NO
af/ONE-SORTED/697.trs
Input rules:
   [ h(h(c,a),b) -> b,
     a -> h(a,b),
     a -> a ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ h(h(c,a),b) -> b,
     a -> h(a,b),
     a -> a ]
Constructor pattern: [h(?x_1,?x_2),c,b]
Defined pattern: [a]
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: [h(?x_1,?x_2),c,b,a]
Defined pattern: []
Constructor subsystem:
   [ h(h(c,a),b) -> b,
     a -> h(a,b),
     a -> a ]
a -> a
{}
   [  ]
Modified Constructor subsystem:
   [ h(h(c,a),b) -> b,
     a -> h(a,b) ]
Find a quasi-ordering ...
order successfully found
Precedence:
 a : Mul;
 h : Mul;
 c : Mul,  b : Mul;
Rules:
   [ h(h(c,a),b) -> b ]
Check confluence of constructor subsystem...
Check Termination...
Terminating, WCR: CR
Conjectures:
   [ a = h(a,b) ]
STEP 0
ES:
   [ a = h(a,b) ]
HS:
   [ ]
ES0:
   [ a = h(a,b) ]
HS0:
   [ ]
ES1:
   [ a = h(a,b) ]
HS1:
   [ ]
No equation to expand
check Non-Ground-Confluence...
ground constructor terms for instantiation: {c,b,h(c,c),h(c,b),h(b,c),h(b,b)}
ground terms for instantiation: {c:o,b:o,h(c,c):o,h(c,b):o,h(b,c):o,h(b,b):o}
obtain 10 rules by 3 steps unfolding
obtain 52 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),(h,2)}
   Q = {q_0,q_1,q_{a},q_{b},q_{c},q_{h(a,b)},q_{h(c,h(a,b))}}
   Qf = {q_0,q_1}
   Delta = 
   [ a -> q_{a},
     b -> q_1,
     b -> q_{b},
     c -> q_{c},
     h(q_{a},q_{b}) -> q_{a},
     h(q_{a},q_{b}) -> q_{h(a,b)},
     h(q_{c},q_{h(a,b)}) -> q_{h(c,h(a,b))},
     h(q_{h(c,h(a,b))},q_{b}) -> q_0 ]
Witness for Non-Confluence: <h(h(c,h(a,b)),b), b>
: Success(not GCR)
(49 msec.)
0.08