NO
af/ONE-SORTED/716.trs
Input rules:
   [ a -> h(a,f(b)),
     f(f(h(a,a))) -> f(f(f(a))),
     f(h(a,h(a,a))) -> f(a),
     f(h(h(b,a),h(f(c),c))) -> c ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ a -> h(a,f(b)),
     f(f(h(a,a))) -> f(f(f(a))),
     f(h(a,h(a,a))) -> f(a),
     f(h(h(b,a),h(f(c),c))) -> c ]
Constructor pattern: [h(?x_1,?x_2),f(?x_1),b,c]
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),f(?x_1),b,c,a]
Defined pattern: []
Constructor subsystem:
   [ a -> h(a,f(b)),
     f(f(h(a,a))) -> f(f(f(a))),
     f(h(a,h(a,a))) -> f(a),
     f(h(h(b,a),h(f(c),c))) -> c ]
Modified Constructor subsystem:
   [ a -> h(a,f(b)),
     f(f(h(a,a))) -> f(f(f(a))),
     f(h(a,h(a,a))) -> f(a),
     f(h(h(b,a),h(f(c),c))) -> c ]
Find a quasi-ordering ...
order successfully found
Precedence:
 a : Mul;
 f : Mul;
 h : Mul;
 c : Mul,  b : Mul;
Rules:
   [ f(h(a,h(a,a))) -> f(a),
     f(h(h(b,a),h(f(c),c))) -> c ]
Check confluence of constructor subsystem...
Check Termination...
Terminating, WCR: CR
Conjectures:
   [ a = h(a,f(b)),
     f(f(h(a,a))) = f(f(f(a))) ]
STEP 0
ES:
   [ a = h(a,f(b)),
     f(f(h(a,a))) = f(f(f(a))) ]
HS:
   [ ]
ES0:
   [ a = h(a,f(b)),
     f(f(h(a,a))) = f(f(f(a))) ]
HS0:
   [ ]
ES1:
   [ a = h(a,f(b)),
     f(f(h(a,a))) = f(f(f(a))) ]
HS1:
   [ ]
No equation to expand
check Non-Ground-Confluence...
ground constructor terms for instantiation: {b,c,h(b,b),h(b,c),h(c,b),h(c,c),f(b),f(c)}
ground terms for instantiation: {b:o,c:o,h(b,b):o,h(b,c):o,h(c,b):o,h(c,c):o,f(b):o,f(c):o}
obtain 10 rules by 3 steps unfolding
obtain 100 candidates for checking non-joinability
check by TCAP-Approximation (success)
Witness for Non-Confluence: <f(h(h(b,h(a,f(b))),h(f(c),c))) <- f(h(h(b,a),h(f(c),c))) -> c>
: Success(not GCR)
(8 msec.)
0.02