YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(x1)) -> c#(x1)
   a#(a(x1)) -> c#(c(x1))
   a#(a(x1)) -> a#(b(c(c(x1))))
   c#(b(x1)) -> a#(x1)
   c#(b(x1)) -> a#(a(x1))
  TRS:
   a(a(x1)) -> a(b(c(c(x1))))
   c(a(x1)) -> x1
   c(b(x1)) -> a(a(x1))
  TDG Processor:
   DPs:
    a#(a(x1)) -> c#(x1)
    a#(a(x1)) -> c#(c(x1))
    a#(a(x1)) -> a#(b(c(c(x1))))
    c#(b(x1)) -> a#(x1)
    c#(b(x1)) -> a#(a(x1))
   TRS:
    a(a(x1)) -> a(b(c(c(x1))))
    c(a(x1)) -> x1
    c(b(x1)) -> a(a(x1))
   graph:
    c#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> a#(b(c(c(x1))))
    c#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> c#(c(x1))
    c#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> c#(x1)
    c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(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#(a(x1))
    a#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(x1)
    a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(a(x1))
    a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(x1)
    a#(a(x1)) -> a#(b(c(c(x1)))) -> a#(a(x1)) -> a#(b(c(c(x1))))
    a#(a(x1)) -> a#(b(c(c(x1)))) -> a#(a(x1)) -> c#(c(x1))
    a#(a(x1)) -> a#(b(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#(b(c(c(x1))))
     c#(b(x1)) -> a#(x1)
     c#(b(x1)) -> a#(a(x1))
    TRS:
     a(a(x1)) -> a(b(c(c(x1))))
     c(a(x1)) -> x1
     c(b(x1)) -> a(a(x1))
    graph:
     c#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> c#(x1)
     c#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> c#(c(x1))
     c#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> a#(b(c(c(x1))))
     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#(b(c(c(x1))))
     a#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(x1)
     a#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(a(x1))
     a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(x1)
     a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(a(x1))
    SCC Processor:
     #sccs: 1
     #rules: 4
     #arcs: 10/25
     DPs:
      c#(b(x1)) -> a#(a(x1))
      a#(a(x1)) -> c#(c(x1))
      c#(b(x1)) -> a#(x1)
      a#(a(x1)) -> c#(x1)
     TRS:
      a(a(x1)) -> a(b(c(c(x1))))
      c(a(x1)) -> x1
      c(b(x1)) -> a(a(x1))
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       a(a(x1)) -> a(b(c(c(x1))))
       c(a(x1)) -> x1
       c(b(x1)) -> a(a(x1))
      interpretation:
       [c#](x0) = [0  -&]x0 + [0],
       
                 [-& 0 ]     [0]
       [c](x0) = [0  -&]x0 + [1],
       
       [a#](x0) = [0  -&]x0 + [0],
       
                 [1  0 ]     [2]
       [a](x0) = [0  -&]x0 + [0],
       
                 [1 0]     [2]
       [b](x0) = [2 1]x0 + [3]
      orientation:
       c#(b(x1)) = [1 0]x1 + [2] >= [1 0]x1 + [2] = a#(a(x1))
       
       a#(a(x1)) = [1 0]x1 + [2] >= [-& 0 ]x1 + [0] = c#(c(x1))
       
       c#(b(x1)) = [1 0]x1 + [2] >= [0  -&]x1 + [0] = a#(x1)
       
       a#(a(x1)) = [1 0]x1 + [2] >= [0  -&]x1 + [0] = c#(x1)
       
                  [2 1]     [3]    [2 1]     [3]                 
       a(a(x1)) = [1 0]x1 + [2] >= [1 0]x1 + [2] = a(b(c(c(x1))))
       
                  [0  -&]     [0]           
       c(a(x1)) = [1  0 ]x1 + [2] >= x1 = x1
       
                  [2 1]     [3]    [2 1]     [3]           
       c(b(x1)) = [1 0]x1 + [2] >= [1 0]x1 + [2] = a(a(x1))
      problem:
       DPs:
        c#(b(x1)) -> a#(a(x1))
        a#(a(x1)) -> c#(c(x1))
       TRS:
        a(a(x1)) -> a(b(c(c(x1))))
        c(a(x1)) -> x1
        c(b(x1)) -> a(a(x1))
      Restore Modifier:
       DPs:
        c#(b(x1)) -> a#(a(x1))
        a#(a(x1)) -> c#(c(x1))
       TRS:
        a(a(x1)) -> a(b(c(c(x1))))
        c(a(x1)) -> x1
        c(b(x1)) -> a(a(x1))
       EDG Processor:
        DPs:
         c#(b(x1)) -> a#(a(x1))
         a#(a(x1)) -> c#(c(x1))
        TRS:
         a(a(x1)) -> a(b(c(c(x1))))
         c(a(x1)) -> x1
         c(b(x1)) -> a(a(x1))
        graph:
         c#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> c#(c(x1))
         a#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(a(x1))
        Bounds Processor:
         bound: 0
         enrichment: match-dp
         automaton:
          final states: {1}
          transitions:
           f50() -> 2*
           a0(39) -> 40*
           a0(15) -> 16*
           a0(26) -> 27*
           a0(25) -> 26*
           a0(51) -> 52*
           a0(2) -> 3*
           a{#,0}(3) -> 1*
           c{#,0}(8) -> 9*
           b0(33) -> 34*
           b0(14) -> 15*
           c0(17) -> 18*
           c0(13) -> 14*
           c0(32) -> 33*
           c0(7) -> 8*
           c0(41) -> 42*
           c0(31) -> 32*
           27 -> 18,8,13
           42 -> 32*
           14 -> 25*
           16 -> 52,3
           2 -> 14,25,31,33,8,7
           52 -> 8*
           26 -> 14,25
           8 -> 13*
           40 -> 25*
           1 -> 9*
           34 -> 26*
           9 -> 1*
           3 -> 51*
           39 -> 42,32,33,41
           18 -> 8*
           15 -> 14,25,33,31,17
           51 -> 14,25,33,31
           25 -> 33,32,31
           33 -> 39*
         problem:
          DPs:
           a#(a(x1)) -> c#(c(x1))
          TRS:
           a(a(x1)) -> a(b(c(c(x1))))
           c(a(x1)) -> x1
           c(b(x1)) -> a(a(x1))
         Restore Modifier:
          DPs:
           a#(a(x1)) -> c#(c(x1))
          TRS:
           a(a(x1)) -> a(b(c(c(x1))))
           c(a(x1)) -> x1
           c(b(x1)) -> a(a(x1))
          EDG Processor:
           DPs:
            a#(a(x1)) -> c#(c(x1))
           TRS:
            a(a(x1)) -> a(b(c(c(x1))))
            c(a(x1)) -> x1
            c(b(x1)) -> a(a(x1))
           graph:
            
           SCC Processor:
            #sccs: 0
            #rules: 0
            #arcs: 0/1