YES
(ignored inputs)COMMENT the following rules are removed from the original TRS g ( f ( a ( ) ) ) -> a ( )
Rewrite Rules:
   [ f(f(g(g(?x)))) -> f(a),
     g(a) -> a,
     f(a) -> a,
     f(f(f(?x))) -> a,
     f(f(a)) -> a ]
Apply Direct Methods...
Inner CPs:
   [ f(f(g(a))) = f(a),
     f(f(a)) = a,
     f(f(f(a))) = a,
     f(f(a)) = a,
     f(a) = a,
     f(f(a)) = a,
     f(a) = a,
     f(a) = a,
     f(f(a)) = a ]
Outer CPs:
   [  ]
not Overlay, check Termination...
Terminating, WCR
Knuth & Bendix
Direct Methods: CR

Combined result: CR
/tmp/filetEeGbk.trs: Success(CR)
(0 msec.)