> c#(a(x1)) -> c#(c(c(x1))) -> c#(b(x1))
      a#(c(x1)) -> a#(x1) -> a#(c(x1)) -> c#(c(a(x1)))
      a#(c(x1)) -> a#(x1) -> a#(c(x1)) -> c#(a(x1))
      a#(c(x1)) -> a#(x1) -> a#(c(x1)) -> a#(x1)
      a#(b(b(a(x1)))) -> c#(a(b(x1))) ->
      c#(c(c(x1))) -> c#(b(x1))
      a#(b(b(a(x1)))) -> a#(c(a(b(x1)))) ->
      a#(c(x1)) -> c#(c(a(x1)))
      a#(b(b(a(x1)))) -> a#(c(a(b(x1)))) ->
      a#(c(x1)) -> c#(a(x1))
      a#(b(b(a(x1)))) -> a#(c(a(b(x1)))) -> a#(c(x1)) -> a#(x1)
     SCC Processor:
      #sccs: 1
      #rules: 1
      #arcs: 9/49
      DPs:
       a#(c(x1)) -> a#(x1)
      TRS:
       a(b(b(a(x1)))) -> a(c(a(b(x1))))
       a(c(x1)) -> c(c(a(x1)))
       c(c(c(x1))) -> b(c(b(x1)))
      Matrix Interpretation Processor: dim=3
       
       interpretation:
        [a#](x0) = [1 1 0]x0 + [1],
        
                  [0 1 0]     [1]
        [c](x0) = [1 0 0]x0 + [0]
                  [0 0 0]     [0],
        
                  [0 0 0]  
        [b](x0) = [0 1 1]x0
                  [0 1 1]  ,
        
                  [1 1 0]     [0]
        [a](x0) = [1 1 0]x0 + [1]
                  [0 0 1]     [0]
       orientation:
        a#(c(x1)) = [1 1 0]x1 + [2] >= [1 1 0]x1 + [1] = a#(x1)
        
                         [2 2 2]     [2]    [0 2 2]     [2]                 
        a(b(b(a(x1)))) = [2 2 2]x1 + [3] >= [0 2 2]x1 + [3] = a(c(a(b(x1))))
                         [2 2 2]     [2]    [0 0 0]     [0]                 
        
                   [1 1 0]     [1]    [1 1 0]     [1]              
        a(c(x1)) = [1 1 0]x1 + [2] >= [1 1 0]x1 + [2] = c(c(a(x1)))
                   [0 0 0]     [0]    [0 0 0]     [0]              
        
                      [0 1 0]     [2]    [0]              
        c(c(c(x1))) = [1 0 0]x1 + [1] >= [0] = b(c(b(x1)))
                      [0 0 0]     [0]    [0]              
       problem:
        DPs:
         
        TRS:
         a(b(b(a(x1)))) -> a(c(a(b(x1))))
         a(c(x1)) -> c(c(a(x1)))
         c(c(c(x1))) -> b(c(b(x1)))
       Qed