YES

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

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