YES
af/ONE-SORTED/223.trs
Input rules:
   [ f(f(a)) -> f(f(f(a))),
     f(f(a)) -> f(a) ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ f(f(a)) -> f(f(f(a))),
     f(f(a)) -> f(a) ]
Constructor pattern: [f(?x_1),a]
Defined pattern: []
Constructor subsystem:
   [ f(f(a)) -> f(f(f(a))),
     f(f(a)) -> f(a) ]
Modified Constructor subsystem:
   [ f(f(a)) -> f(f(f(a))),
     f(f(a)) -> f(a) ]
Find a quasi-ordering ...
order successfully found
Precedence:
 a : Mul;
 f : Mul;
Rules:
   [ f(f(a)) -> f(a) ]
Check confluence of constructor subsystem...
Check Termination...
Terminating, WCR: CR
Conjectures:
   [ f(f(a)) = f(f(f(a))) ]
STEP 0
ES:
   [ f(f(a)) = f(f(f(a))) ]
HS:
   [ ]
ES0:
   [ f(a) = f(a) ]
HS0:
   [ ]
ES1:
   [ ]
HS1:
   [ ]
: Success(GCR)
(2 msec.)
0.02