MAYBE
af/ONE-SORTED/81.trs
Input rules:
   [ g(f(a)) -> f(g(f(a))),
     g(f(a)) -> f(f(a)),
     f(f(a)) -> f(a) ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ g(f(a)) -> f(g(f(a))),
     g(f(a)) -> f(f(a)),
     f(f(a)) -> f(a) ]
Constructor pattern: [g(?x_1),f(?x_1),a]
Defined pattern: []
Constructor subsystem:
   [ g(f(a)) -> f(g(f(a))),
     g(f(a)) -> f(f(a)),
     f(f(a)) -> f(a) ]
Modified Constructor subsystem:
   [ g(f(a)) -> f(g(f(a))),
     g(f(a)) -> f(f(a)),
     f(f(a)) -> f(a) ]
Find a quasi-ordering ...
order successfully found
Precedence:
 a : Mul;
 g : Mul,  f : Mul;
Rules:
   [ f(f(a)) -> f(a),
     g(f(a)) -> f(f(a)) ]
Check confluence of constructor subsystem...
Check Termination...
unknown Terminating, Linear, Oostrom: CR
Conjectures:
   [ g(f(a)) = f(g(f(a))) ]
STEP 0
ES:
   [ g(f(a)) = f(g(f(a))) ]
HS:
   [ ]
ES0:
   [ g(f(a)) = f(g(f(a))) ]
HS0:
   [ ]
ES1:
   [ g(f(a)) = f(g(f(a))) ]
HS1:
   [ ]
No equation to expand
check Non-Ground-Confluence...
ground constructor terms for instantiation: {a,g(a),f(a)}
ground terms for instantiation: {a:o,g(a):o,f(a):o}
obtain 10 rules by 3 steps unfolding
obtain 33 candidates for checking non-joinability
check by TCAP-Approximation (failure)
check by Ordering(rpo), check by Tree-Automata Approximation (failure)
check by Interpretation(mod2) (failure)
check by Descendants-Approximation, check by Ordering(poly) (failure)
: Failure(unknown)
(1037 msec.)
5.35