YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  a(x1) -> c(b(b(x1)))
  b(c(a(x1))) -> a(a(c(x1)))
  c(x1) -> x1
  DP Processor:
   DPs:
    a#(x1) -> b#(x1)
    a#(x1) -> b#(b(x1))
    a#(x1) -> c#(b(b(x1)))
    b#(c(a(x1))) -> c#(x1)
    b#(c(a(x1))) -> a#(c(x1))
    b#(c(a(x1))) -> a#(a(c(x1)))
   TRS:
    a(x1) -> x1
    a(x1) -> c(b(b(x1)))
    b(c(a(x1))) -> a(a(c(x1)))
    c(x1) -> x1
   TDG Processor:
    DPs:
     a#(x1) -> b#(x1)
     a#(x1) -> b#(b(x1))
     a#(x1) -> c#(b(b(x1)))
     b#(c(a(x1))) -> c#(x1)
     b#(c(a(x1))) -> a#(c(x1))
     b#(c(a(x1))) -> a#(a(c(x1)))
    TRS:
     a(x1) -> x1
     a(x1) -> c(b(b(x1)))
     b(c(a(x1))) -> a(a(c(x1)))
     c(x1) -> x1
    graph:
     b#(c(a(x1))) -> a#(c(x1)) -> a#(x1) -> c#(b(b(x1)))
     b#(c(a(x1))) -> a#(c(x1)) -> a#(x1) -> b#(b(x1))
     b#(c(a(x1))) -> a#(c(x1)) -> a#(x1) -> b#(x1)
     b#(c(a(x1))) -> a#(a(c(x1))) -> a#(x1) -> c#(b(b(x1)))
     b#(c(a(x1))) -> a#(a(c(x1))) -> a#(x1) -> b#(b(x1))
     b#(c(a(x1))) -> a#(a(c(x1))) -> a#(x1) -> b#(x1)
     a#(x1) -> b#(b(x1)) -> b#(c(a(x1))) -> a#(a(c(x1)))
     a#(x1) -> b#(b(x1)) -> b#(c(a(x1))) -> a#(c(x1))
     a#(x1) -> b#(b(x1)) -> b#(c(a(x1))) -> c#(x1)
     a#(x1) -> b#(x1) -> b#(c(a(x1))) -> a#(a(c(x1)))
     a#(x1) -> b#(x1) -> b#(c(a(x1))) -> a#(c(x1))
     a#(x1) -> b#(x1) -> b#(c(a(x1))) -> c#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 4
     #arcs: 12/36
     DPs:
      b#(c(a(x1))) -> a#(c(x1))
      a#(x1) -> b#(x1)
      b#(c(a(x1))) -> a#(a(c(x1)))
      a#(x1) -> b#(b(x1))
     TRS:
      a(x1) -> x1
      a(x1) -> c(b(b(x1)))
      b(c(a(x1))) -> a(a(c(x1)))
      c(x1) -> x1
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       a(x1) -> x1
       a(x1) -> c(b(b(x1)))
       b(c(a(x1))) -> a(a(c(x1)))
       c(x1) -> x1
      interpretation:
       [b#](x0) = [-& 0 ]x0 + [0],
       
                 [0 0]     [-&]
       [c](x0) = [0 0]x0 + [-2],
       
       [a#](x0) = [-& 1 ]x0 + [1],
       
                 [1  1 ]     [1]
       [a](x0) = [-& 0 ]x0 + [0],
       
                 [-& 1 ]     [0 ]
       [b](x0) = [-& -1]x0 + [-&]
      orientation:
       b#(c(a(x1))) = [1 1]x1 + [1] >= [1 1]x1 + [1] = a#(c(x1))
       
       a#(x1) = [-& 1 ]x1 + [1] >= [-& 0 ]x1 + [0] = b#(x1)
       
       b#(c(a(x1))) = [1 1]x1 + [1] >= [1 1]x1 + [1] = a#(a(c(x1)))
       
       a#(x1) = [-& 1 ]x1 + [1] >= [-& -1]x1 + [0] = b#(b(x1))
       
               [1  1 ]     [1]           
       a(x1) = [-& 0 ]x1 + [0] >= x1 = x1
       
               [1  1 ]     [1]    [-& 0 ]     [0]              
       a(x1) = [-& 0 ]x1 + [0] >= [-& 0 ]x1 + [0] = c(b(b(x1)))
       
                     [2 2]     [2]    [2 2]     [2]              
       b(c(a(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = a(a(c(x1)))
       
               [0 0]     [-&]           
       c(x1) = [0 0]x1 + [-2] >= x1 = x1
      problem:
       DPs:
        b#(c(a(x1))) -> a#(c(x1))
        b#(c(a(x1))) -> a#(a(c(x1)))
       TRS:
        a(x1) -> x1
        a(x1) -> c(b(b(x1)))
        b(c(a(x1))) -> a(a(c(x1)))
        c(x1) -> x1
      Restore Modifier:
       DPs:
        b#(c(a(x1))) -> a#(c(x1))
        b#(c(a(x1))) -> a#(a(c(x1)))
       TRS:
        a(x1) -> x1
        a(x1) -> c(b(b(x1)))
        b(c(a(x1))) -> a(a(c(x1)))
        c(x1) -> x1
       EDG Processor:
        DPs:
         b#(c(a(x1))) -> a#(c(x1))
         b#(c(a(x1))) -> a#(a(c(x1)))
        TRS:
         a(x1) -> x1
         a(x1) -> c(b(b(x1)))
         b(c(a(x1))) -> a(a(c(x1)))
         c(x1) -> x1
        graph:
         
        SCC Processor:
         #sccs: 0
         #rules: 0
         #arcs: 0/4