YES

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

Proof:
 String Reversal Processor:
  b(a(x1)) -> x1
  c(b(x1)) -> a(a(x1))
  a(c(x1)) -> c(c(b(b(x1))))
  DP Processor:
   DPs:
    c#(b(x1)) -> a#(x1)
    c#(b(x1)) -> a#(a(x1))
    a#(c(x1)) -> b#(x1)
    a#(c(x1)) -> b#(b(x1))
    a#(c(x1)) -> c#(b(b(x1)))
    a#(c(x1)) -> c#(c(b(b(x1))))
   TRS:
    b(a(x1)) -> x1
    c(b(x1)) -> a(a(x1))
    a(c(x1)) -> c(c(b(b(x1))))
   TDG Processor:
    DPs:
     c#(b(x1)) -> a#(x1)
     c#(b(x1)) -> a#(a(x1))
     a#(c(x1)) -> b#(x1)
     a#(c(x1)) -> b#(b(x1))
     a#(c(x1)) -> c#(b(b(x1)))
     a#(c(x1)) -> c#(c(b(b(x1))))
    TRS:
     b(a(x1)) -> x1
     c(b(x1)) -> a(a(x1))
     a(c(x1)) -> c(c(b(b(x1))))
    graph:
     a#(c(x1)) -> c#(c(b(b(x1)))) -> c#(b(x1)) -> a#(a(x1))
     a#(c(x1)) -> c#(c(b(b(x1)))) -> c#(b(x1)) -> a#(x1)
     a#(c(x1)) -> c#(b(b(x1))) -> c#(b(x1)) -> a#(a(x1))
     a#(c(x1)) -> c#(b(b(x1))) -> c#(b(x1)) -> a#(x1)
     c#(b(x1)) -> a#(a(x1)) -> a#(c(x1)) -> c#(c(b(b(x1))))
     c#(b(x1)) -> a#(a(x1)) -> a#(c(x1)) -> c#(b(b(x1)))
     c#(b(x1)) -> a#(a(x1)) -> a#(c(x1)) -> b#(b(x1))
     c#(b(x1)) -> a#(a(x1)) -> a#(c(x1)) -> b#(x1)
     c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> c#(c(b(b(x1))))
     c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> c#(b(b(x1)))
     c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> b#(b(x1))
     c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> b#(x1)
    EDG Processor:
     DPs:
      c#(b(x1)) -> a#(x1)
      c#(b(x1)) -> a#(a(x1))
      a#(c(x1)) -> b#(x1)
      a#(c(x1)) -> b#(b(x1))
      a#(c(x1)) -> c#(b(b(x1)))
      a#(c(x1)) -> c#(c(b(b(x1))))
     TRS:
      b(a(x1)) -> x1
      c(b(x1)) -> a(a(x1))
      a(c(x1)) -> c(c(b(b(x1))))
     graph:
      a#(c(x1)) -> c#(b(b(x1))) -> c#(b(x1)) -> a#(x1)
      a#(c(x1)) -> c#(b(b(x1))) -> c#(b(x1)) -> a#(a(x1))
      c#(b(x1)) -> a#(a(x1)) -> a#(c(x1)) -> b#(x1)
      c#(b(x1)) -> a#(a(x1)) -> a#(c(x1)) -> b#(b(x1))
      c#(b(x1)) -> a#(a(x1)) -> a#(c(x1)) -> c#(b(b(x1)))
      c#(b(x1)) -> a#(a(x1)) -> a#(c(x1)) -> c#(c(b(b(x1))))
      c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> b#(x1)
      c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> b#(b(x1))
      c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> c#(b(b(x1)))
      c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> c#(c(b(b(x1))))
     SCC Processor:
      #sccs: 1
      #rules: 3
      #arcs: 10/36
      DPs:
       a#(c(x1)) -> c#(b(b(x1)))
       c#(b(x1)) -> a#(a(x1))
       c#(b(x1)) -> a#(x1)
      TRS:
       b(a(x1)) -> x1
       c(b(x1)) -> a(a(x1))
       a(c(x1)) -> c(c(b(b(x1))))
      Arctic Interpretation Processor:
       dimension: 2
       usable rules:
        b(a(x1)) -> x1
        c(b(x1)) -> a(a(x1))
        a(c(x1)) -> c(c(b(b(x1))))
       interpretation:
        [c#](x0) = [2 3]x0 + [0],
        
                  [1 0]     [-&]
        [a](x0) = [0 0]x0 + [0 ],
        
        [a#](x0) = [2 0]x0,
        
                  [-& 0 ]     [0 ]
        [b](x0) = [0  -&]x0 + [-&],
        
                  [1 2]     [2 ]
        [c](x0) = [0 1]x0 + [-&]
       orientation:
        a#(c(x1)) = [3 4]x1 + [4] >= [2 3]x1 + [3] = c#(b(b(x1)))
        
        c#(b(x1)) = [3 2]x1 + [2] >= [3 2]x1 + [0] = a#(a(x1))
        
        c#(b(x1)) = [3 2]x1 + [2] >= [2 0]x1 = a#(x1)
        
                   [0 0]     [0 ]           
        b(a(x1)) = [1 0]x1 + [-&] >= x1 = x1
        
                   [2 1]     [2]    [2 1]     [0]           
        c(b(x1)) = [1 0]x1 + [0] >= [1 0]x1 + [0] = a(a(x1))
        
                   [2 3]     [3]    [2 3]     [3]                 
        a(c(x1)) = [1 2]x1 + [2] >= [1 2]x1 + [2] = c(c(b(b(x1))))
       problem:
        DPs:
         c#(b(x1)) -> a#(a(x1))
        TRS:
         b(a(x1)) -> x1
         c(b(x1)) -> a(a(x1))
         a(c(x1)) -> c(c(b(b(x1))))
       Restore Modifier:
        DPs:
         c#(b(x1)) -> a#(a(x1))
        TRS:
         b(a(x1)) -> x1
         c(b(x1)) -> a(a(x1))
         a(c(x1)) -> c(c(b(b(x1))))
        EDG Processor:
         DPs:
          c#(b(x1)) -> a#(a(x1))
         TRS:
          b(a(x1)) -> x1
          c(b(x1)) -> a(a(x1))
          a(c(x1)) -> c(c(b(b(x1))))
         graph:
          
         SCC Processor:
          #sccs: 0
          #rules: 0
          #arcs: 0/1