MAYBE
af/ONE-SORTED/693.trs
Input rules:
   [ c -> b,
     a -> a,
     b -> b,
     f(f(a)) -> c ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ c -> b,
     a -> a,
     b -> b,
     f(f(a)) -> c ]
Constructor pattern: []
Defined pattern: [f(?x_1),a,b,c]
Constructor subsystem:
   [ ]
Modified Constructor subsystem:
   [ ]
No orientable rules for f(?x_1). Add rules, and retry...
failed to construct defining rules
Retry with a different D/C-partition.
Constructor pattern: [f(?x_1)]
Defined pattern: [a,b,c]
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),a]
Defined pattern: [b,c]
Constructor subsystem:
   [ a -> a ]
a -> a
{}
   [  ]
Modified Constructor subsystem:
   [ ]
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:
   [ a -> a,
     b -> b ]
b -> b
{}
   [  ]
a -> a
{}
   [  ]
Modified Constructor subsystem:
   [ ]
candidate for c:
   [ c -> b ]
Find a quasi-ordering ...
order successfully found
Precedence:
 c : Mul;
 a : Mul;
 b : Mul;
 f : Mul;
Rules:
   [ c -> b ]
Conjectures:
   [ f(f(a)) = c ]
STEP 0
ES:
   [ f(f(a)) = c ]
HS:
   [ ]
ES0:
   [ f(f(a)) = b ]
HS0:
   [ ]
ES1:
   [ f(f(a)) = b ]
HS1:
   [ ]
No equation to expand
check Non-Ground-Confluence...
ground constructor terms for instantiation: {}
ground terms for instantiation: {c:o}
obtain 5 rules by 3 steps unfolding
obtain 4 candidates for checking non-joinability
check by TCAP-Approximation (failure)
check by Ordering(rpo), check by Tree-Automata Approximation (failure)
check by Interpretation(mod2) (failure)
check by Descendants-Approximation, check by Ordering(poly) (failure)
: Failure(unknown)
(36 msec.)
0.16