NO
af/ONE-SORTED/667.trs
Input rules:
   [ f(h(a,c)) -> h(f(b),h(c,h(c,h(f(h(b,b)),a)))),
     h(h(h(f(b),c),b),h(a,h(a,c))) -> h(f(b),h(c,b)),
     a -> h(h(b,b),b),
     c -> a ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ f(h(a,c)) -> h(f(b),h(c,h(c,h(f(h(b,b)),a)))),
     h(h(h(f(b),c),b),h(a,h(a,c))) -> h(f(b),h(c,b)),
     a -> h(h(b,b),b),
     c -> a ]
Constructor pattern: [f(?x_1),h(?x_1,?x_2),b]
Defined pattern: [c,a]
Constructor subsystem:
   [ ]
Modified Constructor subsystem:
   [ ]
candidate for c:
   [ c -> a ]
candidate for a:
   [ a -> h(h(b,b),b) ]
Find a quasi-ordering ...
order successfully found
Precedence:
 c : Mul;
 a : Mul;
 h : Mul;
 b : Mul;
 f : Mul;
Rules:
   [ c -> a,
     a -> h(h(b,b),b) ]
Conjectures:
   [ f(h(a,c)) = h(f(b),h(c,h(c,h(f(h(b,b)),a)))),
     h(h(h(f(b),c),b),h(a,h(a,c))) = h(f(b),h(c,b)) ]
STEP 0
ES:
   [ f(h(a,c)) = h(f(b),h(c,h(c,h(f(h(b,b)),a)))),
     h(h(h(f(b),c),b),h(a,h(a,c))) = h(f(b),h(c,b)) ]
HS:
   [ ]
ES0:
   [ f(h(h(h(b,b),b),h(h(b,b),b))) = h(f(b),h(h(h(b,b),b),h(h(h(b,b),b),h(f(h(b,b)),h(h(b,b),b))))),
     h(h(h(f(b),h(h(b,b),b)),b),h(h(h(b,b),b),h(h(h(b,b),b),h(h(b,b),b)))) = h(f(b),h(h(h(b,b),b),b)) ]
HS0:
   [ ]
ES1:
   [ f(h(h(h(b,b),b),h(h(b,b),b))) = h(f(b),h(h(h(b,b),b),h(h(h(b,b),b),h(f(h(b,b)),h(h(b,b),b))))),
     h(h(h(f(b),h(h(b,b),b)),b),h(h(h(b,b),b),h(h(h(b,b),b),h(h(b,b),b)))) = h(f(b),h(h(h(b,b),b),b)) ]
HS1:
   [ ]
Stopped: the smallest size of equations exceeeds the limit.
check Non-Ground-Confluence...
ground constructor terms for instantiation: {b,f(b),h(b,b)}
ground terms for instantiation: {b:o,f(b):o,h(b,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(f(b),h(a,h(a,h(f(h(b,b)),a)))) <- f(h(a,c)) -> f(h(a,h(h(b,b),b)))>
: Success(not GCR)
(12 msec.)
0.02