YES

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

Proof:
 DP Processor:
  DPs:
   a#(b(x1)) -> a#(x1)
   a#(b(x1)) -> b#(c(a(x1)))
   b#(c(x1)) -> b#(x1)
   b#(c(x1)) -> b#(b(x1))
   a#(c(x1)) -> b#(x1)
   a#(c(x1)) -> a#(b(x1))
  TRS:
   a(b(x1)) -> b(c(a(x1)))
   b(c(x1)) -> c(b(b(x1)))
   a(c(x1)) -> c(a(b(x1)))
  TDG Processor:
   DPs:
    a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> b#(c(a(x1)))
    b#(c(x1)) -> b#(x1)
    b#(c(x1)) -> b#(b(x1))
    a#(c(x1)) -> b#(x1)
    a#(c(x1)) -> a#(b(x1))
   TRS:
    a(b(x1)) -> b(c(a(x1)))
    b(c(x1)) -> c(b(b(x1)))
    a(c(x1)) -> c(a(b(x1)))
   graph:
    b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(b(x1))
    b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(x1)
    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(b(x1))
    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
    a#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(b(x1))
    a#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
    a#(c(x1)) -> a#(b(x1)) -> a#(c(x1)) -> a#(b(x1))
    a#(c(x1)) -> a#(b(x1)) -> a#(c(x1)) -> b#(x1)
    a#(c(x1)) -> a#(b(x1)) -> a#(b(x1)) -> b#(c(a(x1)))
    a#(c(x1)) -> a#(b(x1)) -> a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> b#(c(a(x1))) -> b#(c(x1)) -> b#(b(x1))
    a#(b(x1)) -> b#(c(a(x1))) -> b#(c(x1)) -> b#(x1)
    a#(b(x1)) -> a#(x1) -> a#(c(x1)) -> a#(b(x1))
    a#(b(x1)) -> a#(x1) -> a#(c(x1)) -> b#(x1)
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(c(a(x1)))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
   SCC Processor:
    #sccs: 2
    #rules: 4
    #arcs: 16/36
    DPs:
     a#(c(x1)) -> a#(b(x1))
     a#(b(x1)) -> a#(x1)
    TRS:
     a(b(x1)) -> b(c(a(x1)))
     b(c(x1)) -> c(b(b(x1)))
     a(c(x1)) -> c(a(b(x1)))
    Usable Rule Processor:
     DPs:
      a#(c(x1)) -> a#(b(x1))
      a#(b(x1)) -> a#(x1)
     TRS:
      b(c(x1)) -> c(b(b(x1)))
     Arctic Interpretation Processor:
      dimension: 4
      usable rules:
       b(c(x1)) -> c(b(b(x1)))
      interpretation:
       [a#](x0) = [0 0 0 0]x0 + [0],
       
                 [0  0  0  -&]     [0]
                 [1  1  1  1 ]     [0]
       [c](x0) = [0  0  0  0 ]x0 + [0]
                 [-& 0  0  -&]     [1],
       
                 [0  -& 0  0 ]     [0]
                 [0  0  0  0 ]     [0]
       [b](x0) = [0  -& 0  0 ]x0 + [0]
                 [0  0  0  0 ]     [0]
      orientation:
       a#(c(x1)) = [1 1 1 1]x1 + [1] >= [0 0 0 0]x1 + [0] = a#(b(x1))
       
       a#(b(x1)) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = a#(x1)
       
                  [0 0 0 0]     [1]    [0 0 0 0]     [0]              
                  [1 1 1 1]     [1]    [1 1 1 1]     [1]              
       b(c(x1)) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [0] = c(b(b(x1)))
                  [1 1 1 1]     [1]    [0 0 0 0]     [1]              
      problem:
       DPs:
        a#(b(x1)) -> a#(x1)
       TRS:
        b(c(x1)) -> c(b(b(x1)))
      Restore Modifier:
       DPs:
        a#(b(x1)) -> a#(x1)
       TRS:
        a(b(x1)) -> b(c(a(x1)))
        b(c(x1)) -> c(b(b(x1)))
        a(c(x1)) -> c(a(b(x1)))
       EDG Processor:
        DPs:
         a#(b(x1)) -> a#(x1)
        TRS:
         a(b(x1)) -> b(c(a(x1)))
         b(c(x1)) -> c(b(b(x1)))
         a(c(x1)) -> c(a(b(x1)))
        graph:
         a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
        CDG Processor:
         DPs:
          a#(b(x1)) -> a#(x1)
         TRS:
          a(b(x1)) -> b(c(a(x1)))
          b(c(x1)) -> c(b(b(x1)))
          a(c(x1)) -> c(a(b(x1)))
         graph:
          
         Qed
    
    DPs:
     b#(c(x1)) -> b#(b(x1))
     b#(c(x1)) -> b#(x1)
    TRS:
     a(b(x1)) -> b(c(a(x1)))
     b(c(x1)) -> c(b(b(x1)))
     a(c(x1)) -> c(a(b(x1)))
    Usable Rule Processor:
     DPs:
      b#(c(x1)) -> b#(b(x1))
      b#(c(x1)) -> b#(x1)
     TRS:
      b(c(x1)) -> c(b(b(x1)))
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       b(c(x1)) -> c(b(b(x1)))
      interpretation:
       [b#](x0) = [0 0]x0 + [0],
       
                 [1  0 ]     [0]
       [c](x0) = [-& 1 ]x0 + [1],
       
                 [-& 1 ]     [0]
       [b](x0) = [-& 0 ]x0 + [0]
      orientation:
       b#(c(x1)) = [1 1]x1 + [1] >= [-& 1 ]x1 + [0] = b#(b(x1))
       
       b#(c(x1)) = [1 1]x1 + [1] >= [0 0]x1 + [0] = b#(x1)
       
                  [-& 2 ]     [2]    [-& 2 ]     [2]              
       b(c(x1)) = [-& 1 ]x1 + [1] >= [-& 1 ]x1 + [1] = c(b(b(x1)))
      problem:
       DPs:
        b#(c(x1)) -> b#(b(x1))
       TRS:
        b(c(x1)) -> c(b(b(x1)))
      Restore Modifier:
       DPs:
        b#(c(x1)) -> b#(b(x1))
       TRS:
        a(b(x1)) -> b(c(a(x1)))
        b(c(x1)) -> c(b(b(x1)))
        a(c(x1)) -> c(a(b(x1)))
       EDG Processor:
        DPs:
         b#(c(x1)) -> b#(b(x1))
        TRS:
         a(b(x1)) -> b(c(a(x1)))
         b(c(x1)) -> c(b(b(x1)))
         a(c(x1)) -> c(a(b(x1)))
        graph:
         b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(b(x1))
        Usable Rule Processor:
         DPs:
          b#(c(x1)) -> b#(b(x1))
         TRS:
          b(c(x1)) -> c(b(b(x1)))
         Arctic Interpretation Processor:
          dimension: 3
          usable rules:
           b(c(x1)) -> c(b(b(x1)))
          interpretation:
           [b#](x0) = [1  -& 0 ]x0 + [0],
           
                     [0  0  1 ]     [1 ]
           [c](x0) = [-& 1  1 ]x0 + [-&]
                     [1  1  1 ]     [1 ],
           
                     [-& -& 0 ]     [0]
           [b](x0) = [0  0  0 ]x0 + [0]
                     [0  -& 0 ]     [0]
          orientation:
           b#(c(x1)) = [1 1 2]x1 + [2] >= [0  -& 1 ]x1 + [1] = b#(b(x1))
           
                      [1 1 1]     [1]    [1 0 1]     [1]              
           b(c(x1)) = [1 1 1]x1 + [1] >= [1 1 1]x1 + [1] = c(b(b(x1)))
                      [1 1 1]     [1]    [1 1 1]     [1]              
          problem:
           DPs:
            
           TRS:
            b(c(x1)) -> c(b(b(x1)))
          Qed