YES
TRS:
 {g(a(), x) -> f(b(), x),
  f(a(), x) -> g(a(), x),
  f(a(), x) -> f(b(), x)}
 DP:
  Strict:
   {g#(a(), x) -> f#(b(), x),
    f#(a(), x) -> g#(a(), x),
    f#(a(), x) -> f#(b(), x)}
  Weak:
  {g(a(), x) -> f(b(), x),
   f(a(), x) -> g(a(), x),
   f(a(), x) -> f(b(), x)}
  EDG:
   {(f#(a(), x) -> g#(a(), x), g#(a(), x) -> f#(b(), x))}
   SCCS:
    
    Qed