YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(x1)) -> b#(x1)
   a#(a(x1)) -> c#(b(x1))
   b#(b(x1)) -> c#(x1)
   b#(b(x1)) -> a#(c(x1))
   c#(c(x1)) -> a#(x1)
   c#(c(x1)) -> b#(a(x1))
  TRS:
   a(a(x1)) -> c(b(x1))
   b(b(x1)) -> a(c(x1))
   c(c(x1)) -> b(a(x1))
  TDG Processor:
   DPs:
    a#(a(x1)) -> b#(x1)
    a#(a(x1)) -> c#(b(x1))
    b#(b(x1)) -> c#(x1)
    b#(b(x1)) -> a#(c(x1))
    c#(c(x1)) -> a#(x1)
    c#(c(x1)) -> b#(a(x1))
   TRS:
    a(a(x1)) -> c(b(x1))
    b(b(x1)) -> a(c(x1))
    c(c(x1)) -> b(a(x1))
   graph:
    c#(c(x1)) -> b#(a(x1)) -> b#(b(x1)) -> a#(c(x1))
    c#(c(x1)) -> b#(a(x1)) -> b#(b(x1)) -> c#(x1)
    c#(c(x1)) -> a#(x1) -> a#(a(x1)) -> c#(b(x1))
    c#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1)
    b#(b(x1)) -> c#(x1) -> c#(c(x1)) -> b#(a(x1))
    b#(b(x1)) -> c#(x1) -> c#(c(x1)) -> a#(x1)
    b#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(b(x1))
    b#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(x1)
    a#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> b#(a(x1))
    a#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> a#(x1)
    a#(a(x1)) -> b#(x1) -> b#(b(x1)) -> a#(c(x1))
    a#(a(x1)) -> b#(x1) -> b#(b(x1)) -> c#(x1)
   CDG Processor:
    DPs:
     a#(a(x1)) -> b#(x1)
     a#(a(x1)) -> c#(b(x1))
     b#(b(x1)) -> c#(x1)
     b#(b(x1)) -> a#(c(x1))
     c#(c(x1)) -> a#(x1)
     c#(c(x1)) -> b#(a(x1))
    TRS:
     a(a(x1)) -> c(b(x1))
     b(b(x1)) -> a(c(x1))
     c(c(x1)) -> b(a(x1))
    graph:
     
    Qed