YES
(ignored inputs)COMMENT from the collection of \cite{AT2012}
Rewrite Rules:
   [ max(?x,0) -> ?x,
     max(0,?y) -> ?y,
     max(s(?x),s(?y)) -> s(max(?x,?y)),
     max(?x,?y) -> max(?y,?x) ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [ 0 = 0,
     ?x = max(0,?x),
     ?y_1 = max(?y_1,0),
     s(max(?x_2,?y_2)) = max(s(?y_2),s(?x_2)) ]
Overlay, check Innermost Termination...
unknown Innermost Terminating
unknown Knuth & Bendix
Linear
Development Closed
Direct Methods: CR

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