YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(x1)) -> c#(x1)
   a#(a(x1)) -> c#(c(x1))
   a#(a(x1)) -> a#(c(c(x1)))
   a#(a(x1)) -> a#(b(a(c(c(x1)))))
   c#(b(x1)) -> a#(x1)
  TRS:
   a(a(x1)) -> a(b(a(c(c(x1)))))
   c(a(x1)) -> x1
   c(b(x1)) -> a(x1)
  TDG Processor:
   DPs:
    a#(a(x1)) -> c#(x1)
    a#(a(x1)) -> c#(c(x1))
    a#(a(x1)) -> a#(c(c(x1)))
    a#(a(x1)) -> a#(b(a(c(c(x1)))))
    c#(b(x1)) -> a#(x1)
   TRS:
    a(a(x1)) -> a(b(a(c(c(x1)))))
    c(a(x1)) -> x1
    c(b(x1)) -> a(x1)
   graph:
    c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(a(c(c(x1)))))
    c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(c(c(x1)))
    c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(c(x1))
    c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(x1)
    a#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(x1)
    a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(x1)
    a#(a(x1)) -> a#(b(a(c(c(x1))))) ->
    a#(a(x1)) -> a#(b(a(c(c(x1)))))
    a#(a(x1)) -> a#(b(a(c(c(x1))))) -> a#(a(x1)) -> a#(c(c(x1)))
    a#(a(x1)) -> a#(b(a(c(c(x1))))) -> a#(a(x1)) -> c#(c(x1))
    a#(a(x1)) -> a#(b(a(c(c(x1))))) -> a#(a(x1)) -> c#(x1)
    a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> a#(b(a(c(c(x1)))))
    a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> a#(c(c(x1)))
    a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> c#(c(x1))
    a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> c#(x1)
   EDG Processor:
    DPs:
     a#(a(x1)) -> c#(x1)
     a#(a(x1)) -> c#(c(x1))
     a#(a(x1)) -> a#(c(c(x1)))
     a#(a(x1)) -> a#(b(a(c(c(x1)))))
     c#(b(x1)) -> a#(x1)
    TRS:
     a(a(x1)) -> a(b(a(c(c(x1)))))
     c(a(x1)) -> x1
     c(b(x1)) -> a(x1)
    graph:
     c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(x1)
     c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(c(x1))
     c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(c(c(x1)))
     c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(a(c(c(x1)))))
     a#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(x1)
     a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(x1)
     a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> c#(x1)
     a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> c#(c(x1))
     a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> a#(c(c(x1)))
     a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> a#(b(a(c(c(x1)))))
    SCC Processor:
     #sccs: 1
     #rules: 4
     #arcs: 10/25
     DPs:
      c#(b(x1)) -> a#(x1)
      a#(a(x1)) -> a#(c(c(x1)))
      a#(a(x1)) -> c#(c(x1))
      a#(a(x1)) -> c#(x1)
     TRS:
      a(a(x1)) -> a(b(a(c(c(x1)))))
      c(a(x1)) -> x1
      c(b(x1)) -> a(x1)
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       a(a(x1)) -> a(b(a(c(c(x1)))))
       c(a(x1)) -> x1
       c(b(x1)) -> a(x1)
      interpretation:
       [c#](x0) = [0 1]x0 + [0],
       
                 [-& 0 ]     [0]
       [c](x0) = [0  -&]x0 + [0],
       
       [a#](x0) = [0 1]x0,
       
                 [-& 0 ]     [0]
       [a](x0) = [0  1 ]x0 + [1],
       
                 [0 1]     [2]
       [b](x0) = [0 0]x0 + [0]
      orientation:
       c#(b(x1)) = [1 1]x1 + [2] >= [0 1]x1 = a#(x1)
       
       a#(a(x1)) = [1 2]x1 + [2] >= [0 1]x1 + [1] = a#(c(c(x1)))
       
       a#(a(x1)) = [1 2]x1 + [2] >= [1 0]x1 + [1] = c#(c(x1))
       
       a#(a(x1)) = [1 2]x1 + [2] >= [0 1]x1 + [0] = c#(x1)
       
                  [0 1]     [1]    [0 1]     [1]                    
       a(a(x1)) = [1 2]x1 + [2] >= [1 2]x1 + [2] = a(b(a(c(c(x1)))))
       
                  [0  1 ]     [1]           
       c(a(x1)) = [-& 0 ]x1 + [0] >= x1 = x1
       
                  [0 0]     [0]    [-& 0 ]     [0]        
       c(b(x1)) = [0 1]x1 + [2] >= [0  1 ]x1 + [1] = a(x1)
      problem:
       DPs:
        c#(b(x1)) -> a#(x1)
        a#(a(x1)) -> c#(c(x1))
       TRS:
        a(a(x1)) -> a(b(a(c(c(x1)))))
        c(a(x1)) -> x1
        c(b(x1)) -> a(x1)
      Restore Modifier:
       DPs:
        c#(b(x1)) -> a#(x1)
        a#(a(x1)) -> c#(c(x1))
       TRS:
        a(a(x1)) -> a(b(a(c(c(x1)))))
        c(a(x1)) -> x1
        c(b(x1)) -> a(x1)
       EDG Processor:
        DPs:
         c#(b(x1)) -> a#(x1)
         a#(a(x1)) -> c#(c(x1))
        TRS:
         a(a(x1)) -> a(b(a(c(c(x1)))))
         c(a(x1)) -> x1
         c(b(x1)) -> a(x1)
        graph:
         c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(c(x1))
         a#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(x1)
        Bounds Processor:
         bound: 0
         enrichment: match-dp
         automaton:
          final states: {1}
          transitions:
           f50() -> 2*
           c{#,0}(7) -> 8*
           a{#,0}(2) -> 1*
           c0(20) -> 21*
           c0(27) -> 28*
           c0(6) -> 7*
           b0(22) -> 23*
           a0(23) -> 24*
           a0(21) -> 22*
           a0(11) -> 12*
           24 -> 7*
           7 -> 20*
           12 -> 21,7
           28 -> 20*
           11 -> 21*
           2 -> 11,7,6
           22 -> 12*
           21 -> 28,20,27
           8 -> 1*
           1 -> 8*
           23 -> 21*
         problem:
          DPs:
           a#(a(x1)) -> c#(c(x1))
          TRS:
           a(a(x1)) -> a(b(a(c(c(x1)))))
           c(a(x1)) -> x1
           c(b(x1)) -> a(x1)
         Restore Modifier:
          DPs:
           a#(a(x1)) -> c#(c(x1))
          TRS:
           a(a(x1)) -> a(b(a(c(c(x1)))))
           c(a(x1)) -> x1
           c(b(x1)) -> a(x1)
          EDG Processor:
           DPs:
            a#(a(x1)) -> c#(c(x1))
           TRS:
            a(a(x1)) -> a(b(a(c(c(x1)))))
            c(a(x1)) -> x1
            c(b(x1)) -> a(x1)
           graph:
            
           SCC Processor:
            #sccs: 0
            #rules: 0
            #arcs: 0/1