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
     interpretation:
      [c#](x0) = [1 1]x0 + [0],
      
      [a#](x0) = [0 0]x0 + [0],
      
                [1 0]     [0 ]
      [b](x0) = [0 0]x0 + [-&],
      
                [0  -&]  
      [c](x0) = [0  -&]x0,
      
                [0 1]     [0]
      [a](x0) = [1 1]x0 + [0]
     orientation:
      c#(b(x1)) = [2 1]x1 + [1] >= [1 1]x1 + [0] = c#(x1)
      
      c#(b(x1)) = [2 1]x1 + [1] >= [0  -&]x1 + [0] = a#(c(x1))
      
      a#(a(x1)) = [1 1]x1 + [0] >= [1 1]x1 + [0] = c#(x1)
      
      a#(a(x1)) = [1 1]x1 + [0] >= [1  -&]x1 + [0] = a#(b(c(x1)))
      
              [0 1]     [0]           
      a(x1) = [1 1]x1 + [0] >= x1 = x1
      
                 [2 2]     [1]    [2  -&]     [1]                 
      a(a(x1)) = [2 2]x1 + [1] >= [2  -&]x1 + [1] = b(a(b(c(x1))))
      
              [1 0]     [0 ]           
      b(x1) = [0 0]x1 + [-&] >= x1 = x1
      
                 [1 0]     [0]    [1  -&]     [0]           
      c(b(x1)) = [1 0]x1 + [0] >= [1  -&]x1 + [0] = a(c(x1))
     problem:
      DPs:
       c#(b(x1)) -> 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))
     EDG Processor:
      DPs:
       c#(b(x1)) -> 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))
      graph:
       c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
       a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
       a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> c#(x1)
       a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> a#(b(c(x1)))
      CDG Processor:
       DPs:
        c#(b(x1)) -> 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))
       graph:
        a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> a#(b(c(x1)))
        a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> c#(x1)
       SCC Processor:
        #sccs: 1
        #rules: 1
        #arcs: 2/9
        DPs:
         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
         interpretation:
          [a#](x0) = [-& 0 ]x0 + [1],
          
                    [1 0]     [2]
          [b](x0) = [0 0]x0 + [0],
          
                    [0  -&]     [0]
          [c](x0) = [0  -&]x0 + [0],
          
                    [0 1]     [0]
          [a](x0) = [1 1]x0 + [2]
         orientation:
          a#(a(x1)) = [1 1]x1 + [2] >= [0  -&]x1 + [1] = a#(b(c(x1)))
          
                  [0 1]     [0]           
          a(x1) = [1 1]x1 + [2] >= x1 = x1
          
                     [2 2]     [3]    [2  -&]     [3]                 
          a(a(x1)) = [2 2]x1 + [3] >= [2  -&]x1 + [3] = b(a(b(c(x1))))
          
                  [1 0]     [2]           
          b(x1) = [0 0]x1 + [0] >= x1 = x1
          
                     [1 0]     [2]    [1  -&]     [1]           
          c(b(x1)) = [1 0]x1 + [2] >= [1  -&]x1 + [2] = a(c(x1))
         problem:
          DPs:
           
          TRS:
           a(x1) -> x1
           a(a(x1)) -> b(a(b(c(x1))))
           b(x1) -> x1
           c(b(x1)) -> a(c(x1))
         Qed