YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(x1)) -> c#(x1)
   a#(a(x1)) -> b#(c(x1))
   a#(a(x1)) -> a#(b(c(x1)))
   c#(b(x1)) -> c#(x1)
   c#(b(x1)) -> a#(c(x1))
   c#(b(x1)) -> b#(a(c(x1)))
  TRS:
   a(x1) -> x1
   a(a(x1)) -> a(b(c(x1)))
   b(x1) -> x1
   c(b(x1)) -> b(a(c(x1)))
  TDG Processor:
   DPs:
    a#(a(x1)) -> c#(x1)
    a#(a(x1)) -> b#(c(x1))
    a#(a(x1)) -> a#(b(c(x1)))
    c#(b(x1)) -> c#(x1)
    c#(b(x1)) -> a#(c(x1))
    c#(b(x1)) -> b#(a(c(x1)))
   TRS:
    a(x1) -> x1
    a(a(x1)) -> a(b(c(x1)))
    b(x1) -> x1
    c(b(x1)) -> b(a(c(x1)))
   graph:
    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> b#(a(c(x1)))
    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1))
    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
    c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(c(x1)))
    c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(c(x1))
    c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(x1)
    a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> b#(a(c(x1)))
    a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1))
    a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
    a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> a#(b(c(x1)))
    a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(c(x1))
    a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> c#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 4
    #arcs: 12/36
    DPs:
     c#(b(x1)) -> c#(x1)
     c#(b(x1)) -> a#(c(x1))
     a#(a(x1)) -> c#(x1)
     a#(a(x1)) -> a#(b(c(x1)))
    TRS:
     a(x1) -> x1
     a(a(x1)) -> a(b(c(x1)))
     b(x1) -> x1
     c(b(x1)) -> b(a(c(x1)))
    Arctic Interpretation Processor:
     dimension: 2
     interpretation:
      [c#](x0) = [1 0]x0,
      
      [a#](x0) = [0  -&]x0 + [0],
      
                [0  -&]     [0]
      [b](x0) = [0  1 ]x0 + [2],
      
                [-& 0 ]     [0 ]
      [c](x0) = [-& 0 ]x0 + [-&],
      
                [1 1]     [2]
      [a](x0) = [0 0]x0 + [0]
     orientation:
      c#(b(x1)) = [1 1]x1 + [2] >= [1 0]x1 = c#(x1)
      
      c#(b(x1)) = [1 1]x1 + [2] >= [-& 0 ]x1 + [0] = a#(c(x1))
      
      a#(a(x1)) = [1 1]x1 + [2] >= [1 0]x1 = c#(x1)
      
      a#(a(x1)) = [1 1]x1 + [2] >= [-& 0 ]x1 + [0] = a#(b(c(x1)))
      
              [1 1]     [2]           
      a(x1) = [0 0]x1 + [0] >= x1 = x1
      
                 [2 2]     [3]    [-& 2 ]     [3]              
      a(a(x1)) = [1 1]x1 + [2] >= [-& 1 ]x1 + [2] = a(b(c(x1)))
      
              [0  -&]     [0]           
      b(x1) = [0  1 ]x1 + [2] >= x1 = x1
      
                 [0 1]     [2]    [-& 1 ]     [2]              
      c(b(x1)) = [0 1]x1 + [2] >= [-& 1 ]x1 + [2] = b(a(c(x1)))
     problem:
      DPs:
       c#(b(x1)) -> c#(x1)
       a#(a(x1)) -> c#(x1)
      TRS:
       a(x1) -> x1
       a(a(x1)) -> a(b(c(x1)))
       b(x1) -> x1
       c(b(x1)) -> b(a(c(x1)))
     EDG Processor:
      DPs:
       c#(b(x1)) -> c#(x1)
       a#(a(x1)) -> c#(x1)
      TRS:
       a(x1) -> x1
       a(a(x1)) -> a(b(c(x1)))
       b(x1) -> x1
       c(b(x1)) -> b(a(c(x1)))
      graph:
       c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
       a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
      CDG Processor:
       DPs:
        c#(b(x1)) -> c#(x1)
        a#(a(x1)) -> c#(x1)
       TRS:
        a(x1) -> x1
        a(a(x1)) -> a(b(c(x1)))
        b(x1) -> x1
        c(b(x1)) -> b(a(c(x1)))
       graph:
        
       Qed