NO
af/ONE-SORTED/672.trs
Input rules:
   [ a -> a,
     a -> h(a,b),
     b -> h(b,f(f(b))),
     b -> b,
     h(b,h(f(a),a)) -> a ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ a -> a,
     a -> h(a,b),
     b -> h(b,f(f(b))),
     b -> b,
     h(b,h(f(a),a)) -> a ]
Constructor pattern: [f(?x_1)]
Defined pattern: [b,h(?x_2,?x_3),a]
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),b]
Defined pattern: [h(?x_2,?x_3),a]
Constructor subsystem:
   [ b -> b ]
b -> b
{}
   [  ]
Modified Constructor subsystem:
   [ ]
No orientable rules for h(?x_2,?x_3). Add rules, and retry...
Added rules:
   [ h(b,?x_3) -> h(h(b,f(f(b))),?x_3),
     h(?x_2,b) -> h(?x_2,h(b,f(f(b)))),
     h(f(?x_1),b) -> h(f(?x_1),h(b,f(f(b)))),
     h(b,f(?x_1)) -> h(h(b,f(f(b))),f(?x_1)),
     h(b,b) -> h(h(b,f(f(b))),b) ]
candidate for h(?x_2,?x_3):
No canditates. Supplement rules, and retry...
patlist: 
{?x_2,b}
{f(?x_1),b}
{b,b}
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),b,h(?x_2,?x_3)]
Defined pattern: [a]
Constructor subsystem:
   [ b -> h(b,f(f(b))),
     b -> b ]
b -> b
{}
   [  ]
Modified Constructor subsystem:
   [ b -> h(b,f(f(b))) ]
No orientable rules for a. Add rules, and retry...
failed to construct defining rules
Retry with a different D/C-partition.
Constructor pattern: [f(?x_1),b,h(?x_2,?x_3),a]
Defined pattern: []
Constructor subsystem:
   [ a -> a,
     a -> h(a,b),
     b -> h(b,f(f(b))),
     b -> b,
     h(b,h(f(a),a)) -> a ]
b -> b
{}
   [  ]
a -> a
{}
   [  ]
Modified Constructor subsystem:
   [ a -> h(a,b),
     b -> h(b,f(f(b))),
     h(b,h(f(a),a)) -> a ]
Find a quasi-ordering ...
order successfully found
Precedence:
 f : Mul;
 a : Mul;
 b : Mul;
 h : Mul;
Rules:
   [ h(b,h(f(a),a)) -> a ]
Check confluence of constructor subsystem...
Check Termination...
Terminating, WCR: CR
Conjectures:
   [ a = h(a,b),
     b = h(b,f(f(b))) ]
STEP 0
ES:
   [ a = h(a,b),
     b = h(b,f(f(b))) ]
HS:
   [ ]
ES0:
   [ a = h(a,b),
     b = h(b,f(f(b))) ]
HS0:
   [ ]
ES1:
   [ a = h(a,b),
     b = h(b,f(f(b))) ]
HS1:
   [ ]
No equation to expand
check Non-Ground-Confluence...
ground constructor terms for instantiation: {}
ground terms for instantiation: {a:o}
obtain 10 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),(f,1),(h,2)}
   Q = {q_0,q_1,q_{a},q_{b},q_{f(a)},q_{f(b)},q_{f(f(b))},q_{h(a,b)},q_{h(f(a),h(a,b))}}
   Qf = {q_0,q_1}
   Delta = 
   [ a -> q_1,
     a -> q_{a},
     b -> q_{b},
     f(q_{a}) -> q_{f(a)},
     f(q_{b}) -> q_{f(b)},
     f(q_{f(b)}) -> q_{f(f(b))},
     h(q_1,q_{b}) -> q_1,
     h(q_1,q_{b}) -> q_{a},
     h(q_{a},q_{b}) -> q_{h(a,b)},
     h(q_{b},q_{f(f(b))}) -> q_{b},
     h(q_{b},q_{h(f(a),h(a,b))}) -> q_0,
     h(q_{f(a)},q_{h(a,b)}) -> q_{h(f(a),h(a,b))} ]
Witness for Non-Confluence: <h(b,h(f(a),h(a,b))), a>
: Success(not GCR)
(128 msec.)
0.17