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: 2
    interpretation:
     [b#](x0) = [1 3]x0 + [3],
     
     [c#](x0) = [0 1]x0 + [0],
     
     [a#](x0) = [0 1]x0 + [0],
     
               [-& 0 ]     [0]
     [c](x0) = [0  2 ]x0 + [2],
     
               [0 2]     [2]
     [b](x0) = [0 2]x0 + [2],
     
               [0  -&]     [0]
     [a](x0) = [2  0 ]x0 + [0]
    orientation:
     a#(b(x1)) = [1 3]x1 + [3] >= [1 3]x1 + [3] = c#(b(x1))
     
     b#(x1) = [1 3]x1 + [3] >= [0 1]x1 + [0] = c#(x1)
     
     b#(x1) = [1 3]x1 + [3] >= [1 3]x1 + [3] = a#(c(x1))
     
     b#(x1) = [1 3]x1 + [3] >= [1 3]x1 + [3] = a#(a(c(x1)))
     
     c#(c(x1)) = [1 3]x1 + [3] >= [1 3]x1 + [3] = b#(x1)
     
             [0  -&]     [0]           
     a(x1) = [2  0 ]x1 + [0] >= x1 = x1
     
                [0 2]     [2]    [0 2]     [2]           
     a(b(x1)) = [2 4]x1 + [4] >= [2 4]x1 + [4] = c(b(x1))
     
             [0 2]     [2]    [-& 0 ]     [0]              
     b(x1) = [0 2]x1 + [2] >= [0  2 ]x1 + [2] = a(a(c(x1)))
     
                [0 2]     [2]    [0 2]     [2]        
     c(c(x1)) = [2 4]x1 + [4] >= [0 2]x1 + [2] = b(x1)
    problem:
     DPs:
      a#(b(x1)) -> c#(b(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)
    EDG Processor:
     DPs:
      a#(b(x1)) -> c#(b(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) -> 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#(c(x1))
      c#(c(x1)) -> b#(x1) -> b#(x1) -> a#(a(c(x1)))
      a#(b(x1)) -> c#(b(x1)) -> c#(c(x1)) -> b#(x1)
     Arctic Interpretation Processor:
      dimension: 2
      interpretation:
       [b#](x0) = [1 0]x0,
       
       [c#](x0) = [0 0]x0,
       
       [a#](x0) = [0 1]x0,
       
                 [1  0 ]  
       [c](x0) = [0  -&]x0,
       
                 [1 0]  
       [b](x0) = [1 0]x0,
       
                 [0  1 ]  
       [a](x0) = [-& 0 ]x0
      orientation:
       a#(b(x1)) = [2 1]x1 >= [1 0]x1 = c#(b(x1))
       
       b#(x1) = [1 0]x1 >= [1 0]x1 = a#(c(x1))
       
       b#(x1) = [1 0]x1 >= [1 0]x1 = a#(a(c(x1)))
       
       c#(c(x1)) = [1 0]x1 >= [1 0]x1 = b#(x1)
       
               [0  1 ]             
       a(x1) = [-& 0 ]x1 >= x1 = x1
       
                  [2 1]      [2 1]             
       a(b(x1)) = [1 0]x1 >= [1 0]x1 = c(b(x1))
       
               [1 0]      [1  0 ]                
       b(x1) = [1 0]x1 >= [0  -&]x1 = a(a(c(x1)))
       
                  [2 1]      [1 0]          
       c(c(x1)) = [1 0]x1 >= [1 0]x1 = b(x1)
      problem:
       DPs:
        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)
      EDG Processor:
       DPs:
        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:
        c#(c(x1)) -> b#(x1) -> b#(x1) -> a#(a(c(x1)))
        c#(c(x1)) -> b#(x1) -> b#(x1) -> a#(c(x1))
       SCC Processor:
        #sccs: 0
        #rules: 0
        #arcs: 2/9