MAYBE
af/ONE-SORTED/512.trs
Input rules:
   [ a -> b,
     f(?x:o,a) -> f(b,b),
     f(b,?x:o) -> f(b,b),
     f(f(?x:o,?y:o),?z:o) -> f(b,b) ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ a -> b,
     f(?x:o,a) -> f(b,b),
     f(b,?x:o) -> f(b,b),
     f(f(?x:o,?y:o),?z:o) -> f(b,b) ]
Constructor pattern: [b,f(?x_1,?x_2)]
Defined pattern: [a]
Constructor subsystem:
   [ f(b,?x) -> f(b,b),
     f(f(?x,?y),?z) -> f(b,b) ]
f(b,?x) -> f(b,b)
{?x:=b}
   [ {?x:=f(?x_1,?x_2)} ]
Modified Constructor subsystem:
   [ f(b,f(?x_1,?x_2)) -> f(b,b),
     f(f(?x,?y),?z) -> f(b,b) ]
candidate for a:
   [ a -> b ]
Find a quasi-ordering ...
order successfully found
Precedence:
 f : Mul;
 a : Mul;
 b : Mul;
Rules:
   [ a -> b,
     f(b,f(?x_1,?x_2)) -> f(b,b),
     f(f(?x,?y),?z) -> f(b,b) ]
Check confluence of constructor subsystem...
Check Termination...
Terminating, WCR: CR
Conjectures:
   [ f(?x,a) = f(b,b) ]
STEP 0
ES:
   [ f(?x,a) = f(b,b) ]
HS:
   [ ]
ES0:
   [ f(?x,b) = f(b,b) ]
HS0:
   [ ]
ES1:
   [ f(?x,b) = f(b,b) ]
HS1:
   [ ]
No equation to expand
check Non-Ground-Confluence...
ground constructor terms for instantiation: {b,f(b,b)}
ground terms for instantiation: {b:o,f(b,b):o}
obtain 5 rules by 3 steps unfolding
obtain 1 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)
(18 msec.)
0.07