NO
af/ONE-SORTED/80.trs
Input rules:
   [ a -> f(a,b),
     f(a,b) -> f(b,a) ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ a -> f(a,b),
     f(a,b) -> f(b,a) ]
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 -> f(a,b),
     f(a,b) -> f(b,a) ]
Modified Constructor subsystem:
   [ a -> f(a,b),
     f(a,b) -> f(b,a) ]
Find a quasi-ordering ...
order successfully found
Precedence:
 b : Mul,  a : Mul;
 f : Mul;
Rules:
   [ f(a,b) -> f(b,a) ]
Check confluence of constructor subsystem...
Check Termination...
unknown Terminating, Linear, Oostrom: CR
Conjectures:
   [ a = f(a,b) ]
STEP 0
ES:
   [ a = f(a,b) ]
HS:
   [ ]
ES0:
   [ a = f(a,b) ]
HS0:
   [ ]
ES1:
   [ a = f(a,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 10 rules by 3 steps unfolding
obtain 100 candidates for checking non-joinability
check by TCAP-Approximation (success)
Witness for Non-Confluence: <f(f(b,a),b) <- a -> f(b,a)>
: Success(not GCR)
(6 msec.)
0.02