YES

Problem:
 a(a(x1)) -> a(b(b(c(x1))))
 c(a(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))))
   c(a(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))))
    c(a(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))))
     c(a(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))))
      c(a(x1)) -> x1
      c(b(x1)) -> a(c(x1))
     Arctic Interpretation Processor:
      dimension: 2
      interpretation:
       [c#](x0) = [3 0]x0,
       
       [a#](x0) = [-& 3 ]x0 + [0],
       
                 [1  0 ]     [1]
       [b](x0) = [0  -&]x0 + [1],
       
                 [-& 0 ]     [0 ]
       [c](x0) = [0  -&]x0 + [-&],
       
                 [-& 0 ]     [1]
       [a](x0) = [0  1 ]x0 + [1]
      orientation:
       c#(b(x1)) = [4 3]x1 + [4] >= [3 0]x1 = c#(x1)
       
       c#(b(x1)) = [4 3]x1 + [4] >= [3  -&]x1 + [0] = a#(c(x1))
       
       a#(a(x1)) = [3 4]x1 + [4] >= [3 0]x1 = c#(x1)
       
                  [0 1]     [1]    [0 1]     [1]                 
       a(a(x1)) = [1 2]x1 + [2] >= [1 2]x1 + [2] = a(b(b(c(x1))))
       
                  [0  1 ]     [1]           
       c(a(x1)) = [-& 0 ]x1 + [1] >= x1 = x1
       
                  [0  -&]     [1]    [0  -&]     [1]           
       c(b(x1)) = [1  0 ]x1 + [1] >= [1  0 ]x1 + [1] = a(c(x1))
      problem:
       DPs:
        a#(a(x1)) -> c#(x1)
       TRS:
        a(a(x1)) -> a(b(b(c(x1))))
        c(a(x1)) -> x1
        c(b(x1)) -> a(c(x1))
      EDG Processor:
       DPs:
        a#(a(x1)) -> c#(x1)
       TRS:
        a(a(x1)) -> a(b(b(c(x1))))
        c(a(x1)) -> x1
        c(b(x1)) -> a(c(x1))
       graph:
        
       Qed