NO
af/ONE-SORTED/658.trs
Input rules:
   [ f(f(f(f(a)))) -> a,
     c -> h(f(f(c)),f(f(h(f(f(a)),h(h(b,h(c,c)),f(c)))))),
     f(a) -> c,
     b -> f(a),
     f(a) -> f(c) ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ f(f(f(f(a)))) -> a,
     c -> h(f(f(c)),f(f(h(f(f(a)),h(h(b,h(c,c)),f(c)))))),
     f(a) -> c,
     b -> f(a),
     f(a) -> f(c) ]
Constructor pattern: [f(?x_1),a,h(?x_1,?x_2)]
Defined pattern: [b,c]
Constructor subsystem:
   [ f(f(f(f(a)))) -> a ]
Modified Constructor subsystem:
   [ f(f(f(f(a)))) -> a ]
candidate for b:
   [ b -> 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),a,h(?x_1,?x_2),c]
Defined pattern: [b]
Constructor subsystem:
   [ f(f(f(f(a)))) -> a,
     f(a) -> c,
     f(a) -> f(c) ]
Modified Constructor subsystem:
   [ f(f(f(f(a)))) -> a,
     f(a) -> c,
     f(a) -> f(c) ]
candidate for b:
   [ b -> f(a) ]
Find a quasi-ordering ...
order successfully found
Precedence:
 b : Mul;
 h : Mul;
 f : Mul;
 c : Mul;
 a : Mul;
Rules:
   [ b -> f(a),
     f(f(f(f(a)))) -> a,
     f(a) -> c ]
Check confluence of constructor subsystem...
Check Termination...
Terminating, not WCR: not CR
...failed
failed to find an ordering.
Try to supplement auxiliary rules.
{}{c}{}{}{f(c)}Supplemented Rules:
   [ ]
failed to supplement auxiliary rules
Retry with a different D/C-partition.
Constructor pattern: [f(?x_1),a,h(?x_1,?x_2),c,b]
Defined pattern: []
Constructor subsystem:
   [ f(f(f(f(a)))) -> a,
     c -> h(f(f(c)),f(f(h(f(f(a)),h(h(b,h(c,c)),f(c)))))),
     f(a) -> c,
     b -> f(a),
     f(a) -> f(c) ]
Modified Constructor subsystem:
   [ f(f(f(f(a)))) -> a,
     c -> h(f(f(c)),f(f(h(f(f(a)),h(h(b,h(c,c)),f(c)))))),
     f(a) -> c,
     b -> f(a),
     f(a) -> f(c) ]
Find a quasi-ordering ...
order successfully found
Precedence:
 h : Mul;
 c : Mul;
 a : Mul;
 f : Mul;
 b : Mul;
Rules:
   [ f(f(f(f(a)))) -> a ]
Check confluence of constructor subsystem...
Check Termination...
Terminating, WCR: CR
Conjectures:
   [ c = h(f(f(c)),f(f(h(f(f(a)),h(h(b,h(c,c)),f(c)))))),
     f(a) = c,
     b = f(a),
     f(a) = f(c) ]
STEP 0
ES:
   [ c = h(f(f(c)),f(f(h(f(f(a)),h(h(b,h(c,c)),f(c)))))),
     f(a) = c,
     b = f(a),
     f(a) = f(c) ]
HS:
   [ ]
ES0:
   [ c = h(f(f(c)),f(f(h(f(f(a)),h(h(b,h(c,c)),f(c)))))),
     f(a) = c,
     b = f(a),
     f(a) = f(c) ]
HS0:
   [ ]
ES1:
   [ c = h(f(f(c)),f(f(h(f(f(a)),h(h(b,h(c,c)),f(c)))))),
     f(a) = c,
     b = f(a),
     f(a) = f(c) ]
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 11 rules by 3 steps unfolding
obtain 100 candidates for checking non-joinability
check by TCAP-Approximation (success)
Witness for Non-Confluence: <f(f(f(h(f(f(c)),f(f(h(f(c),h(h(b,h(c,c)),f(c))))))))) <- f(f(f(b))) -> a>
: Success(not GCR)
(51 msec.)
0.06