YES

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

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