YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(x1)) -> b#(x1)
   a#(a(x1)) -> a#(b(x1))
   a#(a(x1)) -> b#(a(b(x1)))
   b#(b(x1)) -> c#(b(x1))
   b#(b(x1)) -> a#(c(b(x1)))
   c#(c(x1)) -> a#(x1)
   c#(c(x1)) -> b#(a(x1))
   c#(c(x1)) -> c#(b(a(x1)))
   a#(b(x1)) -> a#(x1)
   a#(b(x1)) -> b#(a(x1))
  TRS:
   a(a(x1)) -> b(a(b(x1)))
   b(b(x1)) -> a(c(b(x1)))
   c(c(x1)) -> c(b(a(x1)))
   a(b(x1)) -> b(a(x1))
   b(c(x1)) -> c(x1)
  TDG Processor:
   DPs:
    a#(a(x1)) -> b#(x1)
    a#(a(x1)) -> a#(b(x1))
    a#(a(x1)) -> b#(a(b(x1)))
    b#(b(x1)) -> c#(b(x1))
    b#(b(x1)) -> a#(c(b(x1)))
    c#(c(x1)) -> a#(x1)
    c#(c(x1)) -> b#(a(x1))
    c#(c(x1)) -> c#(b(a(x1)))
    a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> b#(a(x1))
   TRS:
    a(a(x1)) -> b(a(b(x1)))
    b(b(x1)) -> a(c(b(x1)))
    c(c(x1)) -> c(b(a(x1)))
    a(b(x1)) -> b(a(x1))
    b(c(x1)) -> c(x1)
   graph:
    c#(c(x1)) -> c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1)))
    c#(c(x1)) -> c#(b(a(x1))) -> c#(c(x1)) -> b#(a(x1))
    c#(c(x1)) -> c#(b(a(x1))) -> c#(c(x1)) -> a#(x1)
    c#(c(x1)) -> b#(a(x1)) -> b#(b(x1)) -> a#(c(b(x1)))
    c#(c(x1)) -> b#(a(x1)) -> b#(b(x1)) -> c#(b(x1))
    c#(c(x1)) -> a#(x1) -> a#(b(x1)) -> b#(a(x1))
    c#(c(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
    c#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(b(x1)))
    c#(c(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(x1))
    c#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1)
    b#(b(x1)) -> c#(b(x1)) -> c#(c(x1)) -> c#(b(a(x1)))
    b#(b(x1)) -> c#(b(x1)) -> c#(c(x1)) -> b#(a(x1))
    b#(b(x1)) -> c#(b(x1)) -> c#(c(x1)) -> a#(x1)
    b#(b(x1)) -> a#(c(b(x1))) -> a#(b(x1)) -> b#(a(x1))
    b#(b(x1)) -> a#(c(b(x1))) -> a#(b(x1)) -> a#(x1)
    b#(b(x1)) -> a#(c(b(x1))) -> a#(a(x1)) -> b#(a(b(x1)))
    b#(b(x1)) -> a#(c(b(x1))) -> a#(a(x1)) -> a#(b(x1))
    b#(b(x1)) -> a#(c(b(x1))) -> a#(a(x1)) -> b#(x1)
    a#(b(x1)) -> b#(a(x1)) -> b#(b(x1)) -> a#(c(b(x1)))
    a#(b(x1)) -> b#(a(x1)) -> b#(b(x1)) -> c#(b(x1))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(a(x1))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(b(x1)))
    a#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(x1))
    a#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1)
    a#(a(x1)) -> b#(a(b(x1))) -> b#(b(x1)) -> a#(c(b(x1)))
    a#(a(x1)) -> b#(a(b(x1))) -> b#(b(x1)) -> c#(b(x1))
    a#(a(x1)) -> b#(x1) -> b#(b(x1)) -> a#(c(b(x1)))
    a#(a(x1)) -> b#(x1) -> b#(b(x1)) -> c#(b(x1))
    a#(a(x1)) -> a#(b(x1)) -> a#(b(x1)) -> b#(a(x1))
    a#(a(x1)) -> a#(b(x1)) -> a#(b(x1)) -> a#(x1)
    a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> b#(a(b(x1)))
    a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> a#(b(x1))
    a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> b#(x1)
   CDG Processor:
    DPs:
     a#(a(x1)) -> b#(x1)
     a#(a(x1)) -> a#(b(x1))
     a#(a(x1)) -> b#(a(b(x1)))
     b#(b(x1)) -> c#(b(x1))
     b#(b(x1)) -> a#(c(b(x1)))
     c#(c(x1)) -> a#(x1)
     c#(c(x1)) -> b#(a(x1))
     c#(c(x1)) -> c#(b(a(x1)))
     a#(b(x1)) -> a#(x1)
     a#(b(x1)) -> b#(a(x1))
    TRS:
     a(a(x1)) -> b(a(b(x1)))
     b(b(x1)) -> a(c(b(x1)))
     c(c(x1)) -> c(b(a(x1)))
     a(b(x1)) -> b(a(x1))
     b(c(x1)) -> c(x1)
    graph:
     c#(c(x1)) -> c#(b(a(x1))) -> c#(c(x1)) -> a#(x1)
     c#(c(x1)) -> c#(b(a(x1))) -> c#(c(x1)) -> b#(a(x1))
     c#(c(x1)) -> c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1)))
     c#(c(x1)) -> b#(a(x1)) -> b#(b(x1)) -> c#(b(x1))
     c#(c(x1)) -> b#(a(x1)) -> b#(b(x1)) -> a#(c(b(x1)))
     c#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1)
     c#(c(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(x1))
     c#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(b(x1)))
     c#(c(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
     c#(c(x1)) -> a#(x1) -> a#(b(x1)) -> b#(a(x1))
     b#(b(x1)) -> c#(b(x1)) -> c#(c(x1)) -> a#(x1)
     b#(b(x1)) -> c#(b(x1)) -> c#(c(x1)) -> b#(a(x1))
     b#(b(x1)) -> c#(b(x1)) -> c#(c(x1)) -> c#(b(a(x1)))
     a#(b(x1)) -> b#(a(x1)) -> b#(b(x1)) -> c#(b(x1))
     a#(b(x1)) -> b#(a(x1)) -> b#(b(x1)) -> a#(c(b(x1)))
     a#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1)
     a#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(x1))
     a#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(b(x1)))
     a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
     a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(a(x1))
     a#(a(x1)) -> b#(a(b(x1))) -> b#(b(x1)) -> c#(b(x1))
     a#(a(x1)) -> b#(a(b(x1))) -> b#(b(x1)) -> a#(c(b(x1)))
     a#(a(x1)) -> b#(x1) -> b#(b(x1)) -> c#(b(x1))
     a#(a(x1)) -> b#(x1) -> b#(b(x1)) -> a#(c(b(x1)))
     a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> b#(x1)
     a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> a#(b(x1))
     a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> b#(a(b(x1)))
     a#(a(x1)) -> a#(b(x1)) -> a#(b(x1)) -> a#(x1)
     a#(a(x1)) -> a#(b(x1)) -> a#(b(x1)) -> b#(a(x1))
    SCC Processor:
     #sccs: 1
     #rules: 9
     #arcs: 29/100
     DPs:
      c#(c(x1)) -> c#(b(a(x1)))
      c#(c(x1)) -> b#(a(x1))
      b#(b(x1)) -> c#(b(x1))
      c#(c(x1)) -> a#(x1)
      a#(b(x1)) -> b#(a(x1))
      a#(b(x1)) -> a#(x1)
      a#(a(x1)) -> b#(a(b(x1)))
      a#(a(x1)) -> a#(b(x1))
      a#(a(x1)) -> b#(x1)
     TRS:
      a(a(x1)) -> b(a(b(x1)))
      b(b(x1)) -> a(c(b(x1)))
      c(c(x1)) -> c(b(a(x1)))
      a(b(x1)) -> b(a(x1))
      b(c(x1)) -> c(x1)
     Arctic Interpretation Processor:
      dimension: 2
      interpretation:
       [c#](x0) = [-& 0 ]x0 + [0],
       
       [b#](x0) = [0 0]x0 + [0],
       
       [a#](x0) = [0 0]x0 + [0],
       
                 [-& -&]     [0]
       [c](x0) = [0  0 ]x0 + [1],
       
                 [0  0 ]     [1]
       [b](x0) = [-& 0 ]x0 + [0],
       
                 [0  0 ]     [1]
       [a](x0) = [-& -&]x0 + [0]
      orientation:
       c#(c(x1)) = [0 0]x1 + [1] >= [0] = c#(b(a(x1)))
       
       c#(c(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b#(a(x1))
       
       b#(b(x1)) = [0 0]x1 + [1] >= [-& 0 ]x1 + [0] = c#(b(x1))
       
       c#(c(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [0] = a#(x1)
       
       a#(b(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b#(a(x1))
       
       a#(b(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [0] = a#(x1)
       
       a#(a(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b#(a(b(x1)))
       
       a#(a(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [1] = a#(b(x1))
       
       a#(a(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [0] = b#(x1)
       
                  [0  0 ]     [1]    [0  0 ]     [1]              
       a(a(x1)) = [-& -&]x1 + [0] >= [-& -&]x1 + [0] = b(a(b(x1)))
       
                  [0  0 ]     [1]    [0  0 ]     [1]              
       b(b(x1)) = [-& 0 ]x1 + [0] >= [-& -&]x1 + [0] = a(c(b(x1)))
       
                  [-& -&]     [0]    [-& -&]     [0]              
       c(c(x1)) = [0  0 ]x1 + [1] >= [0  0 ]x1 + [1] = c(b(a(x1)))
       
                  [0  0 ]     [1]    [0  0 ]     [1]           
       a(b(x1)) = [-& -&]x1 + [0] >= [-& -&]x1 + [0] = b(a(x1))
       
                  [0 0]     [1]    [-& -&]     [0]        
       b(c(x1)) = [0 0]x1 + [1] >= [0  0 ]x1 + [1] = c(x1)
      problem:
       DPs:
        c#(c(x1)) -> b#(a(x1))
        b#(b(x1)) -> c#(b(x1))
        c#(c(x1)) -> a#(x1)
        a#(b(x1)) -> b#(a(x1))
        a#(b(x1)) -> a#(x1)
        a#(a(x1)) -> b#(a(b(x1)))
        a#(a(x1)) -> a#(b(x1))
        a#(a(x1)) -> b#(x1)
       TRS:
        a(a(x1)) -> b(a(b(x1)))
        b(b(x1)) -> a(c(b(x1)))
        c(c(x1)) -> c(b(a(x1)))
        a(b(x1)) -> b(a(x1))
        b(c(x1)) -> c(x1)
      EDG Processor:
       DPs:
        c#(c(x1)) -> b#(a(x1))
        b#(b(x1)) -> c#(b(x1))
        c#(c(x1)) -> a#(x1)
        a#(b(x1)) -> b#(a(x1))
        a#(b(x1)) -> a#(x1)
        a#(a(x1)) -> b#(a(b(x1)))
        a#(a(x1)) -> a#(b(x1))
        a#(a(x1)) -> b#(x1)
       TRS:
        a(a(x1)) -> b(a(b(x1)))
        b(b(x1)) -> a(c(b(x1)))
        c(c(x1)) -> c(b(a(x1)))
        a(b(x1)) -> b(a(x1))
        b(c(x1)) -> c(x1)
       graph:
        c#(c(x1)) -> b#(a(x1)) -> b#(b(x1)) -> c#(b(x1))
        c#(c(x1)) -> a#(x1) -> a#(b(x1)) -> b#(a(x1))
        c#(c(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
        c#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(b(x1)))
        c#(c(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(x1))
        c#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1)
        b#(b(x1)) -> c#(b(x1)) -> c#(c(x1)) -> b#(a(x1))
        b#(b(x1)) -> c#(b(x1)) -> c#(c(x1)) -> a#(x1)
        a#(b(x1)) -> b#(a(x1)) -> b#(b(x1)) -> c#(b(x1))
        a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(a(x1))
        a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
        a#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(b(x1)))
        a#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(x1))
        a#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1)
        a#(a(x1)) -> b#(a(b(x1))) -> b#(b(x1)) -> c#(b(x1))
        a#(a(x1)) -> b#(x1) -> b#(b(x1)) -> c#(b(x1))
        a#(a(x1)) -> a#(b(x1)) -> a#(b(x1)) -> b#(a(x1))
        a#(a(x1)) -> a#(b(x1)) -> a#(b(x1)) -> a#(x1)
        a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> b#(a(b(x1)))
        a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> a#(b(x1))
        a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> b#(x1)
       Arctic Interpretation Processor:
        dimension: 2
        interpretation:
         [c#](x0) = [0 2]x0,
         
         [b#](x0) = [0 2]x0,
         
         [a#](x0) = [2 0]x0,
         
                   [0 0]  
         [c](x0) = [0 0]x0,
         
                   [0  0 ]  
         [b](x0) = [-& 0 ]x0,
         
                   [0  0 ]  
         [a](x0) = [-& -&]x0
        orientation:
         c#(c(x1)) = [2 2]x1 >= [0 0]x1 = b#(a(x1))
         
         b#(b(x1)) = [0 2]x1 >= [0 2]x1 = c#(b(x1))
         
         c#(c(x1)) = [2 2]x1 >= [2 0]x1 = a#(x1)
         
         a#(b(x1)) = [2 2]x1 >= [0 0]x1 = b#(a(x1))
         
         a#(b(x1)) = [2 2]x1 >= [2 0]x1 = a#(x1)
         
         a#(a(x1)) = [2 2]x1 >= [0 0]x1 = b#(a(b(x1)))
         
         a#(a(x1)) = [2 2]x1 >= [2 2]x1 = a#(b(x1))
         
         a#(a(x1)) = [2 2]x1 >= [0 2]x1 = b#(x1)
         
                    [0  0 ]      [0  0 ]                
         a(a(x1)) = [-& -&]x1 >= [-& -&]x1 = b(a(b(x1)))
         
                    [0  0 ]      [0  0 ]                
         b(b(x1)) = [-& 0 ]x1 >= [-& -&]x1 = a(c(b(x1)))
         
                    [0 0]      [0 0]                
         c(c(x1)) = [0 0]x1 >= [0 0]x1 = c(b(a(x1)))
         
                    [0  0 ]      [0  0 ]             
         a(b(x1)) = [-& -&]x1 >= [-& -&]x1 = b(a(x1))
         
                    [0 0]      [0 0]          
         b(c(x1)) = [0 0]x1 >= [0 0]x1 = c(x1)
        problem:
         DPs:
          b#(b(x1)) -> c#(b(x1))
          c#(c(x1)) -> a#(x1)
          a#(b(x1)) -> a#(x1)
          a#(a(x1)) -> a#(b(x1))
          a#(a(x1)) -> b#(x1)
         TRS:
          a(a(x1)) -> b(a(b(x1)))
          b(b(x1)) -> a(c(b(x1)))
          c(c(x1)) -> c(b(a(x1)))
          a(b(x1)) -> b(a(x1))
          b(c(x1)) -> c(x1)
        EDG Processor:
         DPs:
          b#(b(x1)) -> c#(b(x1))
          c#(c(x1)) -> a#(x1)
          a#(b(x1)) -> a#(x1)
          a#(a(x1)) -> a#(b(x1))
          a#(a(x1)) -> b#(x1)
         TRS:
          a(a(x1)) -> b(a(b(x1)))
          b(b(x1)) -> a(c(b(x1)))
          c(c(x1)) -> c(b(a(x1)))
          a(b(x1)) -> b(a(x1))
          b(c(x1)) -> c(x1)
         graph:
          c#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1)
          c#(c(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(x1))
          c#(c(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
          b#(b(x1)) -> c#(b(x1)) -> c#(c(x1)) -> a#(x1)
          a#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1)
          a#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(x1))
          a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
          a#(a(x1)) -> b#(x1) -> b#(b(x1)) -> c#(b(x1))
          a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> b#(x1)
          a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> a#(b(x1))
          a#(a(x1)) -> a#(b(x1)) -> a#(b(x1)) -> a#(x1)
         Arctic Interpretation Processor:
          dimension: 3
          interpretation:
           [c#](x0) = [0 1 0]x0 + [0],
           
           [b#](x0) = [0 0 0]x0 + [0],
           
           [a#](x0) = [1 1 0]x0 + [1],
           
                     [-& 0  -&]     [0]
           [c](x0) = [0  1  0 ]x0 + [0]
                     [0  1  0 ]     [1],
           
                     [0  0  0 ]     [0]
           [b](x0) = [-& 0  -&]x0 + [0]
                     [-& 1  0 ]     [1],
           
                     [1  0  0 ]     [0]
           [a](x0) = [-& -& -&]x0 + [0]
                     [0  -& -&]     [1]
          orientation:
           b#(b(x1)) = [0 1 0]x1 + [1] >= [0 1 0]x1 + [1] = c#(b(x1))
           
           c#(c(x1)) = [1 2 1]x1 + [1] >= [1 1 0]x1 + [1] = a#(x1)
           
           a#(b(x1)) = [1 1 1]x1 + [1] >= [1 1 0]x1 + [1] = a#(x1)
           
           a#(a(x1)) = [2 1 1]x1 + [1] >= [1 1 1]x1 + [1] = a#(b(x1))
           
           a#(a(x1)) = [2 1 1]x1 + [1] >= [0 0 0]x1 + [0] = b#(x1)
           
                      [2  1  1 ]     [1]    [1  1  1 ]     [1]              
           a(a(x1)) = [-& -& -&]x1 + [0] >= [-& -& -&]x1 + [0] = b(a(b(x1)))
                      [1  0  0 ]     [1]    [0  0  0 ]     [1]              
           
                      [0  1  0 ]     [1]    [0  1  0 ]     [1]              
           b(b(x1)) = [-& 0  -&]x1 + [0] >= [-& -& -&]x1 + [0] = a(c(b(x1)))
                      [-& 1  0 ]     [1]    [-& 0  -&]     [1]              
           
                      [0 1 0]     [0]    [-& -& -&]     [0]              
           c(c(x1)) = [1 2 1]x1 + [1] >= [1  0  0 ]x1 + [1] = c(b(a(x1)))
                      [1 2 1]     [1]    [1  0  0 ]     [1]              
           
                      [1  1  1 ]     [1]    [1  0  0 ]     [1]           
           a(b(x1)) = [-& -& -&]x1 + [0] >= [-& -& -&]x1 + [0] = b(a(x1))
                      [0  0  0 ]     [1]    [0  -& -&]     [1]           
           
                      [0 1 0]     [1]    [-& 0  -&]     [0]        
           b(c(x1)) = [0 1 0]x1 + [0] >= [0  1  0 ]x1 + [0] = c(x1)
                      [1 2 1]     [1]    [0  1  0 ]     [1]        
          problem:
           DPs:
            b#(b(x1)) -> c#(b(x1))
            c#(c(x1)) -> a#(x1)
            a#(b(x1)) -> a#(x1)
            a#(a(x1)) -> a#(b(x1))
           TRS:
            a(a(x1)) -> b(a(b(x1)))
            b(b(x1)) -> a(c(b(x1)))
            c(c(x1)) -> c(b(a(x1)))
            a(b(x1)) -> b(a(x1))
            b(c(x1)) -> c(x1)
          EDG Processor:
           DPs:
            b#(b(x1)) -> c#(b(x1))
            c#(c(x1)) -> a#(x1)
            a#(b(x1)) -> a#(x1)
            a#(a(x1)) -> a#(b(x1))
           TRS:
            a(a(x1)) -> b(a(b(x1)))
            b(b(x1)) -> a(c(b(x1)))
            c(c(x1)) -> c(b(a(x1)))
            a(b(x1)) -> b(a(x1))
            b(c(x1)) -> c(x1)
           graph:
            c#(c(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
            c#(c(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(x1))
            b#(b(x1)) -> c#(b(x1)) -> c#(c(x1)) -> a#(x1)
            a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
            a#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(x1))
            a#(a(x1)) -> a#(b(x1)) -> a#(b(x1)) -> a#(x1)
            a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> a#(b(x1))
           SCC Processor:
            #sccs: 1
            #rules: 2
            #arcs: 7/16
            DPs:
             a#(a(x1)) -> a#(b(x1))
             a#(b(x1)) -> a#(x1)
            TRS:
             a(a(x1)) -> b(a(b(x1)))
             b(b(x1)) -> a(c(b(x1)))
             c(c(x1)) -> c(b(a(x1)))
             a(b(x1)) -> b(a(x1))
             b(c(x1)) -> c(x1)
            Arctic Interpretation Processor:
             dimension: 1
             interpretation:
              [a#](x0) = -2x0 + 1,
              
              [c](x0) = 0,
              
              [b](x0) = 2x0 + 3,
              
              [a](x0) = 4x0 + 5
             orientation:
              a#(a(x1)) = 2x1 + 3 >= x1 + 1 = a#(b(x1))
              
              a#(b(x1)) = x1 + 1 >= -2x1 + 1 = a#(x1)
              
              a(a(x1)) = 8x1 + 9 >= 8x1 + 9 = b(a(b(x1)))
              
              b(b(x1)) = 4x1 + 5 >= 5 = a(c(b(x1)))
              
              c(c(x1)) = 0 >= 0 = c(b(a(x1)))
              
              a(b(x1)) = 6x1 + 7 >= 6x1 + 7 = b(a(x1))
              
              b(c(x1)) = 3 >= 0 = c(x1)
             problem:
              DPs:
               a#(b(x1)) -> a#(x1)
              TRS:
               a(a(x1)) -> b(a(b(x1)))
               b(b(x1)) -> a(c(b(x1)))
               c(c(x1)) -> c(b(a(x1)))
               a(b(x1)) -> b(a(x1))
               b(c(x1)) -> c(x1)
             EDG Processor:
              DPs:
               a#(b(x1)) -> a#(x1)
              TRS:
               a(a(x1)) -> b(a(b(x1)))
               b(b(x1)) -> a(c(b(x1)))
               c(c(x1)) -> c(b(a(x1)))
               a(b(x1)) -> b(a(x1))
               b(c(x1)) -> c(x1)
              graph:
               a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
              CDG Processor:
               DPs:
                a#(b(x1)) -> a#(x1)
               TRS:
                a(a(x1)) -> b(a(b(x1)))
                b(b(x1)) -> a(c(b(x1)))
                c(c(x1)) -> c(b(a(x1)))
                a(b(x1)) -> b(a(x1))
                b(c(x1)) -> c(x1)
               graph:
                
               Qed