YES
af/ONE-SORTED/82.trs
Input rules:
   [ f(a) -> f(f(a)),
     f(?x:o) -> f(a) ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ f(a) -> f(f(a)),
     f(?x:o) -> f(a) ]
Constructor pattern: [a]
Defined pattern: [f(?x_1)]
Constructor subsystem:
   [ ]
Modified Constructor subsystem:
   [ ]
No orientable rules for f(?x_1). Add rules, and retry...
failed to construct defining rules
Retry with a different D/C-partition.
Constructor pattern: [a,f(?x_1)]
Defined pattern: []
Constructor subsystem:
   [ f(a) -> f(f(a)),
     f(?x) -> f(a) ]
f(?x) -> f(a)
{?x:=a}
   [ {?x:=f(?x_1)} ]
Modified Constructor subsystem:
   [ f(a) -> f(f(a)),
     f(f(?x_1)) -> f(a) ]
Find a quasi-ordering ...
order successfully found
Precedence:
 f : Mul;
 a : Mul;
Rules:
   [ f(f(?x_1)) -> f(a) ]
Check confluence of constructor subsystem...
Check Termination...
Terminating, WCR: CR
Conjectures:
   [ f(a) = f(f(a)) ]
STEP 0
ES:
   [ f(a) = f(f(a)) ]
HS:
   [ ]
ES0:
   [ f(a) = f(a) ]
HS0:
   [ ]
ES1:
   [ ]
HS1:
   [ ]
: Success(GCR)
(1 msec.)
0.02