NO
af/ONE-SORTED/711.trs
Input rules:
   [ f(h(f(b),a)) -> b,
     f(c) -> b,
     b -> f(b) ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ f(h(f(b),a)) -> b,
     f(c) -> b,
     b -> f(b) ]
Constructor pattern: [f(?x_1),h(?x_1,?x_2),a,c]
Defined pattern: [b]
Constructor subsystem:
   [ ]
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),h(?x_1,?x_2),a,c,b]
Defined pattern: []
Constructor subsystem:
   [ f(h(f(b),a)) -> b,
     f(c) -> b,
     b -> f(b) ]
Modified Constructor subsystem:
   [ f(h(f(b),a)) -> b,
     f(c) -> b,
     b -> f(b) ]
Find a quasi-ordering ...
order successfully found
Precedence:
 c : Mul,  b : Mul;
 f : Mul;
 h : Mul;
 a : Mul;
Rules:
   [ f(h(f(b),a)) -> b,
     f(c) -> b ]
Check confluence of constructor subsystem...
Check Termination...
Terminating, WCR: CR
Conjectures:
   [ b = f(b) ]
STEP 0
ES:
   [ b = f(b) ]
HS:
   [ ]
ES0:
   [ b = f(b) ]
HS0:
   [ ]
ES1:
   [ b = f(b) ]
HS1:
   [ ]
No equation to expand
check Non-Ground-Confluence...
ground constructor terms for instantiation: {a,c,f(a),f(c),h(a,a),h(a,c),h(c,a),h(c,c)}
ground terms for instantiation: {a:o,c:o,f(a):o,f(c):o,h(a,a):o,h(a,c):o,h(c,a):o,h(c,c):o}
obtain 11 rules by 3 steps unfolding
obtain 66 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_{h(f(f(b)),a)},q_{a},q_{b},q_{f(b)},q_{f(f(b))}}
   Qf = {q_0,q_1}
   Delta = 
   [ a -> q_{a},
     b -> q_1,
     b -> q_{b},
     f(q_1) -> q_1,
     f(q_1) -> q_{b},
     f(q_{h(f(f(b)),a)}) -> q_0,
     f(q_{b}) -> q_{f(b)},
     f(q_{f(b)}) -> q_{f(f(b))},
     h(q_{f(f(b))},q_{a}) -> q_{h(f(f(b)),a)} ]
Witness for Non-Confluence: <f(h(f(f(b)),a)), b>
: Success(not GCR)
(151 msec.)
0.21