YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(b(x1))) -> a#(x1)
   a#(a(b(x1))) -> a#(a(x1))
   a#(a(b(x1))) -> a#(c(a(a(x1))))
   a#(c(x1)) -> a#(x1)
  TRS:
   a(a(b(x1))) -> c(a(c(a(a(x1)))))
   a(c(x1)) -> b(a(x1))
  EDG Processor:
   DPs:
    a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> a#(c(a(a(x1))))
    a#(c(x1)) -> a#(x1)
   TRS:
    a(a(b(x1))) -> c(a(c(a(a(x1)))))
    a(c(x1)) -> b(a(x1))
   graph:
    a#(c(x1)) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
    a#(c(x1)) -> a#(x1) -> a#(a(b(x1))) -> a#(a(x1))
    a#(c(x1)) -> a#(x1) -> a#(a(b(x1))) -> a#(c(a(a(x1))))
    a#(c(x1)) -> a#(x1) -> a#(c(x1)) -> a#(x1)
    a#(a(b(x1))) -> a#(c(a(a(x1)))) -> a#(c(x1)) -> a#(x1)
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> 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#(c(a(a(x1))))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(c(x1)) -> a#(x1)
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> 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#(c(a(a(x1))))
    a#(a(b(x1))) -> a#(x1) -> a#(c(x1)) -> a#(x1)
   Arctic Interpretation Processor:
    dimension: 4
    interpretation:
     [a#](x0) = [-& 0  0  0 ]x0 + [0],
     
               [-& 0  0  0 ]     [0]
               [0  1  1  1 ]     [1]
     [c](x0) = [-& 0  0  0 ]x0 + [0]
               [-& 0  0  0 ]     [0],
     
               [-& 0  -& 0 ]     [0]
               [-& -& 0  0 ]     [0]
     [a](x0) = [0  -& -& 0 ]x0 + [0]
               [-& -& -& 0 ]     [0],
     
               [1  1  0  1 ]     [1 ]
               [0  0  -& 0 ]     [0 ]
     [b](x0) = [0  0  -& -&]x0 + [-&]
               [0  0  -& 0 ]     [0 ]
    orientation:
     a#(a(b(x1))) = [1 1 0 1]x1 + [1] >= [-& 0  0  0 ]x1 + [0] = a#(x1)
     
     a#(a(b(x1))) = [1 1 0 1]x1 + [1] >= [0  -& 0  0 ]x1 + [0] = a#(a(x1))
     
     a#(a(b(x1))) = [1 1 0 1]x1 + [1] >= [1 1 0 1]x1 + [1] = a#(c(a(a(x1))))
     
     a#(c(x1)) = [0 1 1 1]x1 + [1] >= [-& 0  0  0 ]x1 + [0] = a#(x1)
     
                   [0  0  -& 0 ]     [0]    [0  0  -& 0 ]     [0]                    
                   [1  1  0  1 ]     [1]    [1  1  0  1 ]     [1]                    
     a(a(b(x1))) = [0  0  -& 0 ]x1 + [0] >= [0  0  -& 0 ]x1 + [0] = c(a(c(a(a(x1)))))
                   [0  0  -& 0 ]     [0]    [0  0  -& 0 ]     [0]                    
     
                [0  1  1  1 ]     [1]    [0  1  1  1 ]     [1]           
                [-& 0  0  0 ]     [0]    [-& 0  0  0 ]     [0]           
     a(c(x1)) = [-& 0  0  0 ]x1 + [0] >= [-& 0  0  0 ]x1 + [0] = b(a(x1))
                [-& 0  0  0 ]     [0]    [-& 0  0  0 ]     [0]           
    problem:
     DPs:
      a#(a(b(x1))) -> a#(x1)
      a#(a(b(x1))) -> a#(a(x1))
      a#(a(b(x1))) -> a#(c(a(a(x1))))
     TRS:
      a(a(b(x1))) -> c(a(c(a(a(x1)))))
      a(c(x1)) -> b(a(x1))
    EDG Processor:
     DPs:
      a#(a(b(x1))) -> a#(x1)
      a#(a(b(x1))) -> a#(a(x1))
      a#(a(b(x1))) -> a#(c(a(a(x1))))
     TRS:
      a(a(b(x1))) -> c(a(c(a(a(x1)))))
      a(c(x1)) -> b(a(x1))
     graph:
      a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(c(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))) -> a#(c(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)
     SCC Processor:
      #sccs: 1
      #rules: 2
      #arcs: 6/9
      DPs:
       a#(a(b(x1))) -> a#(a(x1))
       a#(a(b(x1))) -> a#(x1)
      TRS:
       a(a(b(x1))) -> c(a(c(a(a(x1)))))
       a(c(x1)) -> b(a(x1))
      Matrix Interpretation Processor: dim=3
       
       interpretation:
        [a#](x0) = [0 1 0]x0,
        
                  [2 0 1]     [1]
        [c](x0) = [0 0 0]x0 + [0]
                  [0 0 0]     [0],
        
                  [0 2 0]  
        [a](x0) = [0 0 1]x0
                  [1 0 0]  ,
        
                  [0 0 0]     [0]
        [b](x0) = [0 0 0]x0 + [0]
                  [0 1 2]     [1]
       orientation:
        a#(a(b(x1))) = [0 1 2]x1 + [1] >= [0 0 1]x1 = a#(a(x1))
        
        a#(a(b(x1))) = [0 1 2]x1 + [1] >= [0 1 0]x1 = a#(x1)
        
                      [0 2 4]     [2]    [0 2 4]     [2]                    
        a(a(b(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = c(a(c(a(a(x1)))))
                      [0 0 0]     [0]    [0 0 0]     [0]                    
        
                   [0 0 0]     [0]    [0 0 0]     [0]           
        a(c(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(a(x1))
                   [2 0 1]     [1]    [2 0 1]     [1]           
       problem:
        DPs:
         
        TRS:
         a(a(b(x1))) -> c(a(c(a(a(x1)))))
         a(c(x1)) -> b(a(x1))
       Qed