YES

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

Proof:
 DP Processor:
  DPs:
   b#(a(a(x1))) -> c#(x1)
   b#(a(a(x1))) -> b#(c(x1))
   b#(a(a(x1))) -> a#(b(c(x1)))
   c#(a(x1)) -> c#(x1)
   c#(a(x1)) -> a#(c(x1))
   b#(c(a(x1))) -> c#(x1)
   b#(c(a(x1))) -> b#(c(x1))
   b#(c(a(x1))) -> a#(b(c(x1)))
   c#(b(x1)) -> a#(x1)
   c#(b(x1)) -> b#(a(x1))
   a#(c(b(x1))) -> a#(x1)
   a#(c(b(x1))) -> b#(a(x1))
   a#(c(b(x1))) -> c#(b(a(x1)))
  TRS:
   b(a(a(x1))) -> a(b(c(x1)))
   c(a(x1)) -> a(c(x1))
   b(c(a(x1))) -> a(b(c(x1)))
   c(b(x1)) -> b(a(x1))
   a(c(b(x1))) -> c(b(a(x1)))
  TDG Processor:
   DPs:
    b#(a(a(x1))) -> c#(x1)
    b#(a(a(x1))) -> b#(c(x1))
    b#(a(a(x1))) -> a#(b(c(x1)))
    c#(a(x1)) -> c#(x1)
    c#(a(x1)) -> a#(c(x1))
    b#(c(a(x1))) -> c#(x1)
    b#(c(a(x1))) -> b#(c(x1))
    b#(c(a(x1))) -> a#(b(c(x1)))
    c#(b(x1)) -> a#(x1)
    c#(b(x1)) -> b#(a(x1))
    a#(c(b(x1))) -> a#(x1)
    a#(c(b(x1))) -> b#(a(x1))
    a#(c(b(x1))) -> c#(b(a(x1)))
   TRS:
    b(a(a(x1))) -> a(b(c(x1)))
    c(a(x1)) -> a(c(x1))
    b(c(a(x1))) -> a(b(c(x1)))
    c(b(x1)) -> b(a(x1))
    a(c(b(x1))) -> c(b(a(x1)))
   graph:
    a#(c(b(x1))) -> a#(x1) -> a#(c(b(x1))) -> c#(b(a(x1)))
    a#(c(b(x1))) -> a#(x1) -> a#(c(b(x1))) -> b#(a(x1))
    a#(c(b(x1))) -> a#(x1) -> a#(c(b(x1))) -> a#(x1)
    a#(c(b(x1))) -> c#(b(a(x1))) -> c#(b(x1)) -> b#(a(x1))
    a#(c(b(x1))) -> c#(b(a(x1))) -> c#(b(x1)) -> a#(x1)
    a#(c(b(x1))) -> c#(b(a(x1))) -> c#(a(x1)) -> a#(c(x1))
    a#(c(b(x1))) -> c#(b(a(x1))) -> c#(a(x1)) -> c#(x1)
    a#(c(b(x1))) -> b#(a(x1)) -> b#(c(a(x1))) -> a#(b(c(x1)))
    a#(c(b(x1))) -> b#(a(x1)) -> b#(c(a(x1))) -> b#(c(x1))
    a#(c(b(x1))) -> b#(a(x1)) -> b#(c(a(x1))) -> c#(x1)
    a#(c(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(c(x1)))
    a#(c(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(c(x1))
    a#(c(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> c#(x1)
    c#(b(x1)) -> a#(x1) -> a#(c(b(x1))) -> c#(b(a(x1)))
    c#(b(x1)) -> a#(x1) -> a#(c(b(x1))) -> b#(a(x1))
    c#(b(x1)) -> a#(x1) -> a#(c(b(x1))) -> a#(x1)
    c#(b(x1)) -> b#(a(x1)) -> b#(c(a(x1))) -> a#(b(c(x1)))
    c#(b(x1)) -> b#(a(x1)) -> b#(c(a(x1))) -> b#(c(x1))
    c#(b(x1)) -> b#(a(x1)) -> b#(c(a(x1))) -> c#(x1)
    c#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(c(x1)))
    c#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(c(x1))
    c#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> c#(x1)
    c#(a(x1)) -> a#(c(x1)) -> a#(c(b(x1))) -> c#(b(a(x1)))
    c#(a(x1)) -> a#(c(x1)) -> a#(c(b(x1))) -> b#(a(x1))
    c#(a(x1)) -> a#(c(x1)) -> a#(c(b(x1))) -> a#(x1)
    c#(a(x1)) -> c#(x1) -> c#(b(x1)) -> b#(a(x1))
    c#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(x1)
    c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(c(x1))
    c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1)
    b#(c(a(x1))) -> a#(b(c(x1))) -> a#(c(b(x1))) -> c#(b(a(x1)))
    b#(c(a(x1))) -> a#(b(c(x1))) -> a#(c(b(x1))) -> b#(a(x1))
    b#(c(a(x1))) -> a#(b(c(x1))) -> a#(c(b(x1))) -> a#(x1)
    b#(c(a(x1))) -> c#(x1) -> c#(b(x1)) -> b#(a(x1))
    b#(c(a(x1))) -> c#(x1) -> c#(b(x1)) -> a#(x1)
    b#(c(a(x1))) -> c#(x1) -> c#(a(x1)) -> a#(c(x1))
    b#(c(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(x1)
    b#(c(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> a#(b(c(x1)))
    b#(c(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> b#(c(x1))
    b#(c(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> c#(x1)
    b#(c(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> a#(b(c(x1)))
    b#(c(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> b#(c(x1))
    b#(c(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> c#(x1)
    b#(a(a(x1))) -> a#(b(c(x1))) -> a#(c(b(x1))) -> c#(b(a(x1)))
    b#(a(a(x1))) -> a#(b(c(x1))) -> a#(c(b(x1))) -> b#(a(x1))
    b#(a(a(x1))) -> a#(b(c(x1))) -> a#(c(b(x1))) -> a#(x1)
    b#(a(a(x1))) -> c#(x1) -> c#(b(x1)) -> b#(a(x1))
    b#(a(a(x1))) -> c#(x1) -> c#(b(x1)) -> a#(x1)
    b#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> a#(c(x1))
    b#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(x1)
    b#(a(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> a#(b(c(x1)))
    b#(a(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> b#(c(x1))
    b#(a(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> c#(x1)
    b#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> a#(b(c(x1)))
    b#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> b#(c(x1))
    b#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> c#(x1)
   Arctic Interpretation Processor:
    dimension: 1
    interpretation:
     [a#](x0) = x0,
     
     [c#](x0) = x0 + 0,
     
     [b#](x0) = 4x0 + 0,
     
     [c](x0) = x0,
     
     [b](x0) = 4x0 + 0,
     
     [a](x0) = x0
    orientation:
     b#(a(a(x1))) = 4x1 + 0 >= x1 + 0 = c#(x1)
     
     b#(a(a(x1))) = 4x1 + 0 >= 4x1 + 0 = b#(c(x1))
     
     b#(a(a(x1))) = 4x1 + 0 >= 4x1 + 0 = a#(b(c(x1)))
     
     c#(a(x1)) = x1 + 0 >= x1 + 0 = c#(x1)
     
     c#(a(x1)) = x1 + 0 >= x1 = a#(c(x1))
     
     b#(c(a(x1))) = 4x1 + 0 >= x1 + 0 = c#(x1)
     
     b#(c(a(x1))) = 4x1 + 0 >= 4x1 + 0 = b#(c(x1))
     
     b#(c(a(x1))) = 4x1 + 0 >= 4x1 + 0 = a#(b(c(x1)))
     
     c#(b(x1)) = 4x1 + 0 >= x1 = a#(x1)
     
     c#(b(x1)) = 4x1 + 0 >= 4x1 + 0 = b#(a(x1))
     
     a#(c(b(x1))) = 4x1 + 0 >= x1 = a#(x1)
     
     a#(c(b(x1))) = 4x1 + 0 >= 4x1 + 0 = b#(a(x1))
     
     a#(c(b(x1))) = 4x1 + 0 >= 4x1 + 0 = c#(b(a(x1)))
     
     b(a(a(x1))) = 4x1 + 0 >= 4x1 + 0 = a(b(c(x1)))
     
     c(a(x1)) = x1 >= x1 = a(c(x1))
     
     b(c(a(x1))) = 4x1 + 0 >= 4x1 + 0 = a(b(c(x1)))
     
     c(b(x1)) = 4x1 + 0 >= 4x1 + 0 = b(a(x1))
     
     a(c(b(x1))) = 4x1 + 0 >= 4x1 + 0 = c(b(a(x1)))
    problem:
     DPs:
      b#(a(a(x1))) -> c#(x1)
      b#(a(a(x1))) -> b#(c(x1))
      b#(a(a(x1))) -> a#(b(c(x1)))
      c#(a(x1)) -> c#(x1)
      c#(a(x1)) -> a#(c(x1))
      b#(c(a(x1))) -> c#(x1)
      b#(c(a(x1))) -> b#(c(x1))
      b#(c(a(x1))) -> a#(b(c(x1)))
      c#(b(x1)) -> b#(a(x1))
      a#(c(b(x1))) -> b#(a(x1))
      a#(c(b(x1))) -> c#(b(a(x1)))
     TRS:
      b(a(a(x1))) -> a(b(c(x1)))
      c(a(x1)) -> a(c(x1))
      b(c(a(x1))) -> a(b(c(x1)))
      c(b(x1)) -> b(a(x1))
      a(c(b(x1))) -> c(b(a(x1)))
    EDG Processor:
     DPs:
      b#(a(a(x1))) -> c#(x1)
      b#(a(a(x1))) -> b#(c(x1))
      b#(a(a(x1))) -> a#(b(c(x1)))
      c#(a(x1)) -> c#(x1)
      c#(a(x1)) -> a#(c(x1))
      b#(c(a(x1))) -> c#(x1)
      b#(c(a(x1))) -> b#(c(x1))
      b#(c(a(x1))) -> a#(b(c(x1)))
      c#(b(x1)) -> b#(a(x1))
      a#(c(b(x1))) -> b#(a(x1))
      a#(c(b(x1))) -> c#(b(a(x1)))
     TRS:
      b(a(a(x1))) -> a(b(c(x1)))
      c(a(x1)) -> a(c(x1))
      b(c(a(x1))) -> a(b(c(x1)))
      c(b(x1)) -> b(a(x1))
      a(c(b(x1))) -> c(b(a(x1)))
     graph:
      a#(c(b(x1))) -> c#(b(a(x1))) -> c#(a(x1)) -> c#(x1)
      a#(c(b(x1))) -> c#(b(a(x1))) -> c#(a(x1)) -> a#(c(x1))
      a#(c(b(x1))) -> c#(b(a(x1))) -> c#(b(x1)) -> b#(a(x1))
      a#(c(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> c#(x1)
      a#(c(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(c(x1))
      a#(c(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(c(x1)))
      a#(c(b(x1))) -> b#(a(x1)) -> b#(c(a(x1))) -> c#(x1)
      a#(c(b(x1))) -> b#(a(x1)) -> b#(c(a(x1))) -> b#(c(x1))
      a#(c(b(x1))) -> b#(a(x1)) -> b#(c(a(x1))) -> a#(b(c(x1)))
      c#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> c#(x1)
      c#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(c(x1))
      c#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(c(x1)))
      c#(b(x1)) -> b#(a(x1)) -> b#(c(a(x1))) -> c#(x1)
      c#(b(x1)) -> b#(a(x1)) -> b#(c(a(x1))) -> b#(c(x1))
      c#(b(x1)) -> b#(a(x1)) -> b#(c(a(x1))) -> a#(b(c(x1)))
      c#(a(x1)) -> a#(c(x1)) -> a#(c(b(x1))) -> b#(a(x1))
      c#(a(x1)) -> a#(c(x1)) -> a#(c(b(x1))) -> c#(b(a(x1)))
      c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1)
      c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(c(x1))
      c#(a(x1)) -> c#(x1) -> c#(b(x1)) -> b#(a(x1))
      b#(c(a(x1))) -> a#(b(c(x1))) -> a#(c(b(x1))) -> b#(a(x1))
      b#(c(a(x1))) -> a#(b(c(x1))) -> a#(c(b(x1))) -> c#(b(a(x1)))
      b#(c(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(x1)
      b#(c(a(x1))) -> c#(x1) -> c#(a(x1)) -> a#(c(x1))
      b#(c(a(x1))) -> c#(x1) -> c#(b(x1)) -> b#(a(x1))
      b#(c(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> c#(x1)
      b#(c(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> b#(c(x1))
      b#(c(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> a#(b(c(x1)))
      b#(c(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> c#(x1)
      b#(c(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> b#(c(x1))
      b#(c(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> a#(b(c(x1)))
      b#(a(a(x1))) -> a#(b(c(x1))) -> a#(c(b(x1))) -> b#(a(x1))
      b#(a(a(x1))) -> a#(b(c(x1))) -> a#(c(b(x1))) -> c#(b(a(x1)))
      b#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(x1)
      b#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> a#(c(x1))
      b#(a(a(x1))) -> c#(x1) -> c#(b(x1)) -> b#(a(x1))
      b#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> c#(x1)
      b#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> b#(c(x1))
      b#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> a#(b(c(x1)))
      b#(a(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> c#(x1)
      b#(a(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> b#(c(x1))
      b#(a(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> a#(b(c(x1)))
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [a#](x0) = x0,
       
       [c#](x0) = x0 + 0,
       
       [b#](x0) = 3x0 + 0,
       
       [c](x0) = 1x0 + -3,
       
       [b](x0) = 4x0 + 2,
       
       [a](x0) = 1x0 + -1
      orientation:
       b#(a(a(x1))) = 5x1 + 3 >= x1 + 0 = c#(x1)
       
       b#(a(a(x1))) = 5x1 + 3 >= 4x1 + 0 = b#(c(x1))
       
       b#(a(a(x1))) = 5x1 + 3 >= 5x1 + 2 = a#(b(c(x1)))
       
       c#(a(x1)) = 1x1 + 0 >= x1 + 0 = c#(x1)
       
       c#(a(x1)) = 1x1 + 0 >= 1x1 + -3 = a#(c(x1))
       
       b#(c(a(x1))) = 5x1 + 3 >= x1 + 0 = c#(x1)
       
       b#(c(a(x1))) = 5x1 + 3 >= 4x1 + 0 = b#(c(x1))
       
       b#(c(a(x1))) = 5x1 + 3 >= 5x1 + 2 = a#(b(c(x1)))
       
       c#(b(x1)) = 4x1 + 2 >= 4x1 + 2 = b#(a(x1))
       
       a#(c(b(x1))) = 5x1 + 3 >= 4x1 + 2 = b#(a(x1))
       
       a#(c(b(x1))) = 5x1 + 3 >= 5x1 + 3 = c#(b(a(x1)))
       
       b(a(a(x1))) = 6x1 + 4 >= 6x1 + 3 = a(b(c(x1)))
       
       c(a(x1)) = 2x1 + 0 >= 2x1 + -1 = a(c(x1))
       
       b(c(a(x1))) = 6x1 + 4 >= 6x1 + 3 = a(b(c(x1)))
       
       c(b(x1)) = 5x1 + 3 >= 5x1 + 3 = b(a(x1))
       
       a(c(b(x1))) = 6x1 + 4 >= 6x1 + 4 = c(b(a(x1)))
      problem:
       DPs:
        b#(a(a(x1))) -> a#(b(c(x1)))
        c#(a(x1)) -> c#(x1)
        c#(a(x1)) -> a#(c(x1))
        b#(c(a(x1))) -> a#(b(c(x1)))
        c#(b(x1)) -> b#(a(x1))
        a#(c(b(x1))) -> c#(b(a(x1)))
       TRS:
        b(a(a(x1))) -> a(b(c(x1)))
        c(a(x1)) -> a(c(x1))
        b(c(a(x1))) -> a(b(c(x1)))
        c(b(x1)) -> b(a(x1))
        a(c(b(x1))) -> c(b(a(x1)))
      EDG Processor:
       DPs:
        b#(a(a(x1))) -> a#(b(c(x1)))
        c#(a(x1)) -> c#(x1)
        c#(a(x1)) -> a#(c(x1))
        b#(c(a(x1))) -> a#(b(c(x1)))
        c#(b(x1)) -> b#(a(x1))
        a#(c(b(x1))) -> c#(b(a(x1)))
       TRS:
        b(a(a(x1))) -> a(b(c(x1)))
        c(a(x1)) -> a(c(x1))
        b(c(a(x1))) -> a(b(c(x1)))
        c(b(x1)) -> b(a(x1))
        a(c(b(x1))) -> c(b(a(x1)))
       graph:
        a#(c(b(x1))) -> c#(b(a(x1))) -> c#(b(x1)) -> b#(a(x1))
        a#(c(b(x1))) -> c#(b(a(x1))) -> c#(a(x1)) -> a#(c(x1))
        a#(c(b(x1))) -> c#(b(a(x1))) -> c#(a(x1)) -> c#(x1)
        c#(b(x1)) -> b#(a(x1)) -> b#(c(a(x1))) -> a#(b(c(x1)))
        c#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(c(x1)))
        c#(a(x1)) -> a#(c(x1)) -> a#(c(b(x1))) -> c#(b(a(x1)))
        c#(a(x1)) -> c#(x1) -> c#(b(x1)) -> b#(a(x1))
        c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(c(x1))
        c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1)
        b#(c(a(x1))) -> a#(b(c(x1))) -> a#(c(b(x1))) -> c#(b(a(x1)))
        b#(a(a(x1))) -> a#(b(c(x1))) -> a#(c(b(x1))) -> c#(b(a(x1)))
       Arctic Interpretation Processor:
        dimension: 1
        interpretation:
         [a#](x0) = 1x0 + 2,
         
         [c#](x0) = 8x0 + 0,
         
         [b#](x0) = 8,
         
         [c](x0) = 7x0,
         
         [b](x0) = 0,
         
         [a](x0) = x0 + 0
        orientation:
         b#(a(a(x1))) = 8 >= 2 = a#(b(c(x1)))
         
         c#(a(x1)) = 8x1 + 8 >= 8x1 + 0 = c#(x1)
         
         c#(a(x1)) = 8x1 + 8 >= 8x1 + 2 = a#(c(x1))
         
         b#(c(a(x1))) = 8 >= 2 = a#(b(c(x1)))
         
         c#(b(x1)) = 8 >= 8 = b#(a(x1))
         
         a#(c(b(x1))) = 8 >= 8 = c#(b(a(x1)))
         
         b(a(a(x1))) = 0 >= 0 = a(b(c(x1)))
         
         c(a(x1)) = 7x1 + 7 >= 7x1 + 0 = a(c(x1))
         
         b(c(a(x1))) = 0 >= 0 = a(b(c(x1)))
         
         c(b(x1)) = 7 >= 0 = b(a(x1))
         
         a(c(b(x1))) = 7 >= 7 = c(b(a(x1)))
        problem:
         DPs:
          c#(a(x1)) -> c#(x1)
          c#(a(x1)) -> a#(c(x1))
          c#(b(x1)) -> b#(a(x1))
          a#(c(b(x1))) -> c#(b(a(x1)))
         TRS:
          b(a(a(x1))) -> a(b(c(x1)))
          c(a(x1)) -> a(c(x1))
          b(c(a(x1))) -> a(b(c(x1)))
          c(b(x1)) -> b(a(x1))
          a(c(b(x1))) -> c(b(a(x1)))
        EDG Processor:
         DPs:
          c#(a(x1)) -> c#(x1)
          c#(a(x1)) -> a#(c(x1))
          c#(b(x1)) -> b#(a(x1))
          a#(c(b(x1))) -> c#(b(a(x1)))
         TRS:
          b(a(a(x1))) -> a(b(c(x1)))
          c(a(x1)) -> a(c(x1))
          b(c(a(x1))) -> a(b(c(x1)))
          c(b(x1)) -> b(a(x1))
          a(c(b(x1))) -> c(b(a(x1)))
         graph:
          a#(c(b(x1))) -> c#(b(a(x1))) -> c#(a(x1)) -> c#(x1)
          a#(c(b(x1))) -> c#(b(a(x1))) -> c#(a(x1)) -> a#(c(x1))
          a#(c(b(x1))) -> c#(b(a(x1))) -> c#(b(x1)) -> b#(a(x1))
          c#(a(x1)) -> a#(c(x1)) -> a#(c(b(x1))) -> c#(b(a(x1)))
          c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1)
          c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(c(x1))
          c#(a(x1)) -> c#(x1) -> c#(b(x1)) -> b#(a(x1))
         SCC Processor:
          #sccs: 1
          #rules: 3
          #arcs: 7/16
          DPs:
           a#(c(b(x1))) -> c#(b(a(x1)))
           c#(a(x1)) -> a#(c(x1))
           c#(a(x1)) -> c#(x1)
          TRS:
           b(a(a(x1))) -> a(b(c(x1)))
           c(a(x1)) -> a(c(x1))
           b(c(a(x1))) -> a(b(c(x1)))
           c(b(x1)) -> b(a(x1))
           a(c(b(x1))) -> c(b(a(x1)))
          Arctic Interpretation Processor:
           dimension: 1
           interpretation:
            [a#](x0) = 1x0,
            
            [c#](x0) = 1x0 + -16,
            
            [c](x0) = 8x0,
            
            [b](x0) = 8x0 + -8,
            
            [a](x0) = 8x0 + -16
           orientation:
            a#(c(b(x1))) = 17x1 + 1 >= 17x1 + -7 = c#(b(a(x1)))
            
            c#(a(x1)) = 9x1 + -15 >= 9x1 = a#(c(x1))
            
            c#(a(x1)) = 9x1 + -15 >= 1x1 + -16 = c#(x1)
            
            b(a(a(x1))) = 24x1 + 0 >= 24x1 + 0 = a(b(c(x1)))
            
            c(a(x1)) = 16x1 + -8 >= 16x1 + -16 = a(c(x1))
            
            b(c(a(x1))) = 24x1 + 0 >= 24x1 + 0 = a(b(c(x1)))
            
            c(b(x1)) = 16x1 + 0 >= 16x1 + -8 = b(a(x1))
            
            a(c(b(x1))) = 24x1 + 8 >= 24x1 + 0 = c(b(a(x1)))
           problem:
            DPs:
             a#(c(b(x1))) -> c#(b(a(x1)))
             c#(a(x1)) -> a#(c(x1))
            TRS:
             b(a(a(x1))) -> a(b(c(x1)))
             c(a(x1)) -> a(c(x1))
             b(c(a(x1))) -> a(b(c(x1)))
             c(b(x1)) -> b(a(x1))
             a(c(b(x1))) -> c(b(a(x1)))
           EDG Processor:
            DPs:
             a#(c(b(x1))) -> c#(b(a(x1)))
             c#(a(x1)) -> a#(c(x1))
            TRS:
             b(a(a(x1))) -> a(b(c(x1)))
             c(a(x1)) -> a(c(x1))
             b(c(a(x1))) -> a(b(c(x1)))
             c(b(x1)) -> b(a(x1))
             a(c(b(x1))) -> c(b(a(x1)))
            graph:
             a#(c(b(x1))) -> c#(b(a(x1))) -> c#(a(x1)) -> a#(c(x1))
             c#(a(x1)) -> a#(c(x1)) -> a#(c(b(x1))) -> c#(b(a(x1)))
            Matrix Interpretation Processor: dim=3
             
             interpretation:
              [a#](x0) = [1 0 0]x0,
              
              [c#](x0) = [1 0 0]x0,
              
                        [1 0 1]  
              [c](x0) = [1 1 0]x0
                        [0 1 1]  ,
              
                        [0 1 0]     [0]
              [b](x0) = [0 0 1]x0 + [1]
                        [1 0 0]     [0],
              
                        [1 0 1]     [1]
              [a](x0) = [1 1 0]x0 + [0]
                        [0 1 1]     [0]
             orientation:
              a#(c(b(x1))) = [1 1 0]x1 >= [1 1 0]x1 = c#(b(a(x1)))
              
              c#(a(x1)) = [1 0 1]x1 + [1] >= [1 0 1]x1 = a#(c(x1))
              
                            [2 1 1]     [1]    [2 1 1]     [1]              
              b(a(a(x1))) = [1 2 1]x1 + [1] >= [1 2 1]x1 + [1] = a(b(c(x1)))
                            [1 1 2]     [2]    [1 1 2]     [1]              
              
                         [1 1 2]     [1]    [1 1 2]     [1]           
              c(a(x1)) = [2 1 1]x1 + [1] >= [2 1 1]x1 + [0] = a(c(x1))
                         [1 2 1]     [0]    [1 2 1]     [0]           
              
                            [2 1 1]     [1]    [2 1 1]     [1]              
              b(c(a(x1))) = [1 2 1]x1 + [1] >= [1 2 1]x1 + [1] = a(b(c(x1)))
                            [1 1 2]     [1]    [1 1 2]     [1]              
              
                         [1 1 0]     [0]    [1 1 0]     [0]           
              c(b(x1)) = [0 1 1]x1 + [1] >= [0 1 1]x1 + [1] = b(a(x1))
                         [1 0 1]     [1]    [1 0 1]     [1]           
              
                            [2 1 1]     [2]    [2 1 1]     [1]              
              a(c(b(x1))) = [1 2 1]x1 + [1] >= [1 2 1]x1 + [1] = c(b(a(x1)))
                            [1 1 2]     [2]    [1 1 2]     [2]              
             problem:
              DPs:
               a#(c(b(x1))) -> c#(b(a(x1)))
              TRS:
               b(a(a(x1))) -> a(b(c(x1)))
               c(a(x1)) -> a(c(x1))
               b(c(a(x1))) -> a(b(c(x1)))
               c(b(x1)) -> b(a(x1))
               a(c(b(x1))) -> c(b(a(x1)))
             EDG Processor:
              DPs:
               a#(c(b(x1))) -> c#(b(a(x1)))
              TRS:
               b(a(a(x1))) -> a(b(c(x1)))
               c(a(x1)) -> a(c(x1))
               b(c(a(x1))) -> a(b(c(x1)))
               c(b(x1)) -> b(a(x1))
               a(c(b(x1))) -> c(b(a(x1)))
              graph:
               
              Qed