NO
af/ONE-SORTED/670.trs
Input rules:
   [ c -> f(c),
     c -> c,
     f(a) -> b,
     a -> c ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ c -> f(c),
     c -> c,
     f(a) -> b,
     a -> c ]
Constructor pattern: [f(?x_1),b]
Defined pattern: [a,c]
Constructor subsystem:
   [ ]
Modified Constructor subsystem:
   [ ]
candidate for a:
   [ a -> c ]
No orientable rules for c. Add rules, and retry...
failed to construct defining rules
Retry with a different D/C-partition.
Constructor pattern: [f(?x_1),b,c]
Defined pattern: [a]
Constructor subsystem:
   [ c -> f(c),
     c -> c ]
c -> c
{}
   [  ]
Modified Constructor subsystem:
   [ c -> f(c) ]
candidate for a:
   [ a -> c ]
Find a quasi-ordering ...
failed to find an ordering.
Try to supplement auxiliary rules.
{c}{c}{}{}Supplemented Rules:
   [ ]
failed to supplement auxiliary rules
Retry with a different D/C-partition.
Constructor pattern: [f(?x_1),b,c,a]
Defined pattern: []
Constructor subsystem:
   [ c -> f(c),
     c -> c,
     f(a) -> b,
     a -> c ]
c -> c
{}
   [  ]
Modified Constructor subsystem:
   [ c -> f(c),
     f(a) -> b,
     a -> c ]
Find a quasi-ordering ...
order successfully found
Precedence:
 f : Mul;
 a : Mul;
 c : Mul,  b : Mul;
Rules:
   [ f(a) -> b,
     a -> c ]
Check confluence of constructor subsystem...
Check Termination...
Terminating, not WCR: not CR
...failed
failed to find an ordering.
Try to supplement auxiliary rules.
{c}{c}{}{}Supplemented Rules:
   [ ]
failed to supplement auxiliary rules
check Non-Ground-Confluence...
ground constructor terms for instantiation: {b,f(b)}
ground terms for instantiation: {b:o,f(b):o}
obtain 10 rules by 3 steps unfolding
obtain 31 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(c) <- f(a) -> b>
: Success(not GCR)
(11 msec.)
0.03