YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(x1)) -> b#(c(x1))
   a#(a(x1)) -> b#(b(c(x1)))
   a#(a(x1)) -> b#(b(b(c(x1))))
   b#(c(b(x1))) -> b#(c(x1))
   b#(c(b(x1))) -> a#(b(c(x1)))
  TRS:
   a(a(x1)) -> b(b(b(c(x1))))
   b(c(b(x1))) -> a(b(c(x1)))
  TDG Processor:
   DPs:
    a#(a(x1)) -> b#(c(x1))
    a#(a(x1)) -> b#(b(c(x1)))
    a#(a(x1)) -> b#(b(b(c(x1))))
    b#(c(b(x1))) -> b#(c(x1))
    b#(c(b(x1))) -> a#(b(c(x1)))
   TRS:
    a(a(x1)) -> b(b(b(c(x1))))
    b(c(b(x1))) -> a(b(c(x1)))
   graph:
    b#(c(b(x1))) -> b#(c(x1)) -> b#(c(b(x1))) -> a#(b(c(x1)))
    b#(c(b(x1))) -> b#(c(x1)) -> b#(c(b(x1))) -> b#(c(x1))
    b#(c(b(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(b(b(c(x1))))
    b#(c(b(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(b(c(x1)))
    b#(c(b(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(c(x1))
    a#(a(x1)) -> b#(b(b(c(x1)))) -> b#(c(b(x1))) -> a#(b(c(x1)))
    a#(a(x1)) -> b#(b(b(c(x1)))) -> b#(c(b(x1))) -> b#(c(x1))
    a#(a(x1)) -> b#(b(c(x1))) -> b#(c(b(x1))) -> a#(b(c(x1)))
    a#(a(x1)) -> b#(b(c(x1))) -> b#(c(b(x1))) -> b#(c(x1))
    a#(a(x1)) -> b#(c(x1)) -> b#(c(b(x1))) -> a#(b(c(x1)))
    a#(a(x1)) -> b#(c(x1)) -> b#(c(b(x1))) -> b#(c(x1))
   EDG Processor:
    DPs:
     a#(a(x1)) -> b#(c(x1))
     a#(a(x1)) -> b#(b(c(x1)))
     a#(a(x1)) -> b#(b(b(c(x1))))
     b#(c(b(x1))) -> b#(c(x1))
     b#(c(b(x1))) -> a#(b(c(x1)))
    TRS:
     a(a(x1)) -> b(b(b(c(x1))))
     b(c(b(x1))) -> a(b(c(x1)))
    graph:
     b#(c(b(x1))) -> b#(c(x1)) -> b#(c(b(x1))) -> b#(c(x1))
     b#(c(b(x1))) -> b#(c(x1)) -> b#(c(b(x1))) -> a#(b(c(x1)))
     b#(c(b(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(c(x1))
     b#(c(b(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(b(c(x1)))
     b#(c(b(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(b(b(c(x1))))
     a#(a(x1)) -> b#(c(x1)) -> b#(c(b(x1))) -> b#(c(x1))
     a#(a(x1)) -> b#(c(x1)) -> b#(c(b(x1))) -> a#(b(c(x1)))
    SCC Processor:
     #sccs: 1
     #rules: 3
     #arcs: 7/25
     DPs:
      b#(c(b(x1))) -> b#(c(x1))
      b#(c(b(x1))) -> a#(b(c(x1)))
      a#(a(x1)) -> b#(c(x1))
     TRS:
      a(a(x1)) -> b(b(b(c(x1))))
      b(c(b(x1))) -> a(b(c(x1)))
     Arctic Interpretation Processor:
      dimension: 4
      usable rules:
       a(a(x1)) -> b(b(b(c(x1))))
       b(c(b(x1))) -> a(b(c(x1)))
      interpretation:
       [b#](x0) = [-& 0  0  0 ]x0 + [0],
       
       [a#](x0) = [0 0 0 0]x0 + [0],
       
                 [0  0  0  0 ]     [0]
                 [-& 0  0  0 ]     [0]
       [b](x0) = [-& 1  0  0 ]x0 + [0]
                 [-& 0  0  0 ]     [0],
       
                 [-& 1  0  0 ]     [0 ]
                 [-& -& -& -&]     [-&]
       [c](x0) = [-& 0  0  0 ]x0 + [-&]
                 [-& 0  0  0 ]     [-&],
       
                 [-& 1  1  1 ]     [1]
                 [0  0  0  0 ]     [0]
       [a](x0) = [0  0  0  0 ]x0 + [0]
                 [0  0  0  -&]     [0]
      orientation:
       b#(c(b(x1))) = [-& 1  0  0 ]x1 + [0] >= [-& 0  0  0 ]x1 + [0] = b#(c(x1))
       
       b#(c(b(x1))) = [-& 1  0  0 ]x1 + [0] >= [-& 1  0  0 ]x1 + [0] = a#(b(c(x1)))
       
       a#(a(x1)) = [0 1 1 1]x1 + [1] >= [-& 0  0  0 ]x1 + [0] = b#(c(x1))
       
                  [1 1 1 1]     [1]    [-& 1  1  1 ]     [1]                 
                  [0 1 1 1]     [1]    [-& 1  1  1 ]     [1]                 
       a(a(x1)) = [0 1 1 1]x1 + [1] >= [-& 1  1  1 ]x1 + [1] = b(b(b(c(x1))))
                  [0 1 1 1]     [1]    [-& 1  1  1 ]     [1]                 
       
                     [-& 1  1  1 ]     [1]    [-& 1  1  1 ]     [1]              
                     [-& 1  0  0 ]     [0]    [-& 1  0  0 ]     [0]              
       b(c(b(x1))) = [-& 1  0  0 ]x1 + [0] >= [-& 1  0  0 ]x1 + [0] = a(b(c(x1)))
                     [-& 1  0  0 ]     [0]    [-& 1  0  0 ]     [0]              
      problem:
       DPs:
        b#(c(b(x1))) -> b#(c(x1))
        b#(c(b(x1))) -> a#(b(c(x1)))
       TRS:
        a(a(x1)) -> b(b(b(c(x1))))
        b(c(b(x1))) -> a(b(c(x1)))
      Restore Modifier:
       DPs:
        b#(c(b(x1))) -> b#(c(x1))
        b#(c(b(x1))) -> a#(b(c(x1)))
       TRS:
        a(a(x1)) -> b(b(b(c(x1))))
        b(c(b(x1))) -> a(b(c(x1)))
       EDG Processor:
        DPs:
         b#(c(b(x1))) -> b#(c(x1))
         b#(c(b(x1))) -> a#(b(c(x1)))
        TRS:
         a(a(x1)) -> b(b(b(c(x1))))
         b(c(b(x1))) -> a(b(c(x1)))
        graph:
         b#(c(b(x1))) -> b#(c(x1)) -> b#(c(b(x1))) -> a#(b(c(x1)))
         b#(c(b(x1))) -> b#(c(x1)) -> b#(c(b(x1))) -> b#(c(x1))
        SCC Processor:
         #sccs: 1
         #rules: 1
         #arcs: 2/4
         DPs:
          b#(c(b(x1))) -> b#(c(x1))
         TRS:
          a(a(x1)) -> b(b(b(c(x1))))
          b(c(b(x1))) -> a(b(c(x1)))
         Usable Rule Processor:
          DPs:
           b#(c(b(x1))) -> b#(c(x1))
          TRS:
           
          Arctic Interpretation Processor:
           dimension: 4
           usable rules:
            
           interpretation:
            [b#](x0) = [-& 0  0  0 ]x0 + [0],
            
                      [0  1  1  0 ]     [1 ]
                      [1  0  0  0 ]     [0 ]
            [b](x0) = [0  0  1  -&]x0 + [1 ]
                      [1  0  1  1 ]     [-&],
            
                      [-& 0  0  0 ]     [0]
                      [-& 0  0  0 ]     [0]
            [c](x0) = [0  0  0  0 ]x0 + [0]
                      [-& 0  0  0 ]     [0]
           orientation:
            b#(c(b(x1))) = [1 1 1 1]x1 + [1] >= [0 0 0 0]x1 + [0] = b#(c(x1))
           problem:
            DPs:
             
            TRS:
             
           Qed