NO
af/ONE-SORTED/739.trs
Input rules:
   [ a -> a,
     g(g(a)) -> b,
     g(g(?x:o)) -> g(g(g(b))) ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ a -> a,
     g(g(a)) -> b,
     g(g(?x:o)) -> g(g(g(b))) ]
Constructor pattern: [g(?x_1),b]
Defined pattern: [a]
Constructor subsystem:
   [ g(g(?x)) -> g(g(g(b))) ]
g(g(?x)) -> g(g(g(b)))
{?x:=g(b)}
   [ {?x:=g(g(?x_1))};
     {?x:=b} ]
Modified Constructor subsystem:
   [ g(g(g(g(?x_1)))) -> g(g(g(b))),
     g(g(b)) -> g(g(g(b))) ]
No orientable rules for a. Add rules, and retry...
failed to construct defining rules
Retry with a different D/C-partition.
Constructor pattern: [g(?x_1),b,a]
Defined pattern: []
Constructor subsystem:
   [ a -> a,
     g(g(a)) -> b,
     g(g(?x)) -> g(g(g(b))) ]
g(g(?x)) -> g(g(g(b)))
{?x:=g(b)}
   [ {?x:=g(g(?x_1))};
     {?x:=g(a)};
     {?x:=b};
     {?x:=a} ]
a -> a
{}
   [  ]
Modified Constructor subsystem:
   [ g(g(a)) -> b,
     g(g(g(g(?x_1)))) -> g(g(g(b))),
     g(g(g(a))) -> g(g(g(b))),
     g(g(b)) -> g(g(g(b))),
     g(g(a)) -> g(g(g(b))) ]
Find a quasi-ordering ...
order successfully found
Precedence:
 b : Mul,  a : Mul;
 g : Mul;
Rules:
   [ g(g(a)) -> b,
     g(g(g(a))) -> g(g(g(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}{}{g(b),g(g(b)),g(g(g(b)))}Supplemented Rules:
   [ ]
failed to supplement auxiliary rules
check Non-Ground-Confluence...
ground constructor terms for instantiation: {b,g(b)}
ground terms for instantiation: {b:o,g(b):o}
obtain 3 rules by 3 steps unfolding
obtain 19 candidates for checking non-joinability
check by TCAP-Approximation (failure)
check by Ordering(rpo), check by Tree-Automata Approximation (success)
<F,Q,Q_f,Delta> where
   F = {(a,0),(b,0),(g,1)}
   Q = {q_0,q_1,q_{g(g(b))},q_{b},q_{g(b)}}
   Qf = {q_0,q_1}
   Delta = 
   [ b -> q_1,
     b -> q_{b},
     g(q_{g(g(b))}) -> q_0,
     g(q_{g(g(b))}) -> q_{g(g(b))},
     g(q_{b}) -> q_{g(b)},
     g(q_{g(b)}) -> q_{g(g(b))} ]
Witness for Non-Confluence: <g(g(g(b))), b>
: Success(not GCR)
(13 msec.)
0.03