MAYBE
af/ONE-SORTED/508.trs
Input rules:
   [ a -> b,
     b -> f(a,a),
     f(?x:o,a) -> b ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ a -> b,
     b -> f(a,a),
     f(?x:o,a) -> b ]
Constructor pattern: []
Defined pattern: [f(?x_1,?x_2),b,a]
Constructor subsystem:
   [ ]
Modified Constructor subsystem:
   [ ]
No orientable rules for f(?x_1,?x_2). Add rules, and retry...
failed to construct defining rules
Retry with a different D/C-partition.
Constructor pattern: [f(?x_1,?x_2)]
Defined pattern: [b,a]
Constructor subsystem:
   [ ]
Modified Constructor subsystem:
   [ ]
candidate for b:
   [ b -> f(a,a) ]
candidate for a:
   [ a -> b ]
Find a quasi-ordering ...
encodeSameNthStatus f/0, f/1
encodeSameNthStatus(sub) logArF:1, logArG:1
failed to find an ordering.
Try to supplement auxiliary rules.
{}{}{}Supplemented Rules:
   [ ]
failed to supplement auxiliary rules
check Non-Ground-Confluence...
ground constructor terms for instantiation: {}
ground terms for instantiation: {a:o}
obtain 11 rules by 3 steps unfolding
obtain 100 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)
(450 msec.)
3.12