NO
af/ONE-SORTED/39.trs
Input rules:
   [ f(b) -> a,
     f(b) -> f(c),
     f(c) -> f(b),
     f(c) -> d,
     b -> e,
     c -> e',
     f(e) -> a,
     f(e') -> d ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ f(b) -> a,
     f(b) -> f(c),
     f(c) -> f(b),
     f(c) -> d,
     b -> e,
     c -> e',
     f(e) -> a,
     f(e') -> d ]
Constructor pattern: [f(?x_1),a,d,e,e']
Defined pattern: [c,b]
Constructor subsystem:
   [ f(e) -> a,
     f(e') -> d ]
Modified Constructor subsystem:
   [ f(e) -> a,
     f(e') -> d ]
candidate for c:
   [ c -> e' ]
candidate for b:
   [ b -> e ]
Find a quasi-ordering ...
order successfully found
Precedence:
 d : Mul,  c : Mul,  b : Mul;
 f : Mul;
 e : Mul;
 e' : Mul,  a : Mul;
Rules:
   [ c -> e',
     b -> e,
     f(e) -> a ]
Check confluence of constructor subsystem...
Check Termination...
Terminating, WCR: CR
Conjectures:
   [ f(b) = a,
     f(b) = f(c),
     f(c) = f(b),
     f(c) = d,
     f(e') = d ]
STEP 0
ES:
   [ f(b) = a,
     f(b) = f(c),
     f(c) = f(b),
     f(c) = d,
     f(e') = d ]
HS:
   [ ]
ES0:
   [ a = a,
     a = f(e'),
     f(e') = a,
     f(e') = d,
     f(e') = d ]
HS0:
   [ ]
ES1:
   [ a = f(e'),
     f(e') = a,
     f(e') = d,
     f(e') = d ]
HS1:
   [ ]
No equation to expand
check Non-Ground-Confluence...
ground constructor terms for instantiation: {a,d,e,e',f(a),f(d),f(e),f(e')}
ground terms for instantiation: {a:o,d:o,e:o,e':o,f(a):o,f(d):o,f(e):o,f(e'):o}
obtain 11 rules by 3 steps unfolding
obtain 22 candidates for checking non-joinability
check by TCAP-Approximation (success)
Witness for Non-Confluence: <a <- f(b) -> d>
: Success(not GCR)
(5 msec.)
0.02