YES

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

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