YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(b(x1))) -> a#(x1)
   a#(a(b(x1))) -> b#(a(x1))
   b#(a(a(x1))) -> b#(x1)
   b#(a(a(x1))) -> a#(b(x1))
   b#(a(a(x1))) -> a#(a(b(x1)))
   b#(a(a(x1))) -> a#(a(a(b(x1))))
   a#(c(x1)) -> b#(x1)
  TRS:
   a(a(b(x1))) -> b(a(x1))
   b(a(a(x1))) -> a(a(a(b(x1))))
   a(c(x1)) -> c(b(x1))
  TDG Processor:
   DPs:
    a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> b#(a(x1))
    b#(a(a(x1))) -> b#(x1)
    b#(a(a(x1))) -> a#(b(x1))
    b#(a(a(x1))) -> a#(a(b(x1)))
    b#(a(a(x1))) -> a#(a(a(b(x1))))
    a#(c(x1)) -> b#(x1)
   TRS:
    a(a(b(x1))) -> b(a(x1))
    b(a(a(x1))) -> a(a(a(b(x1))))
    a(c(x1)) -> c(b(x1))
   graph:
    b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(a(b(x1))))
    b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(b(x1)))
    b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(b(x1))
    b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(x1)
    b#(a(a(x1))) -> a#(a(a(b(x1)))) -> a#(c(x1)) -> b#(x1)
    b#(a(a(x1))) -> a#(a(a(b(x1)))) -> a#(a(b(x1))) -> b#(a(x1))
    b#(a(a(x1))) -> a#(a(a(b(x1)))) -> a#(a(b(x1))) -> a#(x1)
    b#(a(a(x1))) -> a#(a(b(x1))) -> a#(c(x1)) -> b#(x1)
    b#(a(a(x1))) -> a#(a(b(x1))) -> a#(a(b(x1))) -> b#(a(x1))
    b#(a(a(x1))) -> a#(a(b(x1))) -> a#(a(b(x1))) -> a#(x1)
    b#(a(a(x1))) -> a#(b(x1)) -> a#(c(x1)) -> b#(x1)
    b#(a(a(x1))) -> a#(b(x1)) -> a#(a(b(x1))) -> b#(a(x1))
    b#(a(a(x1))) -> a#(b(x1)) -> a#(a(b(x1))) -> a#(x1)
    a#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> a#(a(a(b(x1))))
    a#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> a#(a(b(x1)))
    a#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> a#(b(x1))
    a#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> b#(x1)
    a#(a(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(a(a(b(x1))))
    a#(a(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(a(b(x1)))
    a#(a(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(x1))
    a#(a(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(x1)
    a#(a(b(x1))) -> a#(x1) -> a#(c(x1)) -> b#(x1)
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(x1))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
   Arctic Interpretation Processor:
    dimension: 1
    interpretation:
     [b#](x0) = x0 + -16,
     
     [a#](x0) = x0 + -16,
     
     [c](x0) = 14x0 + 0,
     
     [a](x0) = x0 + -16,
     
     [b](x0) = x0 + -16
    orientation:
     a#(a(b(x1))) = x1 + -16 >= x1 + -16 = a#(x1)
     
     a#(a(b(x1))) = x1 + -16 >= x1 + -16 = b#(a(x1))
     
     b#(a(a(x1))) = x1 + -16 >= x1 + -16 = b#(x1)
     
     b#(a(a(x1))) = x1 + -16 >= x1 + -16 = a#(b(x1))
     
     b#(a(a(x1))) = x1 + -16 >= x1 + -16 = a#(a(b(x1)))
     
     b#(a(a(x1))) = x1 + -16 >= x1 + -16 = a#(a(a(b(x1))))
     
     a#(c(x1)) = 14x1 + 0 >= x1 + -16 = b#(x1)
     
     a(a(b(x1))) = x1 + -16 >= x1 + -16 = b(a(x1))
     
     b(a(a(x1))) = x1 + -16 >= x1 + -16 = a(a(a(b(x1))))
     
     a(c(x1)) = 14x1 + 0 >= 14x1 + 0 = c(b(x1))
    problem:
     DPs:
      a#(a(b(x1))) -> a#(x1)
      a#(a(b(x1))) -> b#(a(x1))
      b#(a(a(x1))) -> b#(x1)
      b#(a(a(x1))) -> a#(b(x1))
      b#(a(a(x1))) -> a#(a(b(x1)))
      b#(a(a(x1))) -> a#(a(a(b(x1))))
     TRS:
      a(a(b(x1))) -> b(a(x1))
      b(a(a(x1))) -> a(a(a(b(x1))))
      a(c(x1)) -> c(b(x1))
    EDG Processor:
     DPs:
      a#(a(b(x1))) -> a#(x1)
      a#(a(b(x1))) -> b#(a(x1))
      b#(a(a(x1))) -> b#(x1)
      b#(a(a(x1))) -> a#(b(x1))
      b#(a(a(x1))) -> a#(a(b(x1)))
      b#(a(a(x1))) -> a#(a(a(b(x1))))
     TRS:
      a(a(b(x1))) -> b(a(x1))
      b(a(a(x1))) -> a(a(a(b(x1))))
      a(c(x1)) -> c(b(x1))
     graph:
      b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(x1)
      b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(b(x1))
      b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(b(x1)))
      b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(a(b(x1))))
      b#(a(a(x1))) -> a#(a(a(b(x1)))) -> a#(a(b(x1))) -> a#(x1)
      b#(a(a(x1))) -> a#(a(a(b(x1)))) -> a#(a(b(x1))) -> b#(a(x1))
      b#(a(a(x1))) -> a#(a(b(x1))) -> a#(a(b(x1))) -> a#(x1)
      b#(a(a(x1))) -> a#(a(b(x1))) -> a#(a(b(x1))) -> b#(a(x1))
      b#(a(a(x1))) -> a#(b(x1)) -> a#(a(b(x1))) -> a#(x1)
      b#(a(a(x1))) -> a#(b(x1)) -> a#(a(b(x1))) -> b#(a(x1))
      a#(a(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(x1)
      a#(a(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(x1))
      a#(a(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(a(b(x1)))
      a#(a(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(a(a(b(x1))))
      a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
      a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(x1))
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [b#](x0) = 1x0 + -15,
       
       [a#](x0) = x0,
       
       [c](x0) = 0,
       
       [a](x0) = x0,
       
       [b](x0) = 1x0 + -15
      orientation:
       a#(a(b(x1))) = 1x1 + -15 >= x1 = a#(x1)
       
       a#(a(b(x1))) = 1x1 + -15 >= 1x1 + -15 = b#(a(x1))
       
       b#(a(a(x1))) = 1x1 + -15 >= 1x1 + -15 = b#(x1)
       
       b#(a(a(x1))) = 1x1 + -15 >= 1x1 + -15 = a#(b(x1))
       
       b#(a(a(x1))) = 1x1 + -15 >= 1x1 + -15 = a#(a(b(x1)))
       
       b#(a(a(x1))) = 1x1 + -15 >= 1x1 + -15 = a#(a(a(b(x1))))
       
       a(a(b(x1))) = 1x1 + -15 >= 1x1 + -15 = b(a(x1))
       
       b(a(a(x1))) = 1x1 + -15 >= 1x1 + -15 = a(a(a(b(x1))))
       
       a(c(x1)) = 0 >= 0 = c(b(x1))
      problem:
       DPs:
        a#(a(b(x1))) -> b#(a(x1))
        b#(a(a(x1))) -> b#(x1)
        b#(a(a(x1))) -> a#(b(x1))
        b#(a(a(x1))) -> a#(a(b(x1)))
        b#(a(a(x1))) -> a#(a(a(b(x1))))
       TRS:
        a(a(b(x1))) -> b(a(x1))
        b(a(a(x1))) -> a(a(a(b(x1))))
        a(c(x1)) -> c(b(x1))
      EDG Processor:
       DPs:
        a#(a(b(x1))) -> b#(a(x1))
        b#(a(a(x1))) -> b#(x1)
        b#(a(a(x1))) -> a#(b(x1))
        b#(a(a(x1))) -> a#(a(b(x1)))
        b#(a(a(x1))) -> a#(a(a(b(x1))))
       TRS:
        a(a(b(x1))) -> b(a(x1))
        b(a(a(x1))) -> a(a(a(b(x1))))
        a(c(x1)) -> c(b(x1))
       graph:
        b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(a(b(x1))))
        b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(b(x1)))
        b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(b(x1))
        b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(x1)
        b#(a(a(x1))) -> a#(a(a(b(x1)))) -> a#(a(b(x1))) -> b#(a(x1))
        b#(a(a(x1))) -> a#(a(b(x1))) -> a#(a(b(x1))) -> b#(a(x1))
        b#(a(a(x1))) -> a#(b(x1)) -> a#(a(b(x1))) -> b#(a(x1))
        a#(a(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(a(a(b(x1))))
        a#(a(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(a(b(x1)))
        a#(a(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(x1))
        a#(a(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(x1)
       Matrix Interpretation Processor: dim=4
        
        interpretation:
         [b#](x0) = [0 1 1 0]x0 + [1],
         
         [a#](x0) = [0 0 1 1]x0,
         
                   [0 0 0 0]     [0]
                   [0 0 0 1]     [1]
         [c](x0) = [0 0 0 1]x0 + [1]
                   [0 0 0 0]     [0],
         
                   [0 0 0 1]     [0]
                   [0 0 1 0]     [0]
         [a](x0) = [1 1 0 0]x0 + [0]
                   [0 0 0 0]     [1],
         
                   [0 0 0 1]  
                   [1 1 1 0]  
         [b](x0) = [1 1 1 0]x0
                   [0 0 0 1]  
        orientation:
         a#(a(b(x1))) = [1 1 1 1]x1 + [1] >= [1 1 1 0]x1 + [1] = b#(a(x1))
         
         b#(a(a(x1))) = [1 1 1 1]x1 + [1] >= [0 1 1 0]x1 + [1] = b#(x1)
         
         b#(a(a(x1))) = [1 1 1 1]x1 + [1] >= [1 1 1 1]x1 = a#(b(x1))
         
         b#(a(a(x1))) = [1 1 1 1]x1 + [1] >= [1 1 1 1]x1 + [1] = a#(a(b(x1)))
         
         b#(a(a(x1))) = [1 1 1 1]x1 + [1] >= [1 1 1 1]x1 + [1] = a#(a(a(b(x1))))
         
                       [0 0 0 0]     [1]    [0 0 0 0]     [1]           
                       [1 1 1 1]     [0]    [1 1 1 1]     [0]           
         a(a(b(x1))) = [1 1 1 1]x1 + [0] >= [1 1 1 1]x1 + [0] = b(a(x1))
                       [0 0 0 0]     [1]    [0 0 0 0]     [1]           
         
                       [0 0 0 0]     [1]    [0 0 0 0]     [1]                 
                       [1 1 1 1]     [1]    [1 1 1 1]     [0]                 
         b(a(a(x1))) = [1 1 1 1]x1 + [1] >= [1 1 1 1]x1 + [1] = a(a(a(b(x1))))
                       [0 0 0 0]     [1]    [0 0 0 0]     [1]                 
         
                    [0 0 0 0]     [0]    [0 0 0 0]     [0]           
                    [0 0 0 1]     [1]    [0 0 0 1]     [1]           
         a(c(x1)) = [0 0 0 1]x1 + [1] >= [0 0 0 1]x1 + [1] = c(b(x1))
                    [0 0 0 0]     [1]    [0 0 0 0]     [0]           
        problem:
         DPs:
          a#(a(b(x1))) -> b#(a(x1))
          b#(a(a(x1))) -> b#(x1)
          b#(a(a(x1))) -> a#(a(b(x1)))
          b#(a(a(x1))) -> a#(a(a(b(x1))))
         TRS:
          a(a(b(x1))) -> b(a(x1))
          b(a(a(x1))) -> a(a(a(b(x1))))
          a(c(x1)) -> c(b(x1))
        EDG Processor:
         DPs:
          a#(a(b(x1))) -> b#(a(x1))
          b#(a(a(x1))) -> b#(x1)
          b#(a(a(x1))) -> a#(a(b(x1)))
          b#(a(a(x1))) -> a#(a(a(b(x1))))
         TRS:
          a(a(b(x1))) -> b(a(x1))
          b(a(a(x1))) -> a(a(a(b(x1))))
          a(c(x1)) -> c(b(x1))
         graph:
          b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(x1)
          b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(b(x1)))
          b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(a(b(x1))))
          b#(a(a(x1))) -> a#(a(a(b(x1)))) -> a#(a(b(x1))) -> b#(a(x1))
          b#(a(a(x1))) -> a#(a(b(x1))) -> a#(a(b(x1))) -> b#(a(x1))
          a#(a(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(x1)
          a#(a(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(a(b(x1)))
          a#(a(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(a(a(b(x1))))
         Matrix Interpretation Processor: dim=4
          
          interpretation:
           [b#](x0) = [1 1 1 0]x0,
           
           [a#](x0) = [1 0 0 1]x0,
           
                     [1]
                     [0]
           [c](x0) = [1]
                     [0],
           
                     [0 1 1 0]     [0]
                     [0 0 0 1]     [0]
           [a](x0) = [1 0 0 0]x0 + [0]
                     [0 0 0 0]     [1],
           
                     [1 1 1 0]  
                     [0 0 0 1]  
           [b](x0) = [1 1 1 0]x0
                     [0 0 0 1]  
          orientation:
           a#(a(b(x1))) = [1 1 1 1]x1 + [1] >= [1 1 1 1]x1 = b#(a(x1))
           
           b#(a(a(x1))) = [1 1 1 1]x1 + [1] >= [1 1 1 0]x1 = b#(x1)
           
           b#(a(a(x1))) = [1 1 1 1]x1 + [1] >= [1 1 1 1]x1 + [1] = a#(a(b(x1)))
           
           b#(a(a(x1))) = [1 1 1 1]x1 + [1] >= [1 1 1 1]x1 + [1] = a#(a(a(b(x1))))
           
                         [1 1 1 1]     [0]    [1 1 1 1]     [0]           
                         [0 0 0 0]     [1]    [0 0 0 0]     [1]           
           a(a(b(x1))) = [1 1 1 1]x1 + [0] >= [1 1 1 1]x1 + [0] = b(a(x1))
                         [0 0 0 0]     [1]    [0 0 0 0]     [1]           
           
                         [1 1 1 1]     [1]    [1 1 1 1]     [1]                 
                         [0 0 0 0]     [1]    [0 0 0 0]     [1]                 
           b(a(a(x1))) = [1 1 1 1]x1 + [1] >= [1 1 1 1]x1 + [0] = a(a(a(b(x1))))
                         [0 0 0 0]     [1]    [0 0 0 0]     [1]                 
           
                      [1]    [1]           
                      [0]    [0]           
           a(c(x1)) = [1] >= [1] = c(b(x1))
                      [1]    [0]           
          problem:
           DPs:
            b#(a(a(x1))) -> a#(a(b(x1)))
            b#(a(a(x1))) -> a#(a(a(b(x1))))
           TRS:
            a(a(b(x1))) -> b(a(x1))
            b(a(a(x1))) -> a(a(a(b(x1))))
            a(c(x1)) -> c(b(x1))
          EDG Processor:
           DPs:
            b#(a(a(x1))) -> a#(a(b(x1)))
            b#(a(a(x1))) -> a#(a(a(b(x1))))
           TRS:
            a(a(b(x1))) -> b(a(x1))
            b(a(a(x1))) -> a(a(a(b(x1))))
            a(c(x1)) -> c(b(x1))
           graph:
            
           Qed