NO
af/ONE-SORTED/686.trs
Input rules:
   [ b -> h(c,f(b)),
     a -> c,
     h(h(h(f(a),a),a),f(f(f(h(h(f(b),b),b))))) -> a,
     c -> h(f(h(c,f(f(c)))),f(b)) ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ b -> h(c,f(b)),
     a -> c,
     h(h(h(f(a),a),a),f(f(f(h(h(f(b),b),b))))) -> a,
     c -> h(f(h(c,f(f(c)))),f(b)) ]
Constructor pattern: [f(?x_1)]
Defined pattern: [a,c,h(?x_2,?x_3),b]
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),c]
Defined pattern: [a,h(?x_2,?x_3),b]
Constructor subsystem:
   [ ]
Modified Constructor subsystem:
   [ ]
candidate for a:
   [ a -> c ]
No orientable rules for h(?x_2,?x_3). Add rules, and retry...
Added rules:
   [ h(c,?x_3) -> h(h(f(h(c,f(f(c)))),f(b)),?x_3),
     h(?x_2,c) -> h(?x_2,h(f(h(c,f(f(c)))),f(b))),
     h(f(?x_1),c) -> h(f(?x_1),h(f(h(c,f(f(c)))),f(b))),
     h(c,f(?x_1)) -> h(h(f(h(c,f(f(c)))),f(b)),f(?x_1)),
     h(c,c) -> h(h(f(h(c,f(f(c)))),f(b)),c) ]
candidate for h(?x_2,?x_3):
No canditates. Supplement rules, and retry...
patlist: 
{?x_2,c}
{f(?x_1),c}
{c,c}
Required Patterns: {h(?x_2,f(?x_1))}
failed to construct defining rules
Retry with a different D/C-partition.
Constructor pattern: [f(?x_1),c,h(?x_2,?x_3)]
Defined pattern: [a,b]
Constructor subsystem:
   [ ]
Modified Constructor subsystem:
   [ ]
candidate for a:
   [ a -> c ]
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),c,h(?x_2,?x_3),b]
Defined pattern: [a]
Constructor subsystem:
   [ b -> h(c,f(b)),
     c -> h(f(h(c,f(f(c)))),f(b)) ]
Modified Constructor subsystem:
   [ b -> h(c,f(b)),
     c -> h(f(h(c,f(f(c)))),f(b)) ]
candidate for a:
   [ a -> c ]
Find a quasi-ordering ...
encodeSameNthStatus h/0, h/1
encodeSameNthStatus(sub) logArF:1, logArG:1
failed to find an ordering.
Try to supplement auxiliary rules.
{b}{}{}{c}Supplemented Rules:
   [ ]
failed to supplement auxiliary rules
Retry with a different D/C-partition.
Constructor pattern: [f(?x_1),c,h(?x_2,?x_3),b,a]
Defined pattern: []
Constructor subsystem:
   [ b -> h(c,f(b)),
     a -> c,
     h(h(h(f(a),a),a),f(f(f(h(h(f(b),b),b))))) -> a,
     c -> h(f(h(c,f(f(c)))),f(b)) ]
Modified Constructor subsystem:
   [ b -> h(c,f(b)),
     a -> c,
     h(h(h(f(a),a),a),f(f(f(h(h(f(b),b),b))))) -> a,
     c -> h(f(h(c,f(f(c)))),f(b)) ]
Find a quasi-ordering ...
order successfully found
Precedence:
 c : Mul;
 a : Mul;
 h : Mul;
 f : Mul;
 b : Mul;
Rules:
   [ h(h(h(f(a),a),a),f(f(f(h(h(f(b),b),b))))) -> a ]
Check confluence of constructor subsystem...
Check Termination...
Terminating, WCR: CR
Conjectures:
   [ b = h(c,f(b)),
     a = c,
     c = h(f(h(c,f(f(c)))),f(b)) ]
STEP 0
ES:
   [ b = h(c,f(b)),
     a = c,
     c = h(f(h(c,f(f(c)))),f(b)) ]
HS:
   [ ]
ES0:
   [ b = h(c,f(b)),
     a = c,
     c = h(f(h(c,f(f(c)))),f(b)) ]
HS0:
   [ ]
ES1:
   [ b = h(c,f(b)),
     a = c,
     c = h(f(h(c,f(f(c)))),f(b)) ]
HS1:
   [ ]
No equation to expand
check Non-Ground-Confluence...
ground constructor terms for instantiation: {}
ground terms for instantiation: {b:o}
obtain 11 rules by 3 steps unfolding
obtain 100 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_{f(h(c,f(f(c))))},q_{f(f(h(h(f(b),b),b)))},q_{a},q_{b},q_{c},q_{f(a)},q_{f(b)},q_{f(c)},q_{f(f(c))},q_{f(f(f(h(h(f(b),b),b))))},q_{h(h(f(b),b),b)},q_{f(h(h(f(b),b),b))},q_{h(h(f(a),a),c)},q_{h(f(a),a)},q_{h(f(b),b)},q_{h(c,f(f(c)))}}
   Qf = {q_0,q_1}
   Delta = 
   [ a -> q_1,
     a -> q_{a},
     b -> q_{b},
     c -> q_1,
     c -> q_{a},
     c -> q_{c},
     f(q_{f(f(h(h(f(b),b),b)))}) -> q_{f(f(f(h(h(f(b),b),b))))},
     f(q_{a}) -> q_{f(a)},
     f(q_{b}) -> q_{f(b)},
     f(q_{c}) -> q_{f(c)},
     f(q_{f(c)}) -> q_{f(f(c))},
     f(q_{h(h(f(b),b),b)}) -> q_{f(h(h(f(b),b),b))},
     f(q_{f(h(h(f(b),b),b))}) -> q_{f(f(h(h(f(b),b),b)))},
     f(q_{h(c,f(f(c)))}) -> q_{f(h(c,f(f(c))))},
     h(q_{f(h(c,f(f(c))))},q_{f(b)}) -> q_1,
     h(q_{f(h(c,f(f(c))))},q_{f(b)}) -> q_{a},
     h(q_{f(h(c,f(f(c))))},q_{f(b)}) -> q_{c},
     h(q_{c},q_{f(b)}) -> q_{b},
     h(q_{c},q_{f(f(c))}) -> q_{h(c,f(f(c)))},
     h(q_{f(a)},q_{a}) -> q_{h(f(a),a)},
     h(q_{f(b)},q_{b}) -> q_{h(f(b),b)},
     h(q_{h(h(f(a),a),c)},q_{f(f(f(h(h(f(b),b),b))))}) -> q_0,
     h(q_{h(f(a),a)},q_{c}) -> q_{h(h(f(a),a),c)},
     h(q_{h(f(b),b)},q_{b}) -> q_{h(h(f(b),b),b)} ]
Witness for Non-Confluence: <h(h(h(f(a),a),c),f(f(f(h(h(f(b),b),b))))), a>
: Success(not GCR)
(365 msec.)
0.43