YES

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

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