YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(x1)) -> c#(x1)
   a#(a(x1)) -> b#(c(x1))
   a#(a(x1)) -> a#(b(c(x1)))
   a#(a(x1)) -> b#(a(b(c(x1))))
   c#(b(x1)) -> c#(x1)
   c#(b(x1)) -> a#(c(x1))
  TRS:
   a(x1) -> x1
   a(a(x1)) -> b(a(b(c(x1))))
   b(x1) -> x1
   c(b(x1)) -> a(c(x1))
  TDG Processor:
   DPs:
    a#(a(x1)) -> c#(x1)
    a#(a(x1)) -> b#(c(x1))
    a#(a(x1)) -> a#(b(c(x1)))
    a#(a(x1)) -> b#(a(b(c(x1))))
    c#(b(x1)) -> c#(x1)
    c#(b(x1)) -> a#(c(x1))
   TRS:
    a(x1) -> x1
    a(a(x1)) -> b(a(b(c(x1))))
    b(x1) -> x1
    c(b(x1)) -> a(c(x1))
   graph:
    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1))
    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
    c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(a(b(c(x1))))
    c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(c(x1)))
    c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(c(x1))
    c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(x1)
    a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1))
    a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
    a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(a(b(c(x1))))
    a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> a#(b(c(x1)))
    a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(c(x1))
    a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> c#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 4
    #arcs: 12/36
    DPs:
     c#(b(x1)) -> c#(x1)
     c#(b(x1)) -> a#(c(x1))
     a#(a(x1)) -> c#(x1)
     a#(a(x1)) -> a#(b(c(x1)))
    TRS:
     a(x1) -> x1
     a(a(x1)) -> b(a(b(c(x1))))
     b(x1) -> x1
     c(b(x1)) -> a(c(x1))
    Arctic Interpretation Processor:
     dimension: 2
     usable rules:
      a(x1) -> x1
      a(a(x1)) -> b(a(b(c(x1))))
      b(x1) -> x1
      c(b(x1)) -> a(c(x1))
     interpretation:
      [c#](x0) = [1 0]x0 + [0],
      
                [0  -&]     [0]
      [c](x0) = [1  -&]x0 + [1],
      
      [a#](x0) = [0 0]x0 + [0],
      
                [0 0]     [0]
      [a](x0) = [2 1]x0 + [2],
      
                [1  -&]     [1]
      [b](x0) = [0  0 ]x0 + [0]
     orientation:
      c#(b(x1)) = [2 0]x1 + [2] >= [1 0]x1 + [0] = c#(x1)
      
      c#(b(x1)) = [2 0]x1 + [2] >= [1  -&]x1 + [1] = a#(c(x1))
      
      a#(a(x1)) = [2 1]x1 + [2] >= [1 0]x1 + [0] = c#(x1)
      
      a#(a(x1)) = [2 1]x1 + [2] >= [1  -&]x1 + [1] = a#(b(c(x1)))
      
              [0 0]     [0]           
      a(x1) = [2 1]x1 + [2] >= x1 = x1
      
                 [2 1]     [2]    [2  -&]     [2]                 
      a(a(x1)) = [3 2]x1 + [3] >= [3  -&]x1 + [3] = b(a(b(c(x1))))
      
              [1  -&]     [1]           
      b(x1) = [0  0 ]x1 + [0] >= x1 = x1
      
                 [1  -&]     [1]    [1  -&]     [1]           
      c(b(x1)) = [2  -&]x1 + [2] >= [2  -&]x1 + [2] = a(c(x1))
     problem:
      DPs:
       c#(b(x1)) -> c#(x1)
      TRS:
       a(x1) -> x1
       a(a(x1)) -> b(a(b(c(x1))))
       b(x1) -> x1
       c(b(x1)) -> a(c(x1))
     Restore Modifier:
      DPs:
       c#(b(x1)) -> c#(x1)
      TRS:
       a(x1) -> x1
       a(a(x1)) -> b(a(b(c(x1))))
       b(x1) -> x1
       c(b(x1)) -> a(c(x1))
      EDG Processor:
       DPs:
        c#(b(x1)) -> c#(x1)
       TRS:
        a(x1) -> x1
        a(a(x1)) -> b(a(b(c(x1))))
        b(x1) -> x1
        c(b(x1)) -> a(c(x1))
       graph:
        c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
       Usable Rule Processor:
        DPs:
         c#(b(x1)) -> c#(x1)
        TRS:
         
        Arctic Interpretation Processor:
         dimension: 4
         usable rules:
          
         interpretation:
          [c#](x0) = [0  -& -& -&]x0,
          
                    [1 0 0 0]     [0]
                    [0 0 0 0]     [0]
          [b](x0) = [1 0 0 0]x0 + [0]
                    [0 0 0 0]     [0]
         orientation:
          c#(b(x1)) = [1 0 0 0]x1 + [0] >= [0  -& -& -&]x1 = c#(x1)
         problem:
          DPs:
           
          TRS:
           
         Qed