YES

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

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