YES

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

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