YES

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

Proof:
 DP Processor:
  DPs:
   a#(b(x1)) -> a#(x1)
   a#(b(x1)) -> a#(a(x1))
   a#(b(x1)) -> b#(a(a(x1)))
   b#(c(x1)) -> b#(x1)
   a#(a(x1)) -> a#(c(a(x1)))
  TRS:
   a(b(x1)) -> b(a(a(x1)))
   b(c(x1)) -> c(b(x1))
   a(a(x1)) -> a(c(a(x1)))
  TDG Processor:
   DPs:
    a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> a#(a(x1))
    a#(b(x1)) -> b#(a(a(x1)))
    b#(c(x1)) -> b#(x1)
    a#(a(x1)) -> a#(c(a(x1)))
   TRS:
    a(b(x1)) -> b(a(a(x1)))
    b(c(x1)) -> c(b(x1))
    a(a(x1)) -> a(c(a(x1)))
   graph:
    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
    a#(a(x1)) -> a#(c(a(x1))) -> a#(a(x1)) -> a#(c(a(x1)))
    a#(a(x1)) -> a#(c(a(x1))) -> a#(b(x1)) -> b#(a(a(x1)))
    a#(a(x1)) -> a#(c(a(x1))) -> a#(b(x1)) -> a#(a(x1))
    a#(a(x1)) -> a#(c(a(x1))) -> a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> b#(a(a(x1))) -> b#(c(x1)) -> b#(x1)
    a#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> a#(c(a(x1)))
    a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> b#(a(a(x1)))
    a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> a#(a(x1))
    a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(c(a(x1)))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(a(a(x1)))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(a(x1))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
   EDG Processor:
    DPs:
     a#(b(x1)) -> a#(x1)
     a#(b(x1)) -> a#(a(x1))
     a#(b(x1)) -> b#(a(a(x1)))
     b#(c(x1)) -> b#(x1)
     a#(a(x1)) -> a#(c(a(x1)))
    TRS:
     a(b(x1)) -> b(a(a(x1)))
     b(c(x1)) -> c(b(x1))
     a(a(x1)) -> a(c(a(x1)))
    graph:
     b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
     a#(b(x1)) -> b#(a(a(x1))) -> b#(c(x1)) -> b#(x1)
     a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> a#(x1)
     a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> a#(a(x1))
     a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> b#(a(a(x1)))
     a#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> a#(c(a(x1)))
     a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
     a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(a(x1))
     a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(a(a(x1)))
     a#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(c(a(x1)))
    CDG Processor:
     DPs:
      a#(b(x1)) -> a#(x1)
      a#(b(x1)) -> a#(a(x1))
      a#(b(x1)) -> b#(a(a(x1)))
      b#(c(x1)) -> b#(x1)
      a#(a(x1)) -> a#(c(a(x1)))
     TRS:
      a(b(x1)) -> b(a(a(x1)))
      b(c(x1)) -> c(b(x1))
      a(a(x1)) -> a(c(a(x1)))
     graph:
      a#(b(x1)) -> b#(a(a(x1))) -> b#(c(x1)) -> b#(x1)
      a#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> a#(c(a(x1)))
      a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> b#(a(a(x1)))
      a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> a#(a(x1))
      a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> a#(x1)
      a#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(c(a(x1)))
      a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(a(a(x1)))
      a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(a(x1))
      a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
     SCC Processor:
      #sccs: 1
      #rules: 2
      #arcs: 9/25
      DPs:
       a#(b(x1)) -> a#(a(x1))
       a#(b(x1)) -> a#(x1)
      TRS:
       a(b(x1)) -> b(a(a(x1)))
       b(c(x1)) -> c(b(x1))
       a(a(x1)) -> a(c(a(x1)))
      Arctic Interpretation Processor:
       dimension: 1
       interpretation:
        [a#](x0) = 8x0,
        
        [c](x0) = x0,
        
        [a](x0) = x0,
        
        [b](x0) = 8x0
       orientation:
        a#(b(x1)) = 16x1 >= 8x1 = a#(a(x1))
        
        a#(b(x1)) = 16x1 >= 8x1 = a#(x1)
        
        a(b(x1)) = 8x1 >= 8x1 = b(a(a(x1)))
        
        b(c(x1)) = 8x1 >= 8x1 = c(b(x1))
        
        a(a(x1)) = x1 >= x1 = a(c(a(x1)))
       problem:
        DPs:
         
        TRS:
         a(b(x1)) -> b(a(a(x1)))
         b(c(x1)) -> c(b(x1))
         a(a(x1)) -> a(c(a(x1)))
       Qed