YES

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

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