YES

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

Proof:
 DP Processor:
  DPs:
   a#(b(b(x1))) -> c#(x1)
   c#(c(x1)) -> a#(x1)
   c#(c(x1)) -> c#(a(x1))
   c#(c(x1)) -> a#(b(c(a(x1))))
  TRS:
   a(x1) -> b(x1)
   a(b(b(x1))) -> c(x1)
   c(c(x1)) -> a(b(c(a(x1))))
  TDG Processor:
   DPs:
    a#(b(b(x1))) -> c#(x1)
    c#(c(x1)) -> a#(x1)
    c#(c(x1)) -> c#(a(x1))
    c#(c(x1)) -> a#(b(c(a(x1))))
   TRS:
    a(x1) -> b(x1)
    a(b(b(x1))) -> c(x1)
    c(c(x1)) -> a(b(c(a(x1))))
   graph:
    c#(c(x1)) -> c#(a(x1)) -> c#(c(x1)) -> a#(b(c(a(x1))))
    c#(c(x1)) -> c#(a(x1)) -> c#(c(x1)) -> c#(a(x1))
    c#(c(x1)) -> c#(a(x1)) -> c#(c(x1)) -> a#(x1)
    c#(c(x1)) -> a#(b(c(a(x1)))) -> a#(b(b(x1))) -> c#(x1)
    c#(c(x1)) -> a#(x1) -> a#(b(b(x1))) -> c#(x1)
    a#(b(b(x1))) -> c#(x1) -> c#(c(x1)) -> a#(b(c(a(x1))))
    a#(b(b(x1))) -> c#(x1) -> c#(c(x1)) -> c#(a(x1))
    a#(b(b(x1))) -> c#(x1) -> c#(c(x1)) -> a#(x1)
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     a(x1) -> b(x1)
     a(b(b(x1))) -> c(x1)
     c(c(x1)) -> a(b(c(a(x1))))
    interpretation:
     [c#](x0) = 4x0,
     
     [b](x0) = 2x0,
     
     [a#](x0) = x0,
     
     [a](x0) = 2x0,
     
     [c](x0) = 6x0
    orientation:
     a#(b(b(x1))) = 4x1 >= 4x1 = c#(x1)
     
     c#(c(x1)) = 10x1 >= x1 = a#(x1)
     
     c#(c(x1)) = 10x1 >= 6x1 = c#(a(x1))
     
     c#(c(x1)) = 10x1 >= 10x1 = a#(b(c(a(x1))))
     
     a(x1) = 2x1 >= 2x1 = b(x1)
     
     a(b(b(x1))) = 6x1 >= 6x1 = c(x1)
     
     c(c(x1)) = 12x1 >= 12x1 = a(b(c(a(x1))))
    problem:
     DPs:
      a#(b(b(x1))) -> c#(x1)
      c#(c(x1)) -> a#(b(c(a(x1))))
     TRS:
      a(x1) -> b(x1)
      a(b(b(x1))) -> c(x1)
      c(c(x1)) -> a(b(c(a(x1))))
    Restore Modifier:
     DPs:
      a#(b(b(x1))) -> c#(x1)
      c#(c(x1)) -> a#(b(c(a(x1))))
     TRS:
      a(x1) -> b(x1)
      a(b(b(x1))) -> c(x1)
      c(c(x1)) -> a(b(c(a(x1))))
     EDG Processor:
      DPs:
       a#(b(b(x1))) -> c#(x1)
       c#(c(x1)) -> a#(b(c(a(x1))))
      TRS:
       a(x1) -> b(x1)
       a(b(b(x1))) -> c(x1)
       c(c(x1)) -> a(b(c(a(x1))))
      graph:
       c#(c(x1)) -> a#(b(c(a(x1)))) -> a#(b(b(x1))) -> c#(x1)
       a#(b(b(x1))) -> c#(x1) -> c#(c(x1)) -> a#(b(c(a(x1))))
      Matrix Interpretation Processor: dim=4
       
       interpretation:
        [c#](x0) = [1 0 0 0]x0,
        
                  [0 0 0 0]     [0]
                  [0 0 0 1]     [0]
        [b](x0) = [0 0 0 0]x0 + [1]
                  [1 0 0 0]     [0],
        
        [a#](x0) = [0 1 1 0]x0,
        
                  [0 0 1 0]     [0]
                  [0 1 0 1]     [0]
        [a](x0) = [0 1 0 0]x0 + [1]
                  [1 0 0 0]     [0],
        
                  [0 0 0 0]     [1]
                  [1 0 0 0]     [0]
        [c](x0) = [1 0 0 0]x0 + [0]
                  [0 0 0 0]     [0]
       orientation:
        a#(b(b(x1))) = [1 0 0 0]x1 + [1] >= [1 0 0 0]x1 = c#(x1)
        
        c#(c(x1)) = [1] >= [1] = a#(b(c(a(x1))))
        
                [0 0 1 0]     [0]    [0 0 0 0]     [0]        
                [0 1 0 1]     [0]    [0 0 0 1]     [0]        
        a(x1) = [0 1 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = b(x1)
                [1 0 0 0]     [0]    [1 0 0 0]     [0]        
        
                      [0 0 0 0]     [1]    [0 0 0 0]     [1]        
                      [1 0 0 0]     [0]    [1 0 0 0]     [0]        
        a(b(b(x1))) = [1 0 0 0]x1 + [1] >= [1 0 0 0]x1 + [0] = c(x1)
                      [0 0 0 0]     [0]    [0 0 0 0]     [0]        
        
                   [1]    [1]                 
                   [1]    [1]                 
        c(c(x1)) = [1] >= [1] = a(b(c(a(x1))))
                   [0]    [0]                 
       problem:
        DPs:
         c#(c(x1)) -> a#(b(c(a(x1))))
        TRS:
         a(x1) -> b(x1)
         a(b(b(x1))) -> c(x1)
         c(c(x1)) -> a(b(c(a(x1))))
       Restore Modifier:
        DPs:
         c#(c(x1)) -> a#(b(c(a(x1))))
        TRS:
         a(x1) -> b(x1)
         a(b(b(x1))) -> c(x1)
         c(c(x1)) -> a(b(c(a(x1))))
        EDG Processor:
         DPs:
          c#(c(x1)) -> a#(b(c(a(x1))))
         TRS:
          a(x1) -> b(x1)
          a(b(b(x1))) -> c(x1)
          c(c(x1)) -> a(b(c(a(x1))))
         graph:
          
         SCC Processor:
          #sccs: 0
          #rules: 0
          #arcs: 0/1