NO
af/ONE-SORTED/655.trs
Input rules:
   [ b -> a,
     f(h(b,f(a))) -> f(c),
     c -> h(c,c),
     h(f(f(b)),a) -> c,
     h(a,a) -> a ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ b -> a,
     f(h(b,f(a))) -> f(c),
     c -> h(c,c),
     h(f(f(b)),a) -> c,
     h(a,a) -> a ]
Constructor pattern: [a,f(?x_1),h(?x_1,?x_2)]
Defined pattern: [c,b]
Constructor subsystem:
   [ h(a,a) -> a ]
Modified Constructor subsystem:
   [ h(a,a) -> a ]
No orientable rules for c. Add rules, and retry...
failed to construct defining rules
Retry with a different D/C-partition.
Constructor pattern: [a,f(?x_1),h(?x_1,?x_2),c]
Defined pattern: [b]
Constructor subsystem:
   [ c -> h(c,c),
     h(a,a) -> a ]
Modified Constructor subsystem:
   [ c -> h(c,c),
     h(a,a) -> a ]
candidate for b:
   [ b -> a ]
Find a quasi-ordering ...
order successfully found
Precedence:
 f : Mul;
 c : Mul,  b : Mul;
 a : Mul;
 h : Mul;
Rules:
   [ b -> a,
     h(a,a) -> a ]
Check confluence of constructor subsystem...
Check Termination...
Terminating, WCR: CR
Conjectures:
   [ f(h(b,f(a))) = f(c),
     h(f(f(b)),a) = c,
     c = h(c,c) ]
STEP 0
ES:
   [ f(h(b,f(a))) = f(c),
     h(f(f(b)),a) = c,
     c = h(c,c) ]
HS:
   [ ]
ES0:
   [ f(h(a,f(a))) = f(c),
     h(f(f(a)),a) = c,
     c = h(c,c) ]
HS0:
   [ ]
ES1:
   [ f(h(a,f(a))) = f(c),
     h(f(f(a)),a) = c,
     c = h(c,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 12 rules by 3 steps unfolding
obtain 100 candidates for checking non-joinability
check by TCAP-Approximation (failure)
check by Ordering(rpo), check by Tree-Automata Approximation (success)
Witness for Non-Confluence: <h(f(f(a)),a) <- h(f(f(b)),a) -> c>
: Success(not GCR)
(39 msec.)
0.07