NO
af/ONE-SORTED/676.trs
Input rules:
   [ c -> f(f(c)),
     h(h(h(b,b),f(f(a))),f(f(f(a)))) -> a,
     b -> h(h(f(a),c),f(a)) ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ c -> f(f(c)),
     h(h(h(b,b),f(f(a))),f(f(f(a)))) -> a,
     b -> h(h(f(a),c),f(a)) ]
Constructor pattern: [f(?x_1),h(?x_1,?x_2),a]
Defined pattern: [b,c]
Constructor subsystem:
   [ ]
Modified Constructor subsystem:
   [ ]
candidate for b:
   [ b -> h(h(f(a),c),f(a)) ]
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),a,c]
Defined pattern: [b]
Constructor subsystem:
   [ c -> f(f(c)) ]
Modified Constructor subsystem:
   [ c -> f(f(c)) ]
candidate for b:
   [ b -> h(h(f(a),c),f(a)) ]
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.
{c}{}{}Supplemented Rules:
   [ ]
failed to supplement auxiliary 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:
   [ c -> f(f(c)),
     h(h(h(b,b),f(f(a))),f(f(f(a)))) -> a,
     b -> h(h(f(a),c),f(a)) ]
Modified Constructor subsystem:
   [ c -> f(f(c)),
     h(h(h(b,b),f(f(a))),f(f(f(a)))) -> a,
     b -> h(h(f(a),c),f(a)) ]
Find a quasi-ordering ...
order successfully found
Precedence:
 c : Mul,  b : Mul;
 f : Mul;
 a : Mul;
 h : Mul;
Rules:
   [ h(h(h(b,b),f(f(a))),f(f(f(a)))) -> a ]
Check confluence of constructor subsystem...
Check Termination...
Terminating, WCR: CR
Conjectures:
   [ c = f(f(c)),
     b = h(h(f(a),c),f(a)) ]
STEP 0
ES:
   [ c = f(f(c)),
     b = h(h(f(a),c),f(a)) ]
HS:
   [ ]
ES0:
   [ c = f(f(c)),
     b = h(h(f(a),c),f(a)) ]
HS0:
   [ ]
ES1:
   [ c = f(f(c)),
     b = h(h(f(a),c),f(a)) ]
HS1:
   [ ]
No equation to expand
check Non-Ground-Confluence...
ground constructor terms for instantiation: {a,f(a),h(a,a)}
ground terms for instantiation: {a:o,f(a):o,h(a,a):o}
obtain 10 rules by 3 steps unfolding
obtain 84 candidates for checking non-joinability
check by TCAP-Approximation (success)
Witness for Non-Confluence: <h(h(h(b,h(h(f(a),c),f(a))),f(f(a))),f(f(f(a)))) <- h(h(h(b,b),f(f(a))),f(f(f(a)))) -> a>
: Success(not GCR)
(14 msec.)
0.03