YES

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

Proof:
 DP Processor:
  DPs:
   a#(b(x1)) -> c#(x1)
   a#(b(x1)) -> a#(c(x1))
   a#(b(x1)) -> a#(a(c(x1)))
   a#(b(x1)) -> b#(a(a(c(x1))))
   a#(b(x1)) -> b#(b(a(a(c(x1)))))
  TRS:
   a(x1) -> x1
   a(b(x1)) -> b(b(a(a(c(x1)))))
   b(b(x1)) -> x1
   c(c(x1)) -> x1
  TDG Processor:
   DPs:
    a#(b(x1)) -> c#(x1)
    a#(b(x1)) -> a#(c(x1))
    a#(b(x1)) -> a#(a(c(x1)))
    a#(b(x1)) -> b#(a(a(c(x1))))
    a#(b(x1)) -> b#(b(a(a(c(x1)))))
   TRS:
    a(x1) -> x1
    a(b(x1)) -> b(b(a(a(c(x1)))))
    b(b(x1)) -> x1
    c(c(x1)) -> x1
   graph:
    a#(b(x1)) -> a#(c(x1)) -> a#(b(x1)) -> b#(b(a(a(c(x1)))))
    a#(b(x1)) -> a#(c(x1)) -> a#(b(x1)) -> b#(a(a(c(x1))))
    a#(b(x1)) -> a#(c(x1)) -> a#(b(x1)) -> a#(a(c(x1)))
    a#(b(x1)) -> a#(c(x1)) -> a#(b(x1)) -> a#(c(x1))
    a#(b(x1)) -> a#(c(x1)) -> a#(b(x1)) -> c#(x1)
    a#(b(x1)) -> a#(a(c(x1))) -> a#(b(x1)) -> b#(b(a(a(c(x1)))))
    a#(b(x1)) -> a#(a(c(x1))) -> a#(b(x1)) -> b#(a(a(c(x1))))
    a#(b(x1)) -> a#(a(c(x1))) -> a#(b(x1)) -> a#(a(c(x1)))
    a#(b(x1)) -> a#(a(c(x1))) -> a#(b(x1)) -> a#(c(x1))
    a#(b(x1)) -> a#(a(c(x1))) -> a#(b(x1)) -> c#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 10/25
    DPs:
     a#(b(x1)) -> a#(c(x1))
     a#(b(x1)) -> a#(a(c(x1)))
    TRS:
     a(x1) -> x1
     a(b(x1)) -> b(b(a(a(c(x1)))))
     b(b(x1)) -> x1
     c(c(x1)) -> x1
    Bounds Processor:
     bound: 1
     enrichment: match-dp
     automaton:
      final states: {4}
      transitions:
       a1(23) -> 24*
       a{#,0}(7) -> 4*
       a{#,0}(26) -> 27*
       f60() -> 5*
       c1(22) -> 23*
       a{#,1}(24) -> 25*
       c0(5) -> 6*
       b0(13) -> 14*
       b0(12) -> 13*
       a0(6) -> 7*
       a0(30) -> 31*
       a0(11) -> 12*
       27 -> 4*
       24 -> 30*
       30 -> 31*
       7 -> 11*
       12 -> 14,7,11
       14 -> 24,30,7
       4 -> 27*
       11 -> 12*
       6 -> 7*
       13 -> 22*
       31 -> 12*
       5 -> 23,26,24,31,13,22,6,7
       25 -> 4*
       23 -> 24,26
     problem:
      DPs:
       a#(b(x1)) -> a#(c(x1))
      TRS:
       a(x1) -> x1
       a(b(x1)) -> b(b(a(a(c(x1)))))
       b(b(x1)) -> x1
       c(c(x1)) -> x1
     Restore Modifier:
      DPs:
       a#(b(x1)) -> a#(c(x1))
      TRS:
       a(x1) -> x1
       a(b(x1)) -> b(b(a(a(c(x1)))))
       b(b(x1)) -> x1
       c(c(x1)) -> x1
      EDG Processor:
       DPs:
        a#(b(x1)) -> a#(c(x1))
       TRS:
        a(x1) -> x1
        a(b(x1)) -> b(b(a(a(c(x1)))))
        b(b(x1)) -> x1
        c(c(x1)) -> x1
       graph:
        a#(b(x1)) -> a#(c(x1)) -> a#(b(x1)) -> a#(c(x1))
       Usable Rule Processor:
        DPs:
         a#(b(x1)) -> a#(c(x1))
        TRS:
         c(c(x1)) -> x1
        Arctic Interpretation Processor:
         dimension: 1
         usable rules:
          c(c(x1)) -> x1
         interpretation:
          [b](x0) = 8x0 + 10,
          
          [a#](x0) = x0 + 0,
          
          [c](x0) = 6x0 + 4
         orientation:
          a#(b(x1)) = 8x1 + 10 >= 6x1 + 4 = a#(c(x1))
          
          c(c(x1)) = 12x1 + 10 >= x1 = x1
         problem:
          DPs:
           
          TRS:
           c(c(x1)) -> x1
         Qed