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: 1
     interpretation:
      [a#](x0) = 8x0,
      
      [c#](x0) = x0 + 0,
      
      [a](x0) = 12x0 + -8,
      
      [b](x0) = 4x0 + -16,
      
      [c](x0) = 4x0 + -16
     orientation:
      c#(b(b(x1))) = 8x1 + 0 >= 8x1 = a#(x1)
      
      a#(a(x1)) = 20x1 + 0 >= x1 + 0 = c#(x1)
      
      a#(a(x1)) = 20x1 + 0 >= 12x1 + -8 = a#(c(x1))
      
      a#(a(x1)) = 20x1 + 0 >= 20x1 + 0 = c#(b(a(c(x1))))
      
      c(b(b(x1))) = 12x1 + -8 >= 12x1 + -8 = a(x1)
      
      c(x1) = 4x1 + -16 >= 4x1 + -16 = b(x1)
      
      a(a(x1)) = 24x1 + 4 >= 24x1 + 4 = c(b(a(c(x1))))
     problem:
      DPs:
       c#(b(b(x1))) -> a#(x1)
       a#(a(x1)) -> 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))))
     EDG Processor:
      DPs:
       c#(b(b(x1))) -> a#(x1)
       a#(a(x1)) -> 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)) -> 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#(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#(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)
        a#(a(x1)) -> c#(x1) -> c#(b(b(x1))) -> a#(x1)
       SCC Processor:
        #sccs: 0
        #rules: 0
        #arcs: 2/9