YES

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

Proof:
 DP Processor:
  DPs:
   b#(b(b(x1))) -> a#(x1)
   a#(a(x1)) -> b#(a(x1))
   a#(a(x1)) -> a#(b(a(x1)))
   b#(c(x1)) -> a#(x1)
   b#(c(x1)) -> a#(a(x1))
   a#(c(x1)) -> b#(x1)
   a#(c(x1)) -> b#(b(x1))
   a#(a(a(x1))) -> b#(a(a(x1)))
  TRS:
   b(b(b(x1))) -> a(x1)
   a(a(x1)) -> a(b(a(x1)))
   b(c(x1)) -> c(a(a(x1)))
   a(c(x1)) -> c(b(b(x1)))
   a(a(a(x1))) -> b(a(a(x1)))
  TDG Processor:
   DPs:
    b#(b(b(x1))) -> a#(x1)
    a#(a(x1)) -> b#(a(x1))
    a#(a(x1)) -> a#(b(a(x1)))
    b#(c(x1)) -> a#(x1)
    b#(c(x1)) -> a#(a(x1))
    a#(c(x1)) -> b#(x1)
    a#(c(x1)) -> b#(b(x1))
    a#(a(a(x1))) -> b#(a(a(x1)))
   TRS:
    b(b(b(x1))) -> a(x1)
    a(a(x1)) -> a(b(a(x1)))
    b(c(x1)) -> c(a(a(x1)))
    a(c(x1)) -> c(b(b(x1)))
    a(a(a(x1))) -> b(a(a(x1)))
   graph:
    a#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> a#(a(x1))
    a#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> a#(x1)
    a#(c(x1)) -> b#(b(x1)) -> b#(b(b(x1))) -> a#(x1)
    a#(c(x1)) -> b#(x1) -> b#(c(x1)) -> a#(a(x1))
    a#(c(x1)) -> b#(x1) -> b#(c(x1)) -> a#(x1)
    a#(c(x1)) -> b#(x1) -> b#(b(b(x1))) -> a#(x1)
    a#(a(a(x1))) -> b#(a(a(x1))) -> b#(c(x1)) -> a#(a(x1))
    a#(a(a(x1))) -> b#(a(a(x1))) -> b#(c(x1)) -> a#(x1)
    a#(a(a(x1))) -> b#(a(a(x1))) -> b#(b(b(x1))) -> a#(x1)
    a#(a(x1)) -> a#(b(a(x1))) -> a#(a(a(x1))) -> b#(a(a(x1)))
    a#(a(x1)) -> a#(b(a(x1))) -> a#(c(x1)) -> b#(b(x1))
    a#(a(x1)) -> a#(b(a(x1))) -> a#(c(x1)) -> b#(x1)
    a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1)))
    a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(x1))
    a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(a(x1))
    a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(x1)
    a#(a(x1)) -> b#(a(x1)) -> b#(b(b(x1))) -> a#(x1)
    b#(c(x1)) -> a#(a(x1)) -> a#(a(a(x1))) -> b#(a(a(x1)))
    b#(c(x1)) -> a#(a(x1)) -> a#(c(x1)) -> b#(b(x1))
    b#(c(x1)) -> a#(a(x1)) -> a#(c(x1)) -> b#(x1)
    b#(c(x1)) -> a#(a(x1)) -> a#(a(x1)) -> a#(b(a(x1)))
    b#(c(x1)) -> a#(a(x1)) -> a#(a(x1)) -> b#(a(x1))
    b#(c(x1)) -> a#(x1) -> a#(a(a(x1))) -> b#(a(a(x1)))
    b#(c(x1)) -> a#(x1) -> a#(c(x1)) -> b#(b(x1))
    b#(c(x1)) -> a#(x1) -> a#(c(x1)) -> b#(x1)
    b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1)))
    b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(x1))
    b#(b(b(x1))) -> a#(x1) -> a#(a(a(x1))) -> b#(a(a(x1)))
    b#(b(b(x1))) -> a#(x1) -> a#(c(x1)) -> b#(b(x1))
    b#(b(b(x1))) -> a#(x1) -> a#(c(x1)) -> b#(x1)
    b#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1)))
    b#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> b#(a(x1))
   Arctic Interpretation Processor:
    dimension: 1
    interpretation:
     [a#](x0) = x0,
     
     [b#](x0) = x0,
     
     [c](x0) = 1x0 + -16,
     
     [a](x0) = x0,
     
     [b](x0) = x0
    orientation:
     b#(b(b(x1))) = x1 >= x1 = a#(x1)
     
     a#(a(x1)) = x1 >= x1 = b#(a(x1))
     
     a#(a(x1)) = x1 >= x1 = a#(b(a(x1)))
     
     b#(c(x1)) = 1x1 + -16 >= x1 = a#(x1)
     
     b#(c(x1)) = 1x1 + -16 >= x1 = a#(a(x1))
     
     a#(c(x1)) = 1x1 + -16 >= x1 = b#(x1)
     
     a#(c(x1)) = 1x1 + -16 >= x1 = b#(b(x1))
     
     a#(a(a(x1))) = x1 >= x1 = b#(a(a(x1)))
     
     b(b(b(x1))) = x1 >= x1 = a(x1)
     
     a(a(x1)) = x1 >= x1 = a(b(a(x1)))
     
     b(c(x1)) = 1x1 + -16 >= 1x1 + -16 = c(a(a(x1)))
     
     a(c(x1)) = 1x1 + -16 >= 1x1 + -16 = c(b(b(x1)))
     
     a(a(a(x1))) = x1 >= x1 = b(a(a(x1)))
    problem:
     DPs:
      b#(b(b(x1))) -> a#(x1)
      a#(a(x1)) -> b#(a(x1))
      a#(a(x1)) -> a#(b(a(x1)))
      a#(a(a(x1))) -> b#(a(a(x1)))
     TRS:
      b(b(b(x1))) -> a(x1)
      a(a(x1)) -> a(b(a(x1)))
      b(c(x1)) -> c(a(a(x1)))
      a(c(x1)) -> c(b(b(x1)))
      a(a(a(x1))) -> b(a(a(x1)))
    EDG Processor:
     DPs:
      b#(b(b(x1))) -> a#(x1)
      a#(a(x1)) -> b#(a(x1))
      a#(a(x1)) -> a#(b(a(x1)))
      a#(a(a(x1))) -> b#(a(a(x1)))
     TRS:
      b(b(b(x1))) -> a(x1)
      a(a(x1)) -> a(b(a(x1)))
      b(c(x1)) -> c(a(a(x1)))
      a(c(x1)) -> c(b(b(x1)))
      a(a(a(x1))) -> b(a(a(x1)))
     graph:
      a#(a(a(x1))) -> b#(a(a(x1))) -> b#(b(b(x1))) -> a#(x1)
      a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(x1))
      a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1)))
      a#(a(x1)) -> a#(b(a(x1))) -> a#(a(a(x1))) -> b#(a(a(x1)))
      a#(a(x1)) -> b#(a(x1)) -> b#(b(b(x1))) -> a#(x1)
      b#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> b#(a(x1))
      b#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1)))
      b#(b(b(x1))) -> a#(x1) -> a#(a(a(x1))) -> b#(a(a(x1)))
     Arctic Interpretation Processor:
      dimension: 2
      interpretation:
       [a#](x0) = [3 2]x0,
       
       [b#](x0) = [0 3]x0,
       
                 [1 ]
       [c](x0) = [-&],
       
                 [1 0]  
       [a](x0) = [1 0]x0,
       
                 [0 0]  
       [b](x0) = [0 1]x0
      orientation:
       b#(b(b(x1))) = [4 5]x1 >= [3 2]x1 = a#(x1)
       
       a#(a(x1)) = [4 3]x1 >= [4 3]x1 = b#(a(x1))
       
       a#(a(x1)) = [4 3]x1 >= [4 3]x1 = a#(b(a(x1)))
       
       a#(a(a(x1))) = [5 4]x1 >= [5 4]x1 = b#(a(a(x1)))
       
                     [1 2]      [1 0]          
       b(b(b(x1))) = [2 3]x1 >= [1 0]x1 = a(x1)
       
                  [2 1]      [2 1]                
       a(a(x1)) = [2 1]x1 >= [2 1]x1 = a(b(a(x1)))
       
                  [1]    [1 ]              
       b(c(x1)) = [1] >= [-&] = c(a(a(x1)))
       
                  [2]    [1 ]              
       a(c(x1)) = [2] >= [-&] = c(b(b(x1)))
       
                     [3 2]      [2 1]                
       a(a(a(x1))) = [3 2]x1 >= [3 2]x1 = b(a(a(x1)))
      problem:
       DPs:
        a#(a(x1)) -> b#(a(x1))
        a#(a(x1)) -> a#(b(a(x1)))
        a#(a(a(x1))) -> b#(a(a(x1)))
       TRS:
        b(b(b(x1))) -> a(x1)
        a(a(x1)) -> a(b(a(x1)))
        b(c(x1)) -> c(a(a(x1)))
        a(c(x1)) -> c(b(b(x1)))
        a(a(a(x1))) -> b(a(a(x1)))
      EDG Processor:
       DPs:
        a#(a(x1)) -> b#(a(x1))
        a#(a(x1)) -> a#(b(a(x1)))
        a#(a(a(x1))) -> b#(a(a(x1)))
       TRS:
        b(b(b(x1))) -> a(x1)
        a(a(x1)) -> a(b(a(x1)))
        b(c(x1)) -> c(a(a(x1)))
        a(c(x1)) -> c(b(b(x1)))
        a(a(a(x1))) -> b(a(a(x1)))
       graph:
        a#(a(x1)) -> a#(b(a(x1))) -> a#(a(a(x1))) -> b#(a(a(x1)))
        a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1)))
        a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(x1))
       SCC Processor:
        #sccs: 1
        #rules: 1
        #arcs: 3/9
        DPs:
         a#(a(x1)) -> a#(b(a(x1)))
        TRS:
         b(b(b(x1))) -> a(x1)
         a(a(x1)) -> a(b(a(x1)))
         b(c(x1)) -> c(a(a(x1)))
         a(c(x1)) -> c(b(b(x1)))
         a(a(a(x1))) -> b(a(a(x1)))
        Arctic Interpretation Processor:
         dimension: 2
         interpretation:
          [a#](x0) = [-& 0 ]x0 + [0],
          
                    [2]
          [c](x0) = [0],
          
                    [0 0]     [0]
          [a](x0) = [2 2]x0 + [2],
          
                    [2  0 ]     [0]
          [b](x0) = [0  -&]x0 + [0]
         orientation:
          a#(a(x1)) = [2 2]x1 + [2] >= [0 0]x1 + [0] = a#(b(a(x1)))
          
                        [6 4]     [4]    [0 0]     [0]        
          b(b(b(x1))) = [4 2]x1 + [2] >= [2 2]x1 + [2] = a(x1)
          
                     [2 2]     [2]    [2 2]     [2]              
          a(a(x1)) = [4 4]x1 + [4] >= [4 4]x1 + [4] = a(b(a(x1)))
          
                     [4]    [2]              
          b(c(x1)) = [2] >= [0] = c(a(a(x1)))
          
                     [2]    [2]              
          a(c(x1)) = [4] >= [0] = c(b(b(x1)))
          
                        [4 4]     [4]    [4 4]     [4]              
          a(a(a(x1))) = [6 6]x1 + [6] >= [2 2]x1 + [2] = b(a(a(x1)))
         problem:
          DPs:
           
          TRS:
           b(b(b(x1))) -> a(x1)
           a(a(x1)) -> a(b(a(x1)))
           b(c(x1)) -> c(a(a(x1)))
           a(c(x1)) -> c(b(b(x1)))
           a(a(a(x1))) -> b(a(a(x1)))
         Qed