NO
af/ONE-SORTED/674.trs
Input rules:
   [ b -> f(f(b)),
     c -> b,
     f(f(c)) -> a ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ b -> f(f(b)),
     c -> b,
     f(f(c)) -> a ]
Constructor pattern: [f(?x_1),a]
Defined pattern: [c,b]
Constructor subsystem:
   [ ]
Modified Constructor subsystem:
   [ ]
candidate for c:
   [ c -> b ]
No orientable rules for b. Add rules, and retry...
failed to construct defining rules
Retry with a different D/C-partition.
Constructor pattern: [f(?x_1),a,b]
Defined pattern: [c]
Constructor subsystem:
   [ b -> f(f(b)) ]
Modified Constructor subsystem:
   [ b -> f(f(b)) ]
candidate for c:
   [ c -> b ]
Find a quasi-ordering ...
failed to find an ordering.
Try to supplement auxiliary rules.
{b}{}{}Supplemented Rules:
   [ ]
failed to supplement auxiliary rules
Retry with a different D/C-partition.
Constructor pattern: [f(?x_1),a,b,c]
Defined pattern: []
Constructor subsystem:
   [ b -> f(f(b)),
     c -> b,
     f(f(c)) -> a ]
Modified Constructor subsystem:
   [ b -> f(f(b)),
     c -> b,
     f(f(c)) -> a ]
Find a quasi-ordering ...
order successfully found
Precedence:
 a : Mul;
 f : Mul;
 c : Mul,  b : Mul;
Rules:
   [ c -> b ]
Check confluence of constructor subsystem...
Check Termination...
unknown Terminating, Linear, Oostrom: CR
Conjectures:
   [ b = f(f(b)),
     f(f(c)) = a ]
STEP 0
ES:
   [ b = f(f(b)),
     f(f(c)) = a ]
HS:
   [ ]
ES0:
   [ b = f(f(b)),
     f(f(c)) = a ]
HS0:
   [ ]
ES1:
   [ b = f(f(b)),
     f(f(c)) = a ]
HS1:
   [ ]
No equation to expand
check Non-Ground-Confluence...
ground constructor terms for instantiation: {a,f(a)}
ground terms for instantiation: {a:o,f(a):o}
obtain 10 rules by 3 steps unfolding
obtain 25 candidates for checking non-joinability
check by TCAP-Approximation (failure)
check by Ordering(rpo), check by Tree-Automata Approximation (success)
Witness for Non-Confluence: <f(f(b)) <- f(f(c)) -> a>
: Success(not GCR)
(12 msec.)
0.03