NO
af/ONE-SORTED/738.trs
Input rules:
   [ a -> a,
     f(b,a) -> f(a,b),
     f(?x:o,a) -> b ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ a -> a,
     f(b,a) -> f(a,b),
     f(?x:o,a) -> b ]
Constructor pattern: [f(?x_1,?x_2),b]
Defined pattern: [a]
Constructor subsystem:
   [ ]
Modified Constructor subsystem:
   [ ]
No orientable rules for a. Add rules, and retry...
failed to construct defining rules
Retry with a different D/C-partition.
Constructor pattern: [f(?x_1,?x_2),b,a]
Defined pattern: []
Constructor subsystem:
   [ a -> a,
     f(b,a) -> f(a,b),
     f(?x,a) -> b ]
a -> a
{}
   [  ]
Modified Constructor subsystem:
   [ f(b,a) -> f(a,b),
     f(?x,a) -> b ]
Find a quasi-ordering ...
order successfully found
Precedence:
 f : Mul;
 b : Mul,  a : Mul;
Rules:
   [ f(?x,a) -> b,
     f(b,a) -> f(a,b) ]
Check confluence of constructor subsystem...
Check Termination...
unknown Terminating, Linear, unknown Oostrom, unknown strongly closed: Can't judge
...failed
failed to find an ordering.
Try to supplement auxiliary rules.
{a}{f(a,b)}{}Supplemented Rules:
   [ ]
failed to supplement auxiliary rules
check Non-Ground-Confluence...
ground constructor terms for instantiation: {b,f(b,b)}
ground terms for instantiation: {b:o,f(b,b):o}
obtain 3 rules by 3 steps unfolding
obtain 3 candidates for checking non-joinability
check by TCAP-Approximation (success)
Witness for Non-Confluence: <f(a,b) <- f(b,a) -> b>
: Success(not GCR)
(3 msec.)
0.02