YES

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

Proof:
 DP Processor:
  DPs:
   a#(b(x1)) -> c#(b(x1))
   b#(x1) -> c#(x1)
   b#(x1) -> a#(c(x1))
   b#(x1) -> a#(a(c(x1)))
   c#(c(x1)) -> b#(x1)
  TRS:
   a(x1) -> x1
   a(b(x1)) -> c(b(x1))
   b(x1) -> a(a(c(x1)))
   c(c(x1)) -> b(x1)
  TDG Processor:
   DPs:
    a#(b(x1)) -> c#(b(x1))
    b#(x1) -> c#(x1)
    b#(x1) -> a#(c(x1))
    b#(x1) -> a#(a(c(x1)))
    c#(c(x1)) -> b#(x1)
   TRS:
    a(x1) -> x1
    a(b(x1)) -> c(b(x1))
    b(x1) -> a(a(c(x1)))
    c(c(x1)) -> b(x1)
   graph:
    b#(x1) -> c#(x1) -> c#(c(x1)) -> b#(x1)
    b#(x1) -> a#(c(x1)) -> a#(b(x1)) -> c#(b(x1))
    b#(x1) -> a#(a(c(x1))) -> a#(b(x1)) -> c#(b(x1))
    c#(c(x1)) -> b#(x1) -> b#(x1) -> a#(a(c(x1)))
    c#(c(x1)) -> b#(x1) -> b#(x1) -> a#(c(x1))
    c#(c(x1)) -> b#(x1) -> b#(x1) -> c#(x1)
    a#(b(x1)) -> c#(b(x1)) -> c#(c(x1)) -> b#(x1)
   Arctic Interpretation Processor:
    dimension: 3
    usable rules:
     a(x1) -> x1
     a(b(x1)) -> c(b(x1))
     b(x1) -> a(a(c(x1)))
     c(c(x1)) -> b(x1)
    interpretation:
     [b#](x0) = [-& 1  0 ]x0 + [1],
     
     [c#](x0) = [-& 1  0 ]x0 + [0],
     
     [a#](x0) = [1 0 0]x0 + [0],
     
               [-& 0  -&]     [0]
     [c](x0) = [-& 1  0 ]x0 + [1]
               [-& 1  0 ]     [0],
     
               [-& 1  0 ]     [1]
     [b](x0) = [-& 1  0 ]x0 + [1]
               [-& 1  0 ]     [1],
     
               [0  -& -&]     [0]
     [a](x0) = [1  0  0 ]x0 + [0]
               [1  -& 0 ]     [0]
    orientation:
     a#(b(x1)) = [-& 2  1 ]x1 + [2] >= [-& 2  1 ]x1 + [2] = c#(b(x1))
     
     b#(x1) = [-& 1  0 ]x1 + [1] >= [-& 1  0 ]x1 + [0] = c#(x1)
     
     b#(x1) = [-& 1  0 ]x1 + [1] >= [-& 1  0 ]x1 + [1] = a#(c(x1))
     
     b#(x1) = [-& 1  0 ]x1 + [1] >= [-& 1  0 ]x1 + [1] = a#(a(c(x1)))
     
     c#(c(x1)) = [-& 2  1 ]x1 + [2] >= [-& 1  0 ]x1 + [1] = b#(x1)
     
             [0  -& -&]     [0]           
     a(x1) = [1  0  0 ]x1 + [0] >= x1 = x1
             [1  -& 0 ]     [0]           
     
                [-& 1  0 ]     [1]    [-& 1  0 ]     [1]           
     a(b(x1)) = [-& 2  1 ]x1 + [2] >= [-& 2  1 ]x1 + [2] = c(b(x1))
                [-& 2  1 ]     [2]    [-& 2  1 ]     [2]           
     
             [-& 1  0 ]     [1]    [-& 0  -&]     [0]              
     b(x1) = [-& 1  0 ]x1 + [1] >= [-& 1  0 ]x1 + [1] = a(a(c(x1)))
             [-& 1  0 ]     [1]    [-& 1  0 ]     [1]              
     
                [-& 1  0 ]     [1]    [-& 1  0 ]     [1]        
     c(c(x1)) = [-& 2  1 ]x1 + [2] >= [-& 1  0 ]x1 + [1] = b(x1)
                [-& 2  1 ]     [2]    [-& 1  0 ]     [1]        
    problem:
     DPs:
      a#(b(x1)) -> c#(b(x1))
      b#(x1) -> c#(x1)
      b#(x1) -> a#(c(x1))
      b#(x1) -> a#(a(c(x1)))
     TRS:
      a(x1) -> x1
      a(b(x1)) -> c(b(x1))
      b(x1) -> a(a(c(x1)))
      c(c(x1)) -> b(x1)
    Restore Modifier:
     DPs:
      a#(b(x1)) -> c#(b(x1))
      b#(x1) -> c#(x1)
      b#(x1) -> a#(c(x1))
      b#(x1) -> a#(a(c(x1)))
     TRS:
      a(x1) -> x1
      a(b(x1)) -> c(b(x1))
      b(x1) -> a(a(c(x1)))
      c(c(x1)) -> b(x1)
     EDG Processor:
      DPs:
       a#(b(x1)) -> c#(b(x1))
       b#(x1) -> c#(x1)
       b#(x1) -> a#(c(x1))
       b#(x1) -> a#(a(c(x1)))
      TRS:
       a(x1) -> x1
       a(b(x1)) -> c(b(x1))
       b(x1) -> a(a(c(x1)))
       c(c(x1)) -> b(x1)
      graph:
       b#(x1) -> a#(c(x1)) -> a#(b(x1)) -> c#(b(x1))
       b#(x1) -> a#(a(c(x1))) -> a#(b(x1)) -> c#(b(x1))
      SCC Processor:
       #sccs: 0
       #rules: 0
       #arcs: 2/16