YES
(ignored inputs)COMMENT [130] Example 4.24 submitted by: Julian Nagele
Rewrite Rules:
   [ f(f(?x)) -> f(g(f(?x),f(?x))) ]
Apply Direct Methods...
Inner CPs:
   [ f(f(g(f(?x),f(?x)))) = f(g(f(f(?x)),f(f(?x)))) ]
Outer CPs:
   [  ]
not Overlay, check Termination...
Terminating, WCR
Knuth & Bendix
Direct Methods: CR

Combined result: CR
763.trs: Success(CR)
(0 msec.)