YES

Problem:
 a(a(x1)) -> a(b(b(c(x1))))
 b(c(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)) -> b#(b(c(x1)))
   a#(a(x1)) -> a#(b(b(c(x1))))
   c#(b(x1)) -> c#(x1)
   c#(b(x1)) -> a#(c(x1))
  TRS:
   a(a(x1)) -> a(b(b(c(x1))))
   b(c(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)) -> b#(b(c(x1)))
    a#(a(x1)) -> a#(b(b(c(x1))))
    c#(b(x1)) -> c#(x1)
    c#(b(x1)) -> a#(c(x1))
   TRS:
    a(a(x1)) -> a(b(b(c(x1))))
    b(c(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)) -> a#(b(b(c(x1))))
    c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(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(b(c(x1)))) -> a#(a(x1)) -> a#(b(b(c(x1))))
    a#(a(x1)) -> a#(b(b(c(x1)))) -> a#(a(x1)) -> b#(b(c(x1)))
    a#(a(x1)) -> a#(b(b(c(x1)))) -> a#(a(x1)) -> b#(c(x1))
    a#(a(x1)) -> a#(b(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(b(c(x1))))
    TRS:
     a(a(x1)) -> a(b(b(c(x1))))
     b(c(x1)) -> x1
     c(b(x1)) -> a(c(x1))
    Arctic Interpretation Processor:
     dimension: 2
     usable rules:
      a(a(x1)) -> a(b(b(c(x1))))
      b(c(x1)) -> x1
      c(b(x1)) -> a(c(x1))
     interpretation:
      [c#](x0) = [2 0]x0 + [0],
      
                [-& 0 ]     [0 ]
      [c](x0) = [0  -&]x0 + [-&],
      
      [a#](x0) = [0  -&]x0 + [0],
      
                [2  0 ]     [2]
      [a](x0) = [0  -&]x0 + [0],
      
                [0 0]     [0]
      [b](x0) = [0 2]x0 + [2]
     orientation:
      c#(b(x1)) = [2 2]x1 + [2] >= [2 0]x1 + [0] = c#(x1)
      
      c#(b(x1)) = [2 2]x1 + [2] >= [-& 0 ]x1 + [0] = a#(c(x1))
      
      a#(a(x1)) = [2 0]x1 + [2] >= [2 0]x1 + [0] = c#(x1)
      
      a#(a(x1)) = [2 0]x1 + [2] >= [2 0]x1 + [2] = a#(b(b(c(x1))))
      
                 [4 2]     [4]    [4 2]     [4]                 
      a(a(x1)) = [2 0]x1 + [2] >= [2 0]x1 + [2] = a(b(b(c(x1))))
      
                 [0 0]     [0]           
      b(c(x1)) = [2 0]x1 + [2] >= x1 = x1
      
                 [0 2]     [2]    [0  2 ]     [2]           
      c(b(x1)) = [0 0]x1 + [0] >= [-& 0 ]x1 + [0] = a(c(x1))
     problem:
      DPs:
       c#(b(x1)) -> c#(x1)
       a#(a(x1)) -> c#(x1)
       a#(a(x1)) -> a#(b(b(c(x1))))
      TRS:
       a(a(x1)) -> a(b(b(c(x1))))
       b(c(x1)) -> x1
       c(b(x1)) -> a(c(x1))
     Restore Modifier:
      DPs:
       c#(b(x1)) -> c#(x1)
       a#(a(x1)) -> c#(x1)
       a#(a(x1)) -> a#(b(b(c(x1))))
      TRS:
       a(a(x1)) -> a(b(b(c(x1))))
       b(c(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(b(c(x1))))
       TRS:
        a(a(x1)) -> a(b(b(c(x1))))
        b(c(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(b(c(x1)))) -> a#(a(x1)) -> c#(x1)
        a#(a(x1)) -> a#(b(b(c(x1)))) -> a#(a(x1)) -> a#(b(b(c(x1))))
       SCC Processor:
        #sccs: 2
        #rules: 2
        #arcs: 4/9
        DPs:
         a#(a(x1)) -> a#(b(b(c(x1))))
        TRS:
         a(a(x1)) -> a(b(b(c(x1))))
         b(c(x1)) -> x1
         c(b(x1)) -> a(c(x1))
        Matrix Interpretation Processor: dim=1
         
         usable rules:
          a(a(x1)) -> a(b(b(c(x1))))
          b(c(x1)) -> x1
          c(b(x1)) -> a(c(x1))
         interpretation:
          [c](x0) = 2x0 + 1,
          
          [a#](x0) = x0 + 4,
          
          [a](x0) = 1/2x0 + 1/2,
          
          [b](x0) = 1/2x0
         orientation:
          a#(a(x1)) = 1/2x1 + 9/2 >= 1/2x1 + 17/4 = a#(b(b(c(x1))))
          
          a(a(x1)) = 1/4x1 + 3/4 >= 1/4x1 + 5/8 = a(b(b(c(x1))))
          
          b(c(x1)) = x1 + 1/2 >= x1 = x1
          
          c(b(x1)) = x1 + 1 >= x1 + 1 = a(c(x1))
         problem:
          DPs:
           
          TRS:
           a(a(x1)) -> a(b(b(c(x1))))
           b(c(x1)) -> x1
           c(b(x1)) -> a(c(x1))
         Qed
        
        DPs:
         c#(b(x1)) -> c#(x1)
        TRS:
         a(a(x1)) -> a(b(b(c(x1))))
         b(c(x1)) -> x1
         c(b(x1)) -> a(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