MAYBE
af/ONE-SORTED/718.trs
Input rules:
   [ h(c,c) -> h(b,f(b)),
     f(h(a,h(c,a))) -> c,
     h(c,b) -> f(a) ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ h(c,c) -> h(b,f(b)),
     f(h(a,h(c,a))) -> c,
     h(c,b) -> f(a) ]
Constructor pattern: [h(?x_1,?x_2),c,b,f(?x_1),a]
Defined pattern: []
Constructor subsystem:
   [ h(c,c) -> h(b,f(b)),
     f(h(a,h(c,a))) -> c,
     h(c,b) -> f(a) ]
Modified Constructor subsystem:
   [ h(c,c) -> h(b,f(b)),
     f(h(a,h(c,a))) -> c,
     h(c,b) -> f(a) ]
Find a quasi-ordering ...
order successfully found
Precedence:
 a : Mul;
 f : Mul;
 h : Mul;
 c : Mul,  b : Mul;
Rules:
   [ f(h(a,h(c,a))) -> c ]
Check confluence of constructor subsystem...
Check Termination...
Terminating, WCR: CR
Conjectures:
   [ h(c,c) = h(b,f(b)),
     h(c,b) = f(a) ]
STEP 0
ES:
   [ h(c,c) = h(b,f(b)),
     h(c,b) = f(a) ]
HS:
   [ ]
ES0:
   [ h(c,c) = h(b,f(b)),
     h(c,b) = f(a) ]
HS0:
   [ ]
ES1:
   [ h(c,c) = h(b,f(b)),
     h(c,b) = f(a) ]
HS1:
   [ ]
No equation to expand
check Non-Ground-Confluence...
ground constructor terms for instantiation: {c,b,a,h(c,c),h(c,b),h(c,a),h(b,c),h(b,b),h(b,a),h(a,c),h(a,b),h(a,a),f(c),f(b),f(a)}
ground terms for instantiation: {c:o,b:o,a:o,h(c,c):o,h(c,b):o,h(c,a):o,h(b,c):o,h(b,b):o,h(b,a):o,h(a,c):o,h(a,b):o,h(a,a):o,f(c):o,f(b):o,f(a):o}
obtain 10 rules by 3 steps unfolding
obtain 6 candidates for checking non-joinability
check by TCAP-Approximation (failure)
check by Ordering(rpo), check by Tree-Automata Approximation (failure)
check by Interpretation(mod2) (failure)
check by Descendants-Approximation, check by Ordering(poly) (failure)
: Failure(unknown)
(182 msec.)
3.13