YES

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

Proof:
 String Reversal Processor:
  c(b(a(x1))) -> b(x1)
  b(b(c(x1))) -> a(x1)
  c(x1) -> b(x1)
  a(a(x1)) -> c(a(b(c(x1))))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [b](x0) = x0 + 3,
    
    [c](x0) = x0 + 3,
    
    [a](x0) = x0 + 9
   orientation:
    c(b(a(x1))) = x1 + 15 >= x1 + 3 = b(x1)
    
    b(b(c(x1))) = x1 + 9 >= x1 + 9 = a(x1)
    
    c(x1) = x1 + 3 >= x1 + 3 = b(x1)
    
    a(a(x1)) = x1 + 18 >= x1 + 18 = c(a(b(c(x1))))
   problem:
    b(b(c(x1))) -> a(x1)
    c(x1) -> b(x1)
    a(a(x1)) -> c(a(b(c(x1))))
   String Reversal Processor:
    c(b(b(x1))) -> a(x1)
    c(x1) -> b(x1)
    a(a(x1)) -> c(b(a(c(x1))))
    DP Processor:
     DPs:
      c#(b(b(x1))) -> a#(x1)
      a#(a(x1)) -> c#(x1)
      a#(a(x1)) -> a#(c(x1))
      a#(a(x1)) -> c#(b(a(c(x1))))
     TRS:
      c(b(b(x1))) -> a(x1)
      c(x1) -> b(x1)
      a(a(x1)) -> c(b(a(c(x1))))
     TDG Processor:
      DPs:
       c#(b(b(x1))) -> a#(x1)
       a#(a(x1)) -> c#(x1)
       a#(a(x1)) -> a#(c(x1))
       a#(a(x1)) -> c#(b(a(c(x1))))
      TRS:
       c(b(b(x1))) -> a(x1)
       c(x1) -> b(x1)
       a(a(x1)) -> c(b(a(c(x1))))
      graph:
       a#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(b(a(c(x1))))
       a#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(c(x1))
       a#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(x1)
       a#(a(x1)) -> c#(b(a(c(x1)))) -> c#(b(b(x1))) -> a#(x1)
       a#(a(x1)) -> c#(x1) -> c#(b(b(x1))) -> a#(x1)
       c#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> c#(b(a(c(x1))))
       c#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> a#(c(x1))
       c#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> c#(x1)
      Arctic Interpretation Processor:
       dimension: 1
       usable rules:
        c(b(b(x1))) -> a(x1)
        c(x1) -> b(x1)
        a(a(x1)) -> c(b(a(c(x1))))
       interpretation:
        [a#](x0) = 2x0,
        
        [b](x0) = 1x0,
        
        [c#](x0) = x0,
        
        [c](x0) = 1x0,
        
        [a](x0) = 3x0
       orientation:
        c#(b(b(x1))) = 2x1 >= 2x1 = a#(x1)
        
        a#(a(x1)) = 5x1 >= x1 = c#(x1)
        
        a#(a(x1)) = 5x1 >= 3x1 = a#(c(x1))
        
        a#(a(x1)) = 5x1 >= 5x1 = c#(b(a(c(x1))))
        
        c(b(b(x1))) = 3x1 >= 3x1 = a(x1)
        
        c(x1) = 1x1 >= 1x1 = b(x1)
        
        a(a(x1)) = 6x1 >= 6x1 = c(b(a(c(x1))))
       problem:
        DPs:
         c#(b(b(x1))) -> a#(x1)
         a#(a(x1)) -> c#(b(a(c(x1))))
        TRS:
         c(b(b(x1))) -> a(x1)
         c(x1) -> b(x1)
         a(a(x1)) -> c(b(a(c(x1))))
       Restore Modifier:
        DPs:
         c#(b(b(x1))) -> a#(x1)
         a#(a(x1)) -> c#(b(a(c(x1))))
        TRS:
         c(b(b(x1))) -> a(x1)
         c(x1) -> b(x1)
         a(a(x1)) -> c(b(a(c(x1))))
        EDG Processor:
         DPs:
          c#(b(b(x1))) -> a#(x1)
          a#(a(x1)) -> c#(b(a(c(x1))))
         TRS:
          c(b(b(x1))) -> a(x1)
          c(x1) -> b(x1)
          a(a(x1)) -> c(b(a(c(x1))))
         graph:
          a#(a(x1)) -> c#(b(a(c(x1)))) -> c#(b(b(x1))) -> a#(x1)
          c#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> c#(b(a(c(x1))))
         Matrix Interpretation Processor: dim=4
          
          interpretation:
           [a#](x0) = [0 0 0 1]x0,
           
                     [0 0 0 0]  
                     [0 0 1 0]  
           [b](x0) = [0 0 0 1]x0
                     [0 0 0 0]  ,
           
           [c#](x0) = [0 1 0 0]x0,
           
                     [0 1 0 0]     [0]
                     [0 1 1 0]     [0]
           [c](x0) = [0 0 0 1]x0 + [0]
                     [0 0 0 0]     [1],
           
                     [0 0 0 1]     [0]
                     [0 0 0 1]     [0]
           [a](x0) = [0 0 0 0]x0 + [0]
                     [0 0 0 0]     [1]
          orientation:
           c#(b(b(x1))) = [0 0 0 1]x1 >= [0 0 0 1]x1 = a#(x1)
           
           a#(a(x1)) = [1] >= [0] = c#(b(a(c(x1))))
           
                         [0 0 0 1]     [0]    [0 0 0 1]     [0]        
                         [0 0 0 1]     [0]    [0 0 0 1]     [0]        
           c(b(b(x1))) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = a(x1)
                         [0 0 0 0]     [1]    [0 0 0 0]     [1]        
           
                   [0 1 0 0]     [0]    [0 0 0 0]          
                   [0 1 1 0]     [0]    [0 0 1 0]          
           c(x1) = [0 0 0 1]x1 + [0] >= [0 0 0 1]x1 = b(x1)
                   [0 0 0 0]     [1]    [0 0 0 0]          
           
                      [1]    [0]                 
                      [1]    [1]                 
           a(a(x1)) = [0] >= [0] = c(b(a(c(x1))))
                      [1]    [1]                 
          problem:
           DPs:
            c#(b(b(x1))) -> a#(x1)
           TRS:
            c(b(b(x1))) -> a(x1)
            c(x1) -> b(x1)
            a(a(x1)) -> c(b(a(c(x1))))
          Restore Modifier:
           DPs:
            c#(b(b(x1))) -> a#(x1)
           TRS:
            c(b(b(x1))) -> a(x1)
            c(x1) -> b(x1)
            a(a(x1)) -> c(b(a(c(x1))))
           EDG Processor:
            DPs:
             c#(b(b(x1))) -> a#(x1)
            TRS:
             c(b(b(x1))) -> a(x1)
             c(x1) -> b(x1)
             a(a(x1)) -> c(b(a(c(x1))))
            graph:
             
            SCC Processor:
             #sccs: 0
             #rules: 0
             #arcs: 0/1