NO
af/ONE-SORTED/708.trs
Input rules:
   [ h(f(f(c)),h(c,h(c,h(h(f(b),f(f(f(f(b))))),b)))) -> h(h(a,a),f(c)),
     h(b,h(c,h(b,h(a,b)))) -> a,
     f(c) -> f(f(a)),
     a -> f(f(b)) ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ h(f(f(c)),h(c,h(c,h(h(f(b),f(f(f(f(b))))),b)))) -> h(h(a,a),f(c)),
     h(b,h(c,h(b,h(a,b)))) -> a,
     f(c) -> f(f(a)),
     a -> f(f(b)) ]
Constructor pattern: [h(?x_1,?x_2),f(?x_1),c,b]
Defined pattern: [a]
Constructor subsystem:
   [ ]
Modified Constructor subsystem:
   [ ]
candidate for a:
   [ a -> f(f(b)) ]
Find a quasi-ordering ...
order successfully found
Precedence:
 h : Mul;
 a : Mul;
 f : Mul;
 c : Mul;
 b : Mul;
Rules:
   [ a -> f(f(b)) ]
Conjectures:
   [ h(b,h(c,h(b,h(a,b)))) = a,
     h(f(f(c)),h(c,h(c,h(h(f(b),f(f(f(f(b))))),b)))) = h(h(a,a),f(c)),
     f(c) = f(f(a)) ]
STEP 0
ES:
   [ h(b,h(c,h(b,h(a,b)))) = a,
     h(f(f(c)),h(c,h(c,h(h(f(b),f(f(f(f(b))))),b)))) = h(h(a,a),f(c)),
     f(c) = f(f(a)) ]
HS:
   [ ]
ES0:
   [ h(b,h(c,h(b,h(f(f(b)),b)))) = f(f(b)),
     h(f(f(c)),h(c,h(c,h(h(f(b),f(f(f(f(b))))),b)))) = h(h(f(f(b)),f(f(b))),f(c)),
     f(c) = f(f(f(f(b)))) ]
HS0:
   [ ]
ES1:
   [ h(b,h(c,h(b,h(f(f(b)),b)))) = f(f(b)),
     h(f(f(c)),h(c,h(c,h(h(f(b),f(f(f(f(b))))),b)))) = h(h(f(f(b)),f(f(b))),f(c)),
     f(c) = f(f(f(f(b)))) ]
HS1:
   [ ]
No equation to expand
check Non-Ground-Confluence...
ground constructor terms for instantiation: {c,b,h(c,c),h(c,b),h(b,c),h(b,b),f(c),f(b)}
ground terms for instantiation: {c:o,b:o,h(c,c):o,h(c,b):o,h(b,c):o,h(b,b):o,f(c):o,f(b):o}
obtain 11 rules by 3 steps unfolding
obtain 100 candidates for checking non-joinability
check by TCAP-Approximation (success)
Witness for Non-Confluence: <h(b,h(c,h(b,h(f(f(b)),b)))) <- h(b,h(c,h(b,h(h(b,h(c,h(b,h(a,b)))),b)))) -> f(f(b))>
: Success(not GCR)
(10 msec.)
0.02