MAYBE
af/ONE-SORTED/731.trs
Input rules:
   [ a -> a,
     a -> b,
     f(b,b) -> f(a,b),
     f(?x:o,a) -> f(a,b) ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ a -> a,
     a -> b,
     f(b,b) -> f(a,b),
     f(?x:o,a) -> f(a,b) ]
Constructor pattern: [b]
Defined pattern: [f(?x_2,?x_3),a]
Constructor subsystem:
   [ ]
Modified Constructor subsystem:
   [ ]
candidate for f(?x_2,?x_3):
   [ f(b,b) -> f(a,b) ]
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.
{a}{}{f(a,b)}{f(a,b)}Supplemented Rules:
   [ f(?x,a) -> f(b,b) ]
Constructor subsystem:
   [ ]
Modified Constructor subsystem:
   [ ]
candidate for f(?x_2,?x_3):
   [ f(b,b) -> f(a,b) ]
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.
{a}{}{f(a,b)}{f(a,b)}{f(b,b)}Supplemented Rules:
   [ ]
failed to supplement auxiliary rules
Retry with a different D/C-partition.
Constructor pattern: [b,f(?x_2,?x_3)]
Defined pattern: [a]
Constructor subsystem:
   [ ]
Modified Constructor subsystem:
   [ ]
candidate for a:
   [ a -> b ]
Find a quasi-ordering ...
order successfully found
Precedence:
 a : Mul;
 b : Mul;
 f : Mul;
Rules:
   [ a -> b ]
Conjectures:
   [ f(?x,a) = f(a,b),
     a = a,
     f(b,b) = f(a,b) ]
STEP 0
ES:
   [ f(?x,a) = f(a,b),
     a = a,
     f(b,b) = f(a,b) ]
HS:
   [ ]
ES0:
   [ f(?x,b) = f(b,b),
     b = b,
     f(b,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}
ground terms for instantiation: {b:o}
obtain 5 rules by 3 steps unfolding
obtain 5 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)
(74 msec.)
0.23