YES

Problem:
 a(b(x1)) -> b(a(a(x1)))
 b(x1) -> c(a(c(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#(x1) -> a#(c(x1))
   a#(a(x1)) -> a#(c(a(x1)))
  TRS:
   a(b(x1)) -> b(a(a(x1)))
   b(x1) -> c(a(c(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#(x1) -> a#(c(x1))
    a#(a(x1)) -> a#(c(a(x1)))
   TRS:
    a(b(x1)) -> b(a(a(x1)))
    b(x1) -> c(a(c(x1)))
    a(a(x1)) -> a(c(a(x1)))
   graph:
    b#(x1) -> a#(c(x1)) -> a#(a(x1)) -> a#(c(a(x1)))
    b#(x1) -> a#(c(x1)) -> a#(b(x1)) -> b#(a(a(x1)))
    b#(x1) -> a#(c(x1)) -> a#(b(x1)) -> a#(a(x1))
    b#(x1) -> a#(c(x1)) -> a#(b(x1)) -> a#(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#(x1) -> a#(c(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#(x1) -> a#(c(x1))
     a#(a(x1)) -> a#(c(a(x1)))
    TRS:
     a(b(x1)) -> b(a(a(x1)))
     b(x1) -> c(a(c(x1)))
     a(a(x1)) -> a(c(a(x1)))
    graph:
     a#(b(x1)) -> b#(a(a(x1))) -> b#(x1) -> a#(c(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)))
    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(x1) -> c(a(c(x1)))
      a(a(x1)) -> a(c(a(x1)))
     KBO Processor:
      argument filtering:
       pi(b) = [0]
       pi(a) = 0
       pi(c) = 0
       pi(a#) = 0
      weight function:
       w0 = 1
       w(a#) = w(c) = 1
       w(a) = w(b) = 0
      precedence:
       a# ~ c ~ a ~ b
      problem:
       DPs:
        
       TRS:
        a(b(x1)) -> b(a(a(x1)))
        b(x1) -> c(a(c(x1)))
        a(a(x1)) -> a(c(a(x1)))
      Qed