NO
af/ONE-SORTED/510.trs
Input rules:
   [ a -> a,
     f(b,?x:o) -> b,
     f(?x:o,a) -> a ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ a -> a,
     f(b,?x:o) -> b,
     f(?x:o,a) -> a ]
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,?x) -> b ]
No orientable rules for a. Add rules, and retry...
failed to construct defining rules
Retry with a different D/C-partition.
Constructor pattern: [b,a]
Defined pattern: [f(?x_2,?x_3)]
Constructor subsystem:
   [ a -> a ]
a -> a
{}
   [  ]
Modified Constructor subsystem:
   [ ]
candidate for f(?x_2,?x_3):
No canditates. Supplement rules, and retry...
patlist: 
{b,?x}
{?x,a}
Required Patterns: {f(a,b)}
failed to construct defining rules
Retry with a different D/C-partition.
Constructor pattern: [b,a,f(?x_2,?x_3)]
Defined pattern: []
Constructor subsystem:
   [ a -> a,
     f(b,?x) -> b,
     f(?x,a) -> a ]
a -> a
{}
   [  ]
Modified Constructor subsystem:
   [ f(b,?x) -> b,
     f(?x,a) -> a ]
Find a quasi-ordering ...
order successfully found
Precedence:
 b : Mul;
 a : Mul;
 f : Mul;
Rules:
   [ f(b,?x) -> b,
     f(?x,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.
{a}{}{}Supplemented Rules:
   [ ]
failed to supplement auxiliary rules
check Non-Ground-Confluence...
ground constructor terms for instantiation: {b}
ground terms for instantiation: {b:o}
obtain 3 rules by 3 steps unfolding
obtain 2 candidates for checking non-joinability
check by TCAP-Approximation (failure)
check by Ordering(rpo), check by Tree-Automata Approximation (success)
Witness for Non-Confluence: <b <- f(b,a) -> a>
: Success(not GCR)
(9 msec.)
0.02