YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(x1)) -> 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))))
   a(b(x1)) -> x1
   c(b(x1)) -> a(c(x1))
  TDG Processor:
   DPs:
    a#(a(x1)) -> 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))))
    a(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)) -> a#(b(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)) -> c#(x1)
   EDG Processor:
    DPs:
     a#(a(x1)) -> 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))))
     a(b(x1)) -> x1
     c(b(x1)) -> a(c(x1))
    graph:
     c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
     c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1))
     c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(x1)
     c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(b(c(x1))))
     a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
     a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1))
    SCC Processor:
     #sccs: 1
     #rules: 3
     #arcs: 6/16
     DPs:
      c#(b(x1)) -> c#(x1)
      c#(b(x1)) -> a#(c(x1))
      a#(a(x1)) -> c#(x1)
     TRS:
      a(a(x1)) -> a(b(b(c(x1))))
      a(b(x1)) -> x1
      c(b(x1)) -> a(c(x1))
     Arctic Interpretation Processor:
      dimension: 3
      usable rules:
       a(a(x1)) -> a(b(b(c(x1))))
       a(b(x1)) -> x1
       c(b(x1)) -> a(c(x1))
      interpretation:
       [c#](x0) = [-& -& 0 ]x0 + [0],
       
                 [0  0  0 ]     [0]
       [c](x0) = [-& -& 0 ]x0 + [0]
                 [-& 0  -&]     [0],
       
       [a#](x0) = [-& 0  0 ]x0 + [0],
       
                 [0  0  1 ]     [-&]
       [a](x0) = [0  -& 0 ]x0 + [0 ]
                 [0  0  1 ]     [1 ],
       
                 [0 0 0]     [0 ]
       [b](x0) = [0 1 0]x0 + [1 ]
                 [0 0 0]     [-&]
      orientation:
       c#(b(x1)) = [0 0 0]x1 + [0] >= [-& -& 0 ]x1 + [0] = c#(x1)
       
       c#(b(x1)) = [0 0 0]x1 + [0] >= [-& 0  0 ]x1 + [0] = a#(c(x1))
       
       a#(a(x1)) = [0 0 1]x1 + [1] >= [-& -& 0 ]x1 + [0] = c#(x1)
       
                  [1 1 2]     [2]    [1 1 2]     [2]                 
       a(a(x1)) = [0 0 1]x1 + [1] >= [0 0 1]x1 + [1] = a(b(b(c(x1))))
                  [1 1 2]     [2]    [1 1 2]     [2]                 
       
                  [1 1 1]     [1]           
       a(b(x1)) = [0 0 0]x1 + [0] >= x1 = x1
                  [1 1 1]     [1]           
       
                  [0 1 0]     [1]    [0 1 0]     [1]           
       c(b(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = a(c(x1))
                  [0 1 0]     [1]    [0 1 0]     [1]           
      problem:
       DPs:
        c#(b(x1)) -> c#(x1)
        c#(b(x1)) -> a#(c(x1))
       TRS:
        a(a(x1)) -> a(b(b(c(x1))))
        a(b(x1)) -> x1
        c(b(x1)) -> a(c(x1))
      Restore Modifier:
       DPs:
        c#(b(x1)) -> c#(x1)
        c#(b(x1)) -> a#(c(x1))
       TRS:
        a(a(x1)) -> a(b(b(c(x1))))
        a(b(x1)) -> x1
        c(b(x1)) -> a(c(x1))
       EDG Processor:
        DPs:
         c#(b(x1)) -> c#(x1)
         c#(b(x1)) -> a#(c(x1))
        TRS:
         a(a(x1)) -> a(b(b(c(x1))))
         a(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)
        SCC Processor:
         #sccs: 1
         #rules: 1
         #arcs: 2/4
         DPs:
          c#(b(x1)) -> c#(x1)
         TRS:
          a(a(x1)) -> a(b(b(c(x1))))
          a(b(x1)) -> x1
          c(b(x1)) -> a(c(x1))
         Usable Rule Processor:
          DPs:
           c#(b(x1)) -> c#(x1)
          TRS:
           
          Arctic Interpretation Processor:
           dimension: 1
           usable rules:
            
           interpretation:
            [c#](x0) = x0,
            
            [b](x0) = 15x0 + 15
           orientation:
            c#(b(x1)) = 15x1 + 15 >= x1 = c#(x1)
           problem:
            DPs:
             
            TRS:
             
           Qed