YES

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

Proof:
 DP Processor:
  DPs:
   a#(c(x1)) -> a#(x1)
   a#(c(x1)) -> a#(a(x1))
   a#(c(x1)) -> b#(c(a(a(x1))))
  TRS:
   a(a(b(x1))) -> c(x1)
   a(c(x1)) -> b(c(a(a(x1))))
   b(c(x1)) -> x1
  TDG Processor:
   DPs:
    a#(c(x1)) -> a#(x1)
    a#(c(x1)) -> a#(a(x1))
    a#(c(x1)) -> b#(c(a(a(x1))))
   TRS:
    a(a(b(x1))) -> c(x1)
    a(c(x1)) -> b(c(a(a(x1))))
    b(c(x1)) -> x1
   graph:
    a#(c(x1)) -> a#(a(x1)) -> a#(c(x1)) -> b#(c(a(a(x1))))
    a#(c(x1)) -> a#(a(x1)) -> a#(c(x1)) -> a#(a(x1))
    a#(c(x1)) -> a#(a(x1)) -> a#(c(x1)) -> a#(x1)
    a#(c(x1)) -> a#(x1) -> a#(c(x1)) -> b#(c(a(a(x1))))
    a#(c(x1)) -> a#(x1) -> a#(c(x1)) -> a#(a(x1))
    a#(c(x1)) -> a#(x1) -> a#(c(x1)) -> a#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 6/9
    DPs:
     a#(c(x1)) -> a#(a(x1))
     a#(c(x1)) -> a#(x1)
    TRS:
     a(a(b(x1))) -> c(x1)
     a(c(x1)) -> b(c(a(a(x1))))
     b(c(x1)) -> x1
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [a#](x0) = 3/2x0 + 6,
      
      [c](x0) = 2x0 + 1,
      
      [a](x0) = 2x0,
      
      [b](x0) = 1/2x0 + 3/2
     orientation:
      a#(c(x1)) = 3x1 + 15/2 >= 3x1 + 6 = a#(a(x1))
      
      a#(c(x1)) = 3x1 + 15/2 >= 3/2x1 + 6 = a#(x1)
      
      a(a(b(x1))) = 2x1 + 6 >= 2x1 + 1 = c(x1)
      
      a(c(x1)) = 4x1 + 2 >= 4x1 + 2 = b(c(a(a(x1))))
      
      b(c(x1)) = x1 + 2 >= x1 = x1
     problem:
      DPs:
       
      TRS:
       a(a(b(x1))) -> c(x1)
       a(c(x1)) -> b(c(a(a(x1))))
       b(c(x1)) -> x1
     Qed