YES

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

Proof:
 DP Processor:
  DPs:
   a#(c(x1)) -> b#(x1)
   a#(c(x1)) -> a#(b(x1))
   a#(c(x1)) -> a#(a(b(x1)))
   a#(c(x1)) -> b#(c(c(a(a(b(x1))))))
  TRS:
   a(b(x1)) -> x1
   a(c(x1)) -> b(c(c(a(a(b(x1))))))
   b(c(x1)) -> x1
  TDG Processor:
   DPs:
    a#(c(x1)) -> b#(x1)
    a#(c(x1)) -> a#(b(x1))
    a#(c(x1)) -> a#(a(b(x1)))
    a#(c(x1)) -> b#(c(c(a(a(b(x1))))))
   TRS:
    a(b(x1)) -> x1
    a(c(x1)) -> b(c(c(a(a(b(x1))))))
    b(c(x1)) -> x1
   graph:
    a#(c(x1)) -> a#(a(b(x1))) -> a#(c(x1)) -> b#(c(c(a(a(b(x1))))))
    a#(c(x1)) -> a#(a(b(x1))) -> a#(c(x1)) -> a#(a(b(x1)))
    a#(c(x1)) -> a#(a(b(x1))) -> a#(c(x1)) -> a#(b(x1))
    a#(c(x1)) -> a#(a(b(x1))) -> a#(c(x1)) -> b#(x1)
    a#(c(x1)) -> a#(b(x1)) -> a#(c(x1)) -> b#(c(c(a(a(b(x1))))))
    a#(c(x1)) -> a#(b(x1)) -> a#(c(x1)) -> a#(a(b(x1)))
    a#(c(x1)) -> a#(b(x1)) -> a#(c(x1)) -> a#(b(x1))
    a#(c(x1)) -> a#(b(x1)) -> a#(c(x1)) -> b#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 8/16
    DPs:
     a#(c(x1)) -> a#(a(b(x1)))
     a#(c(x1)) -> a#(b(x1))
    TRS:
     a(b(x1)) -> x1
     a(c(x1)) -> b(c(c(a(a(b(x1))))))
     b(c(x1)) -> x1
    Arctic Interpretation Processor:
     dimension: 1
     usable rules:
      a(b(x1)) -> x1
      a(c(x1)) -> b(c(c(a(a(b(x1))))))
      b(c(x1)) -> x1
     interpretation:
      [a](x0) = 1x0 + 10,
      
      [a#](x0) = -12x0 + 0,
      
      [b](x0) = -1x0 + 2,
      
      [c](x0) = 1x0 + 14
     orientation:
      a#(c(x1)) = -11x1 + 2 >= -12x1 + 0 = a#(a(b(x1)))
      
      a#(c(x1)) = -11x1 + 2 >= -13x1 + 0 = a#(b(x1))
      
      a(b(x1)) = x1 + 10 >= x1 = x1
      
      a(c(x1)) = 2x1 + 15 >= 2x1 + 14 = b(c(c(a(a(b(x1))))))
      
      b(c(x1)) = x1 + 13 >= x1 = x1
     problem:
      DPs:
       
      TRS:
       a(b(x1)) -> x1
       a(c(x1)) -> b(c(c(a(a(b(x1))))))
       b(c(x1)) -> x1
     Qed