NO
af/ONE-SORTED/706.trs
Input rules:
   [ f(h(c,c)) -> a,
     a -> b,
     f(b) -> f(c),
     c -> f(c) ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ f(h(c,c)) -> a,
     a -> b,
     f(b) -> f(c),
     c -> f(c) ]
Constructor pattern: [f(?x_1),h(?x_1,?x_2),b]
Defined pattern: [a,c]
Constructor subsystem:
   [ ]
Modified Constructor subsystem:
   [ ]
candidate for a:
   [ a -> b ]
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),h(?x_1,?x_2),b,c]
Defined pattern: [a]
Constructor subsystem:
   [ f(b) -> f(c),
     c -> f(c) ]
Modified Constructor subsystem:
   [ f(b) -> f(c),
     c -> f(c) ]
candidate for a:
   [ a -> b ]
Find a quasi-ordering ...
order successfully found
Precedence:
 a : Mul;
 c : Mul,  b : Mul;
 f : Mul;
 h : Mul;
Rules:
   [ a -> b,
     f(b) -> f(c) ]
Check confluence of constructor subsystem...
Check Termination...
unknown Terminating, Linear, Oostrom: CR
Conjectures:
   [ f(h(c,c)) = a,
     c = f(c) ]
STEP 0
ES:
   [ f(h(c,c)) = a,
     c = f(c) ]
HS:
   [ ]
ES0:
   [ f(h(c,c)) = b,
     c = f(c) ]
HS0:
   [ ]
ES1:
   [ f(h(c,c)) = b,
     c = f(c) ]
HS1:
   [ ]
No equation to expand
check Non-Ground-Confluence...
ground constructor terms for instantiation: {b,f(b),h(b,b)}
ground terms for instantiation: {b:o,f(b):o,h(b,b):o}
obtain 10 rules by 3 steps unfolding
obtain 75 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),(c,0),(f,1),(h,2)}
   Q = {q_0,q_1,q_{c},q_{f(c)},q_{h(c,f(c))}}
   Qf = {q_0,q_1}
   Delta = 
   [ a -> q_1,
     b -> q_1,
     c -> q_{c},
     f(q_{c}) -> q_{c},
     f(q_{c}) -> q_{f(c)},
     f(q_{h(c,f(c))}) -> q_0,
     h(q_{c},q_{f(c)}) -> q_{h(c,f(c))} ]
Witness for Non-Confluence: <f(h(c,f(c))), a>
: Success(not GCR)
(83 msec.)
0.12