YES
(ignored inputs)COMMENT from the collection of \cite{AT2012}
Rewrite Rules:
   [ f(0,0) -> f(0,1),
     f(1,0) -> f(0,0),
     f(?x,?y) -> f(?y,?x) ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [ f(0,1) = f(0,0),
     f(0,0) = f(0,1) ]
Overlay, check Innermost Termination...
unknown Innermost Terminating
unknown Knuth & Bendix
Linear
Development Closed
Direct Methods: CR

Final result: CR
150.trs: Success(CR)
(0 msec.)