YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(b(x1))) -> a#(x1)
   a#(a(b(x1))) -> b#(c(a(x1)))
   a#(a(b(x1))) -> a#(b(c(a(x1))))
   a#(a(b(x1))) -> b#(a(b(c(a(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))
  TRS:
   a(a(b(x1))) -> b(a(b(c(a(x1)))))
   b(a(x1)) -> a(b(b(x1)))
   b(c(a(x1))) -> c(a(b(x1)))
  TDG Processor:
   DPs:
    a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> b#(c(a(x1)))
    a#(a(b(x1))) -> a#(b(c(a(x1))))
    a#(a(b(x1))) -> b#(a(b(c(a(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))
   TRS:
    a(a(b(x1))) -> b(a(b(c(a(x1)))))
    b(a(x1)) -> a(b(b(x1)))
    b(c(a(x1))) -> c(a(b(x1)))
   graph:
    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#(b(x1)) -> a#(a(b(x1))) -> b#(a(b(c(a(x1)))))
    b#(c(a(x1))) -> a#(b(x1)) -> a#(a(b(x1))) -> a#(b(c(a(x1))))
    b#(c(a(x1))) -> a#(b(x1)) -> a#(a(b(x1))) -> b#(c(a(x1)))
    b#(c(a(x1))) -> a#(b(x1)) -> a#(a(b(x1))) -> a#(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#(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(c(a(x1)))))
    b#(a(x1)) -> a#(b(b(x1))) -> a#(a(b(x1))) -> a#(b(c(a(x1))))
    b#(a(x1)) -> a#(b(b(x1))) -> a#(a(b(x1))) -> b#(c(a(x1)))
    b#(a(x1)) -> a#(b(b(x1))) -> a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> b#(c(a(x1))) -> b#(c(a(x1))) -> a#(b(x1))
    a#(a(b(x1))) -> b#(c(a(x1))) -> b#(c(a(x1))) -> b#(x1)
    a#(a(b(x1))) -> b#(c(a(x1))) -> b#(a(x1)) -> a#(b(b(x1)))
    a#(a(b(x1))) -> b#(c(a(x1))) -> b#(a(x1)) -> b#(b(x1))
    a#(a(b(x1))) -> b#(c(a(x1))) -> b#(a(x1)) -> b#(x1)
    a#(a(b(x1))) -> b#(a(b(c(a(x1))))) ->
    b#(c(a(x1))) -> a#(b(x1))
    a#(a(b(x1))) -> b#(a(b(c(a(x1))))) -> b#(c(a(x1))) -> b#(x1)
    a#(a(b(x1))) -> b#(a(b(c(a(x1))))) ->
    b#(a(x1)) -> a#(b(b(x1)))
    a#(a(b(x1))) -> b#(a(b(c(a(x1))))) -> b#(a(x1)) -> b#(b(x1))
    a#(a(b(x1))) -> b#(a(b(c(a(x1))))) -> b#(a(x1)) -> b#(x1)
    a#(a(b(x1))) -> a#(b(c(a(x1)))) ->
    a#(a(b(x1))) -> b#(a(b(c(a(x1)))))
    a#(a(b(x1))) -> a#(b(c(a(x1)))) ->
    a#(a(b(x1))) -> a#(b(c(a(x1))))
    a#(a(b(x1))) -> a#(b(c(a(x1)))) -> a#(a(b(x1))) -> b#(c(a(x1)))
    a#(a(b(x1))) -> a#(b(c(a(x1)))) -> a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(b(c(a(x1)))))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(b(c(a(x1))))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(c(a(x1)))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
   EDG Processor:
    DPs:
     a#(a(b(x1))) -> a#(x1)
     a#(a(b(x1))) -> b#(c(a(x1)))
     a#(a(b(x1))) -> a#(b(c(a(x1))))
     a#(a(b(x1))) -> b#(a(b(c(a(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))
    TRS:
     a(a(b(x1))) -> b(a(b(c(a(x1)))))
     b(a(x1)) -> a(b(b(x1)))
     b(c(a(x1))) -> c(a(b(x1)))
    graph:
     b#(c(a(x1))) -> b#(x1) -> b#(a(x1)) -> b#(x1)
     b#(c(a(x1))) -> b#(x1) -> b#(a(x1)) -> b#(b(x1))
     b#(c(a(x1))) -> b#(x1) -> b#(a(x1)) -> a#(b(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))) -> a#(b(x1)) -> a#(a(b(x1))) -> a#(x1)
     b#(c(a(x1))) -> a#(b(x1)) -> a#(a(b(x1))) -> b#(c(a(x1)))
     b#(c(a(x1))) -> a#(b(x1)) -> a#(a(b(x1))) -> a#(b(c(a(x1))))
     b#(c(a(x1))) -> a#(b(x1)) -> a#(a(b(x1))) -> b#(a(b(c(a(x1)))))
     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(b(x1))
     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> a#(b(b(x1)))
     b#(a(x1)) -> b#(b(x1)) -> b#(c(a(x1))) -> b#(x1)
     b#(a(x1)) -> b#(b(x1)) -> b#(c(a(x1))) -> a#(b(x1))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(b(x1))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(b(x1)))
     b#(a(x1)) -> b#(x1) -> b#(c(a(x1))) -> b#(x1)
     b#(a(x1)) -> b#(x1) -> b#(c(a(x1))) -> a#(b(x1))
     b#(a(x1)) -> a#(b(b(x1))) -> a#(a(b(x1))) -> a#(x1)
     b#(a(x1)) -> a#(b(b(x1))) -> a#(a(b(x1))) -> b#(c(a(x1)))
     b#(a(x1)) -> a#(b(b(x1))) -> a#(a(b(x1))) -> a#(b(c(a(x1))))
     b#(a(x1)) -> a#(b(b(x1))) -> a#(a(b(x1))) -> b#(a(b(c(a(x1)))))
     a#(a(b(x1))) -> b#(c(a(x1))) -> b#(c(a(x1))) -> b#(x1)
     a#(a(b(x1))) -> b#(c(a(x1))) -> b#(c(a(x1))) -> a#(b(x1))
     a#(a(b(x1))) -> b#(a(b(c(a(x1))))) -> b#(a(x1)) -> b#(x1)
     a#(a(b(x1))) -> b#(a(b(c(a(x1))))) -> b#(a(x1)) -> b#(b(x1))
     a#(a(b(x1))) -> b#(a(b(c(a(x1))))) ->
     b#(a(x1)) -> a#(b(b(x1)))
     a#(a(b(x1))) -> b#(a(b(c(a(x1))))) -> b#(c(a(x1))) -> b#(x1)
     a#(a(b(x1))) -> b#(a(b(c(a(x1))))) -> b#(c(a(x1))) -> a#(b(x1))
     a#(a(b(x1))) -> a#(b(c(a(x1)))) -> a#(a(b(x1))) -> a#(x1)
     a#(a(b(x1))) -> a#(b(c(a(x1)))) -> a#(a(b(x1))) -> b#(c(a(x1)))
     a#(a(b(x1))) -> a#(b(c(a(x1)))) ->
     a#(a(b(x1))) -> a#(b(c(a(x1))))
     a#(a(b(x1))) -> a#(b(c(a(x1)))) -> a#(a(b(x1))) -> b#(a(b(c(a(x1)))))
     a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
     a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(c(a(x1)))
     a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(b(c(a(x1))))
     a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(b(c(a(x1)))))
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [b#](x0) = 3x0,
      
      [a#](x0) = 4x0,
      
      [c](x0) = x0,
      
      [a](x0) = 1x0,
      
      [b](x0) = x0
     orientation:
      a#(a(b(x1))) = 5x1 >= 4x1 = a#(x1)
      
      a#(a(b(x1))) = 5x1 >= 4x1 = b#(c(a(x1)))
      
      a#(a(b(x1))) = 5x1 >= 5x1 = a#(b(c(a(x1))))
      
      a#(a(b(x1))) = 5x1 >= 5x1 = b#(a(b(c(a(x1)))))
      
      b#(a(x1)) = 4x1 >= 3x1 = b#(x1)
      
      b#(a(x1)) = 4x1 >= 3x1 = b#(b(x1))
      
      b#(a(x1)) = 4x1 >= 4x1 = a#(b(b(x1)))
      
      b#(c(a(x1))) = 4x1 >= 3x1 = b#(x1)
      
      b#(c(a(x1))) = 4x1 >= 4x1 = a#(b(x1))
      
      a(a(b(x1))) = 2x1 >= 2x1 = b(a(b(c(a(x1)))))
      
      b(a(x1)) = 1x1 >= 1x1 = a(b(b(x1)))
      
      b(c(a(x1))) = 1x1 >= 1x1 = c(a(b(x1)))
     problem:
      DPs:
       a#(a(b(x1))) -> a#(b(c(a(x1))))
       a#(a(b(x1))) -> b#(a(b(c(a(x1)))))
       b#(a(x1)) -> a#(b(b(x1)))
       b#(c(a(x1))) -> a#(b(x1))
      TRS:
       a(a(b(x1))) -> b(a(b(c(a(x1)))))
       b(a(x1)) -> a(b(b(x1)))
       b(c(a(x1))) -> c(a(b(x1)))
     EDG Processor:
      DPs:
       a#(a(b(x1))) -> a#(b(c(a(x1))))
       a#(a(b(x1))) -> b#(a(b(c(a(x1)))))
       b#(a(x1)) -> a#(b(b(x1)))
       b#(c(a(x1))) -> a#(b(x1))
      TRS:
       a(a(b(x1))) -> b(a(b(c(a(x1)))))
       b(a(x1)) -> a(b(b(x1)))
       b(c(a(x1))) -> c(a(b(x1)))
      graph:
       b#(c(a(x1))) -> a#(b(x1)) -> a#(a(b(x1))) -> b#(a(b(c(a(x1)))))
       b#(c(a(x1))) -> a#(b(x1)) -> a#(a(b(x1))) -> a#(b(c(a(x1))))
       b#(a(x1)) -> a#(b(b(x1))) -> a#(a(b(x1))) -> b#(a(b(c(a(x1)))))
       b#(a(x1)) -> a#(b(b(x1))) ->
       a#(a(b(x1))) -> a#(b(c(a(x1))))
       a#(a(b(x1))) -> b#(a(b(c(a(x1))))) ->
       b#(c(a(x1))) -> a#(b(x1))
       a#(a(b(x1))) -> b#(a(b(c(a(x1))))) ->
       b#(a(x1)) -> a#(b(b(x1)))
       a#(a(b(x1))) -> a#(b(c(a(x1)))) ->
       a#(a(b(x1))) -> b#(a(b(c(a(x1)))))
       a#(a(b(x1))) -> a#(b(c(a(x1)))) -> a#(a(b(x1))) -> a#(b(c(a(x1))))
      Arctic Interpretation Processor:
       dimension: 1
       interpretation:
        [b#](x0) = x0 + 3,
        
        [a#](x0) = 3,
        
        [c](x0) = 14x0 + 0,
        
        [a](x0) = 2,
        
        [b](x0) = x0 + 0
       orientation:
        a#(a(b(x1))) = 3 >= 3 = a#(b(c(a(x1))))
        
        a#(a(b(x1))) = 3 >= 3 = b#(a(b(c(a(x1)))))
        
        b#(a(x1)) = 3 >= 3 = a#(b(b(x1)))
        
        b#(c(a(x1))) = 16 >= 3 = a#(b(x1))
        
        a(a(b(x1))) = 2 >= 2 = b(a(b(c(a(x1)))))
        
        b(a(x1)) = 2 >= 2 = a(b(b(x1)))
        
        b(c(a(x1))) = 16 >= 16 = c(a(b(x1)))
       problem:
        DPs:
         a#(a(b(x1))) -> a#(b(c(a(x1))))
         a#(a(b(x1))) -> b#(a(b(c(a(x1)))))
         b#(a(x1)) -> a#(b(b(x1)))
        TRS:
         a(a(b(x1))) -> b(a(b(c(a(x1)))))
         b(a(x1)) -> a(b(b(x1)))
         b(c(a(x1))) -> c(a(b(x1)))
       EDG Processor:
        DPs:
         a#(a(b(x1))) -> a#(b(c(a(x1))))
         a#(a(b(x1))) -> b#(a(b(c(a(x1)))))
         b#(a(x1)) -> a#(b(b(x1)))
        TRS:
         a(a(b(x1))) -> b(a(b(c(a(x1)))))
         b(a(x1)) -> a(b(b(x1)))
         b(c(a(x1))) -> c(a(b(x1)))
        graph:
         b#(a(x1)) -> a#(b(b(x1))) -> a#(a(b(x1))) -> a#(b(c(a(x1))))
         b#(a(x1)) -> a#(b(b(x1))) ->
         a#(a(b(x1))) -> b#(a(b(c(a(x1)))))
         a#(a(b(x1))) -> b#(a(b(c(a(x1))))) ->
         b#(a(x1)) -> a#(b(b(x1)))
         a#(a(b(x1))) -> a#(b(c(a(x1)))) ->
         a#(a(b(x1))) -> a#(b(c(a(x1))))
         a#(a(b(x1))) -> a#(b(c(a(x1)))) -> a#(a(b(x1))) -> b#(a(b(c(a(x1)))))
        Arctic Interpretation Processor:
         dimension: 1
         interpretation:
          [b#](x0) = x0 + 13,
          
          [a#](x0) = 4x0 + 0,
          
          [c](x0) = 10,
          
          [a](x0) = 6x0 + 12,
          
          [b](x0) = x0
         orientation:
          a#(a(b(x1))) = 10x1 + 16 >= 14 = a#(b(c(a(x1))))
          
          a#(a(b(x1))) = 10x1 + 16 >= 16 = b#(a(b(c(a(x1)))))
          
          b#(a(x1)) = 6x1 + 13 >= 4x1 + 0 = a#(b(b(x1)))
          
          a(a(b(x1))) = 12x1 + 18 >= 16 = b(a(b(c(a(x1)))))
          
          b(a(x1)) = 6x1 + 12 >= 6x1 + 12 = a(b(b(x1)))
          
          b(c(a(x1))) = 10 >= 10 = c(a(b(x1)))
         problem:
          DPs:
           a#(a(b(x1))) -> b#(a(b(c(a(x1)))))
          TRS:
           a(a(b(x1))) -> b(a(b(c(a(x1)))))
           b(a(x1)) -> a(b(b(x1)))
           b(c(a(x1))) -> c(a(b(x1)))
         EDG Processor:
          DPs:
           a#(a(b(x1))) -> b#(a(b(c(a(x1)))))
          TRS:
           a(a(b(x1))) -> b(a(b(c(a(x1)))))
           b(a(x1)) -> a(b(b(x1)))
           b(c(a(x1))) -> c(a(b(x1)))
          graph:
           
          Qed