NO
af/ONE-SORTED/734.trs
Input rules:
   [ f(a,f(a,?x:o)) -> f(f(a,a),a) ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ f(a,f(a,?x:o)) -> f(f(a,a),a) ]
Constructor pattern: [f(?x_1,?x_2),a]
Defined pattern: []
Constructor subsystem:
   [ f(a,f(a,?x)) -> f(f(a,a),a) ]
Modified Constructor subsystem:
   [ f(a,f(a,?x)) -> f(f(a,a),a) ]
Find a quasi-ordering ...
encodeSameNthStatus f/0, f/1
encodeSameNthStatus(sub) logArF:1, logArG:1
order successfully found
Precedence:
 a : Lex [];
 f : Lex [1,2];
Rules:
   [ f(a,f(a,?x)) -> f(f(a,a),a) ]
Check confluence of constructor subsystem...
Check Termination...
Terminating, not WCR: not CR
...failed
failed to find an ordering.
Try to supplement auxiliary rules.
{f(a,a),f(f(a,a),a)}Supplemented Rules:
   [ ]
failed to supplement auxiliary rules
check Non-Ground-Confluence...
ground constructor terms for instantiation: {a,f(a,a)}
ground terms for instantiation: {a:o,f(a,a):o}
obtain 10 rules by 3 steps unfolding
obtain 5 candidates for checking non-joinability
check by TCAP-Approximation (success)
Witness for Non-Confluence: <f(a,f(f(a,a),a)) <- f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,a))))))))))))))))))))))))) -> f(f(a,a),a)>
: Success(not GCR)
(32 msec.)
0.04